Cheukting/mathqa huggingface dataset:
Question (general): during a certain two - week period , 60 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 3 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 5 a , b ) 6 a , c ) 8 a , d ) 14 a , e ) 20 a
Rationale: "movies : 60 % comedies . 40 % remaining genre . now in this 40 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 3 x . total 4 x . 4 x = 40 ; x = 10 action movies : 10 % drama movies : 30 % we can say that out of 100 z , : comedies : 60 z action : 10 z drama : 30 z now action movies werea this means : a = 10 z . z = ( a / 10 ) comedies : 60 z = 60 * ( a / 10 ) 6 a b is the answer ."
Answer: b
Question (gain): if 15 % of a is the same as 40 % of b , then a : b is :
Options: a ) 5 : 4 , b ) 8 : 3 , c ) 7 : 16 , d ) 2 : 17 , e ) 3 : 5
Rationale: "expl : 15 % of a i = 40 % of b = 15 a / 100 = 40 b / 100 = 8 / 3 = 8 : 3 answer : b"
Answer: b
Question (gain): after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6500 . find the actual price of the good .
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9503 , e ) s . 9980
Rationale: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6500 1 = 6500 / 68.4 100 = ( 6500 * 100 ) / 68.4 = rs . 9503 . answer : option d"
Answer: d
Question (physics): if a man walks at a rate of 10 kmph , he misses a train by 14 minutes . however , if he walks at the rate of 12 kmph , he reaches the station 10 minutes before the arrival of the train . find the distance covered by him to reach the station .
Options: a ) 6 , b ) 15 , c ) 12 , d ) 4 , e ) 8
Rationale: "let the required distance x km difference in the times taken at two speeds = 12 min = 1 / 5 hr ( x / 10 ) - ( x / 12 ) = 1 / 10 x = 6 the required distance is 6 km answer is a"
Answer: a
Question (general): of 32 applicants for a job , 14 had at least 4 years ' experience , 18 had degrees , and 7 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 32 - 7 = 25 aub = a + b - aib aib = 18 + 14 - 25 = 7 answer d"
Answer: d
Question (general): a box contains 10 tablets of medicine a and 10 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "the worst case scenario will be if we remove all 15 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 10 + 2 = 12 tablets . answer : a ."
Answer: a
Question (physics): express a speed of 63 kmph in meters per second ?
Options: a ) 10 mps , b ) 14 mps , c ) 17.5 mps , d ) 19.4 mps , e ) 10.8 mps
Rationale: "63 * 5 / 18 = 17.5 mps answer : c"
Answer: c
Question (general): if w / x = 2 / 3 and w / y = 3 / 5 , then ( x + y ) / y =
Options: a ) 4 / 5 , b ) 9 / 10 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5
Rationale: "w / x = 2 / 3 x = > x = 3 / 2 w and w / y = 3 / 5 = > y = 5 / 3 w ( x + y ) / y = ( 3 / 2 w + 5 / 3 w ) / ( 5 / 3 x ) = 9 / 10 correct option : b"
Answer: b
Question (general): what least number must be subtracted from 42739 so that remaining no . is divisible by 15
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 42739 by 15 we get the remainder 4 , so 4 should be subtracted option b"
Answer: b
Question (geometry): 18 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 279 , d ) 90 , e ) 45
Rationale: "there are 18 business exec and in each handshake 2 business execs are involved . hence 18 c 2 = 153 also , each of 18 exec will shake hand with every 7 other chairmen for total of 126 handshake . total = 153 + 126 = 279 ans : c"
Answer: c
Question (general): for each color copy , print shop x charges $ 1.25 and print shop y charges $ 2.75 . how much greater is the charge for 40 color copies at print shop y than at print shop x ?
Options: a ) $ 48 , b ) $ 54 , c ) $ 60 , d ) $ 66 , e ) $ 72
Rationale: "the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 40 * $ 1.50 = $ 60 the answer is c ."
Answer: c
Question (other): the probability of two events a and b are 0.20 and 0.40 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
Options: a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.55 , e ) 0.6
Rationale: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 20 + . 40 - . 15 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : d"
Answer: d
Question (other): of the diplomats who attended a summit conference : 20 spoke japanese , 32 did not speak russian and 20 % of the diplomats spoke neither japanese nor russian . if 10 % of the diplomats spoke both japanese and russian , then how many diplomats attended the conference ?
Options: a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: 2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer
Answer: d
Question (general): if n = 2.0423 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?
Options: a ) - 0.0053 , b ) - 0.0023 , c ) 0.0007 , d ) 0.0047 , e ) 0.0153
Rationale: n * = 2.04 n * - n = 2.04 - 2.0423 - 0.0023 answer : b
Answer: b
Question (physics): carl can wash all the windows of his house in 6 hours . his wife maggie can wash all the windows in 6 hours . how many hours will it take for both of them working together to wash all the windows ?
Options: a ) 2 , b ) 2 1 / 4 , c ) 3 , d ) 4 1 / 2 , e ) 5
Rationale: "work hrs = ab / ( a + b ) = 36 / 12 = 3 answer is c"
Answer: c
Question (physics): car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 49 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 120 , c ) 140 , d ) 147 , e ) 168
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 49 t or 5 t + 6 = 7 t or t = 3 distance travelled by car x from the time car y began traveling until both cars stopped is 35 x 3 = 105 miles answer : - a"
Answer: a
Question (gain): in a restaurant , the profit is 160 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 57 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: "explanation : let c . p . = rs . 100 . then , profit = rs . 160 , s . p . = rs . 260 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 260 . profit = rs . ( 260 - 112 ) = rs . 148 . required percentage = ( 148 / 260 * 100 ) % = 57 % appox answer : b"
Answer: b
Question (physics): a train 250 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 150 m long ?
Options: a ) 45 sec , b ) 42 sec , c ) 32 sec , d ) 48 sec , e ) 25 sec
Rationale: "total length = 250 + 150 = 400 speed = 45 km / h = ( 45 * 5 ) / 18 = 25 / 2 m / s time = ( 400 * 2 ) / 25 = 32 sec . answer : c"
Answer: c
Question (physics): a can complete the job in 5 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 8 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: a = 1 / 8
Answer: a
Question (general): in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 35 and 200 , then the least and greatest integer on the card would be
Options: a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 13 , d ) 4 and 14 , e ) 5 and 14
Rationale: "given : 35 < x ( x + 1 ) < 200 . now , it ' s better to test the answer choices here rather than to solve : if x = 5 then x ( x + 1 ) = 30 > 35 - - > so , the least value is 5 . test for the largest value : if x = 14 then x ( x + 1 ) = 14 * 15 = 210 > 200 answer : e ."
Answer: e
Question (general): 25 * 25 * 25 * 25 * 25 = 5 ^ ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 3 , e ) 10
Rationale: "solution : 5 ^ 2 * 5 ^ 2 * 5 ^ 2 * 5 ^ 2 * 5 ^ 2 = 5 ^ ( 2 + 2 + 2 + 2 + 2 ) = 5 ^ 10 answer : e"
Answer: e
Question (gain): what quantity of water should taken out to concentrate 21 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 5 liters , b ) 10 liters , c ) 7 liters , d ) 8 liters , e ) 6 liters
Rationale: "required answer is = 21 ( 60 - 40 ) / 60 = 7 liters answer is c"
Answer: c
Question (physics): a and b together can do a work in 6 days . if a alone can do it in 10 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 15 , c ) 77 , d ) 55 , e ) 21
Rationale: "1 / 6 – 1 / 10 = 1 / 15 = > 15 answer : b"
Answer: b
Question (physics): sam and nik start from a and b respectively at the same time and travel towards each other at constant speeds along the same route . sam meets nik at point c on the road which is 600 m away from starting point a and 400 m away from point b . the speed of sam is 50 m / m ( meter / minute ) . how much time did sam take to cover the distance between a and b ?
Options: a ) 10 minutes , b ) 15 minutes , c ) 20 minutes , d ) 22 minutes , e ) 17 minutes
Rationale: total distance from a to b - a - c = 600 m , b - c = 400 m ; therefore a - b = 1000 m ; vs = 50 m / m ; therefore , t = 1000 / 50 = 20 minutes . option c
Answer: c
Question (general): subtract . simplify your answer and write it as a proper fraction or as a whole or mixed number . 4 / 5 - 1 / 5 =
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 5
Rationale: here ' s how to subtract 1 / 5 from 4 / 5 : 4 / 5 − 1 / 5 since our denominators match , we can subtract the numerators . 4 − 1 = 3 so the answer is : 3 / 5 answer : c
Answer: c
Question (other): ratio between two numbers is 3 : 4 and their sum is 420 . find the smaller number ?
Options: a ) 378 , b ) 180 , c ) 820 , d ) 734 , e ) 840
Rationale: explanation : 3 x + 4 x = 420 x = 60 = > 3 x = 180 answer : option 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 30 , what is the greatest possible value of q minus r ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
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 ) < 30 . the greatest multiple of 9 which is less than 30 is 27 . the answer is e .
Answer: e
Question (other): what is the square root of 121 ?
Options: a ) 11 , b ) 12 , c ) 16 , d ) 18 , e ) 25
Rationale: "11 x 11 = 121 answer a"
Answer: a
Question (general): if equation | x / 5 | + | y / 5 | = 2 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 20 , b ) 50 , c ) 200 , d ) 100 , e ) 400
Rationale: the equation can be reduced to intercept form as | x / 10 | + | y / 10 | = 1 , so these are lines in four quadrants with x and y intercept as 10 , so it is a rhombus with diagonals of 20 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 20 * 20 = 200 . answer c .
Answer: c
Question (physics): in a vehicle ' s repair shed , 3 men and 8 boys can do a piece of work in 15 days ; 4 men and 9 boys can do the same work in 12 days . then , 5 men and 5 boys can do double the amount of this work in :
Options: a ) 20 days , b ) 33 days , c ) 24 days , d ) 28 days , e ) none of these
Rationale: explanation : solution : ( 3 * 15 ) men + ( 8 * 15 ) boys = ( 4 * 12 ) men + ( 9 * 12 ) boys 45 m + 120 b = 48 m + 108 b < = > 3 m = 12 b = > 1 m = 4 b . . ' . 3 m + 8 b = ( 3 * 4 ) b + 8 b = 20 b . 5 m + 5 b = ( 5 * 4 ) b + 5 b = 25 b . let the required number of days be x . now , more boys , less days ( ip ) more work , more days ( dp ) boys 25 : 20 } : : 15 : x work 1 : 2 . ' . ( 25 * 1 * x ) = ( 20 * 2 * 15 ) = > x = 40 * 15 / 25 = 24 . answer : c
Answer: c
Question (general): each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 50 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 50
Rationale: "amount earned by james = 40 * x + 10 * 2 x = 60 x therefore , amount earned by james = 60 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 60 x ] ] so x * ( 1.5 y - 45 + 30 ) = 60 x or x * ( 1.5 y - 15 ) = 60 x so 1.5 y - 15 = 60 so 1.5 y = 75 so y = 50 answer is e"
Answer: e
Question (gain): increasing the original price of an article by 8 percent and then increasing the new price by 8 percent is equivalent to increasing the original price by
Options: a ) 16.16 % , b ) 16.32 % , c ) 16.64 % , d ) 17.26 % , e ) 18.56 %
Rationale: "1.08 * 1.08 * x = 1.1664 * x the answer is c ."
Answer: c
Question (physics): if 6 women can color 180 m long cloth in 3 days , then 5 women can color 200 m long cloth in ?
Options: a ) 6 days , b ) 5 days , c ) 4 days , d ) 2 days , e ) 3 days
Rationale: the length of cloth painted by one woman in one day = 180 / 6 × 3 = 10 m no . of days required to paint 200 m cloth by 5 women = 200 / 5 × 10 = 4 days answer : c
Answer: c
Question (gain): sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 210 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 3 of the days were hot , then what was the price of 1 cup on a hot day ?
Options: a ) $ 1.50 , b ) $ 1.64 , c ) $ 2.25 , d ) $ 2.50 , e ) $ 3.25
Rationale: "7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 210 - - > x = 1.308 . 1.25 x = ~ 1.64 . answer : b ."
Answer: b
Question (general): if x ⁄ 2 + 9 ⁄ 4 = 5 ⁄ 4 , what is the value of x ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "x ⁄ 2 + 9 ⁄ 4 = 5 ⁄ 4 let ' s multiply both sides by 4 . 2 x + 9 = 5 2 x = - 4 x = - 2 the answer is a ."
Answer: a
Question (other): how many zeros does 65 ! end with ?
Options: a ) 20 , b ) 15 , c ) 25 , d ) 30 , e ) 32
Rationale: "according to above 65 ! has 65 / 5 + 65 / 25 = 13 + 2 = 15 trailing zeros . answer : b ."
Answer: b
Question (general): the price of a certain painting increased by 30 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 105 % , c ) 110.5 % , d ) 112.5 % , e ) 100 %
Rationale: easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 30 = 130 price at the end of year 2 = 130 - 130 * 0.15 = 130 * 0.85 = 110.5 hence required answer = ( 110.5 / 100 ) * 100 % = 110.5 % answer is c .
Answer: c
Question (general): a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 27 more than the correct answer . find the number .
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 27 25 x = 16 x + 540 9 x = 540 x = 60 the answer is c .
Answer: c
Question (general): in a forest 150 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 20 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 6,000 , c ) 1,250 , d ) 1,500 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 20 / 50 * 100 = 40 % . so , 150 tagged deers comprise 10 % of total # of deers - - > total # of deers = 150 * 40 = 6,000 . answer : b"
Answer: b
Question (gain): the water level in a reservoir has been dropping at the rate of 14 inches per day . exactly 5 days ago , the water level was at w inches . what will be the water level exactly 3 days from now if the rate at which the level is dropping remains the same ?
Options: a ) w − 126 , b ) w − 56 , c ) w − 112 , d ) w + 14 , e ) w + 126
Rationale: "drop = 14 inches / day 5 days ago = w , means now it ' s equal w - 70 and in 3 days = w - 70 - 42 = w - 112 answer c"
Answer: c
Question (gain): what is 15 % of 2 / 3 of 0.6 ?
Options: a ) 0.06 , b ) 0.9 , c ) 9 , d ) 90 , e ) none of the above
Rationale: "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 6 / 10 ) = 180 / 3000 = 0.06 option a"
Answer: a
Question (probability): in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 150 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 110 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Rationale: "the probability of survival for each of the first 3 months of life is 1 - 1 / 10 = 9 / 10 , so of 150 newborn 150 * 9 / 10 * 9 / 10 * 9 / 10 = ~ 110 is expected to survive . answer : a ."
Answer: a
Question (general): the units digit of ( 35 ) ^ ( 7 ) + ( 93 ) ^ ( 45 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "any power of anything ending in 5 always has a units digit of 5 . so the first term has a units digit of 5 . done . the second term takes a little more work . we can ignore the tens digit , and just treat this base as 3 . here is the units digit patter for the powers of 3 . 3 ^ 45 has a units digit of 3 of course 5 + 3 = 8 , d"
Answer: d
Question (other): uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought less of toyota than honda at the ratio of 7 : 3 . if 70 % of the toyota bought and 30 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 76 % , b ) 58 % , c ) 68 % , d ) 89 % , e ) 49 %
Rationale: let total no of vehicles bought be 100 , toyota 70 and honda 30 , so total number of suv ' s bought for toyota and honda respectively 70 * 70 / 100 = 49 and 30 * 30 / 100 = 9 so total 58 suv ' s were bought out of 100 vehicles bought . . so required % is 58 % answer : b
Answer: b
Question (general): how many 4 - digit numbers are completely divisible by 7 ?
Options: a ) 1354 , b ) 1286 , c ) 1178 , d ) 1224 , e ) none
Rationale: "solution : 4 - digit numbers divisible by 7 are : 1001 , 1008 , 1015 … . . 9996 . this is an a . p . in which a = 1001 , d = 7 , l = 9996 . let the number of terms be n . then tn = 9996 . . ' . a + ( n - 1 ) d = 9996 = > 1001 + ( n - 1 ) 7 = 9996 = > ( n - 1 ) 7 = 8995 = > ( n - 1 ) = 8995 / 7 = 1285 = > n = 1286 . . ' . number of terms = 1286 . answer b"
Answer: b
Question (general): what is the units digit of ( 3 ^ 16 ) ( 4 ^ 13 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 16 = 3 ^ 4 * 4 =  3 ^ 0 = 1 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 16 ) ( 4 ^ 13 )  ( 3 ^ 0 ) ( ~ 4 ) = ( ~ 1 ) ( ~ 4 ) = ~ 4 . therefore , the answer is b ."
Answer: b
Question (physics): a can do a piece of work in 10 days , b in 15 days . they work for 5 days . the rest of work finished by c in 2 days . if they get rs 1500 for the whole work , the daily wages of b and c are ?
Options: a ) 225 , b ) 276 , c ) 126 , d ) 187 , e ) 1267
Rationale: explanation : let the total work = 30 units . then capacity of a = 3 units , b = 2 units . now they worked for 5 days . so they must have completed 25 units . rest of the work 5 units done by c in 2 days . so c capacity = 5 / 2 = 2.5 units . given that toatal wages are rs . 1500 for 30 units . so for 1 unit of work they get rs . 50 . now b and c per day work = ( 2 + 2.5 ) = 4.5 units . so their daily wages = 4.5 × 50 = rs . 225 answer : a
Answer: a
Question (general): crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 20 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?
Options: a ) $ 20 , b ) $ 40 , c ) $ 50 , d ) $ 80 , e ) $ 100
Rationale: cost + profit = income ( selling price ) profit now = 0.5 x or x - 50 0.5 x = x - 50 50 = 0.5 x x = 100 $ is selling price so , profit before was 0.2 * 100 = 20 $ cost = 100 - 20 = 80 $ answer : d
Answer: d
Question (gain): if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 900 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 1300 , b ) 1350 , c ) 1400 , d ) 1450 , e ) 1500
Rationale: "let x be the minimum number of questionnaires to be mailed . 0.6 x = 900 x = 1500 the answer is e ."
Answer: e
Question (gain): salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 18 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.18 0.2 x = 0.08 x = 0.4 = 40 % the answer is c ."
Answer: c
Question (general): find the value o f 72519 x 9999 = m ?
Options: a ) 434539873 , b ) 355797990 , c ) 435453490 , d ) m = 725117481 , e ) 873430134
Rationale: "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"
Answer: d
Question (other): ( 4 ! ) ^ n is a factor of 12 ! , but ( 4 ! ) ^ ( n + 1 ) is not factor of 12 ! . what is the value of n ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 12 ! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 4 ! = 24 question can be rephrased as how many 24 ' s are there in 12 ! 12 * 2 = 24 4 * 6 = 24 3 * 8 = 24 value of n = 3 answer : c
Answer: c