Cheukting/mathqa huggingface dataset:
Question (physics): a monkey ascends a greased pole 14 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 25 th , b ) 22 nd , c ) 23 rd , d ) 24 th , e ) none of these
Rationale: "in 2 minutes , he ascends = 1 metre â ˆ ´ 12 metres , he ascends in 24 minutes . â ˆ ´ he reaches the top in 25 th minute . answer a"
Answer: a
Question (gain): due to a reduction of 25 / 4 % in the price of sugar , a man is able to buy 1 kg more for rs . 120 . find the original rate of sugar .
Options: a ) 7 , b ) 8 , c ) 8.5 , d ) 9 , e ) 9.5
Rationale: rate reduced by 6.25 % , so amount rs 120 reduced by = ( 6.25 / 100 ) * 120 = 7.5 so in rs 7.5 extra sugar obtained is 1 kg i . e . new rate is rs . 7.5 per kg thus original rate = [ 7.5 / ( 100 – 6.25 ) ] / 100 = 7.5 / 0.9375 = rs . 8 answer : option b
Answer: b
Question (general): on a test average ( arithmetic mean ) test score for 9 students is 80 . what must be 10 th student ' s score that average score for 10 students to be 82 ?
Options: a ) 100 , b ) 90 , c ) 80 , d ) 70 , e ) 60
Rationale: "( 9 * 80 + x ) / 10 = 82 x = ( 10 * 82 ) - ( 9 * 80 ) x = 820 - 720 total score required 820 - 720 = 100 correct answer is a"
Answer: a
Question (physics): a man can row 4 kmph in still water . when the river is running at 1.8 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 7.13 , b ) 6.19 , c ) 4.12 , d ) 3.19 , e ) 4.21
Rationale: "m = 4 s = 1.8 ds = 5.8 us = 2.2 x / 5.8 + x / 2.2 = 1 x = 1.59 d = 1.59 * 2 = 3.19 answer : b"
Answer: b
Question (gain): the annual interest rate earned by an investment increased by 5 percent from last year to this year . if the annual interest rate earned by the investment this year was 26.25 percent , what was the annual interest rate last year ?
Options: a ) 25 % , b ) 24 % , c ) 23 % , d ) 22 % , e ) 21 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.05 i ( last year ) = 1.05 i ( last year ) 26.25 = 1.05 x i ( last year ) i ( last year ) = 26.25 / 1.05 = 2625 / 105 = 25 % answer : a"
Answer: a
Question (geometry): a certain farmer pays $ 30 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 1210 feet ? ( 43,560 square feet = 1 acre )
Options: a ) $ 5,330
b ) $ 3,360
c ) $ 1,350
d ) $ 300
e ) $ 150
Rationale: basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 300 ( d )
Answer: d
Question (general): how many multiples of 7 are there between 21 and 343 , inclusive ?
Options: a ) 48 , b ) 47 , c ) 46 , d ) 45 , e ) 44
Rationale: "7 * 3 = 21 7 * 49 = 343 total multiples = ( 49 - 3 ) + 1 = 47 include 21 and 343 = 47 answer is b"
Answer: b
Question (gain): in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1600 employees , then the no . of female employees who are computer literate ?
Options: a ) 690 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1600 female employees , 60 % of 1600 . = ( 60 * 1600 ) / 100 = 960 . then male employees , = 640 50 % of male are computer literate , = 320 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1600 ) / 100 = 992 computer literate . thus , female computer literate = 992 - 320 = 672 . answer : option c"
Answer: c
Question (gain): shop offered 20 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 550 , c ) 600 , d ) 700 , e ) 750
Rationale: "sp * ( 80 / 100 ) = 560 sp = 70 * 100 = > cp = 700 answer : d"
Answer: d
Question (gain): the present worth of $ 3600 due in 2 years at 20 % per annum compound interest is ?
Options: a ) $ 1200 , b ) $ 1850 , c ) $ 2010 , d ) $ 3200 , e ) $ 2500
Rationale: present worth = 3600 / ( 1 + 20 / 100 ) ^ 2 = 3600 * 5 / 6 * 5 / 6 = $ 2500 answer is e
Answer: e
Question (physics): if the wheel is 19 cm then the number of revolutions to cover a distance of 1156 cm is ?
Options: a ) 11 , b ) 14 , c ) 18 , d ) 10 , e ) 19
Rationale: 2 * 22 / 7 * 19 * x = 1156 = > x = 9.7 answer : d
Answer: d
Question (gain): harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 60 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1055 , b ) b ) 1075 , c ) c ) 1065 , d ) d ) 1070 , e ) e ) 1100
Rationale: cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 60 × 9 = 540 . total cost he has to pay = 560 + 540 = 1100 . e )
Answer: e
Question (physics): the commuter rail between scottsdale and sherbourne is 200 km of track , and one train makes a round trip in 5 hours . if harsha boards the train at the forest grove station , which is located one fifth of the track ' s length out from scottsdale , how long will it take her to get to sherbourne ?
Options: a ) . 5 hours , b ) 1 hour , c ) 1.5 hours , d ) 2 hours , e ) 2.5 hours
Rationale: distance between scottsdale and sherbourne = 200 km time for a one - way trip between scottsdale and sherbourne : 5 / 2 = 2.5 hours distance between forest grove and scottsdale : 200 / 5 = 40 km distance between forest grove and sherbourne : 40 x 4 = 160 km time between scottsdale and forest grove : 2.5 / 5 = . 5 hours time between forest grove and sherborne : . 5 x 4 = 2 hours .
Answer: d
Question (physics): excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 35 kmph . of how many minutes does the train stop per hour ?
Options: a ) 73 , b ) 83 , c ) 12 , d ) 13 , e ) 28
Rationale: "explanation : t = 10 / 45 * 60 = 13 answer : option d"
Answer: d
Question (general): if the price of a certain bond on may 1 st was 2 / 3 the price of the bond on june 1 st and the price of the bond on july 1 st was 25 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 75 % , c ) 120 % , d ) 133 1 / 3 % , e ) 150 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 2 / 3 * 12 = 8 ; the price on july 1 st = 8 * 1.25 = 10 . the average price of the bond on may 1 st and july 1 st = ( 8 + 10 ) / 2 = 9 . the price of the bond on june 1 st ( 12 ) is 4 / 3 times ( 134 % ) the average price of the bond on may 1 st and july 1 st . answer : d ."
Answer: d
Question (physics): to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 10 hours a day ?
Options: a ) 28.8 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 10 = 200 therefore number of days = 5760 / 200 = 28.8 days ans = a"
Answer: a
Question (physics): two good train each 900 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12.2 sec , b ) 24.9 sec , c ) 86.4 sec , d ) 60.2 sec , e ) none
Rationale: "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 900 + 900 ) m = 1000 m . required time = ( 1800 x 6 / 125 ) sec = 86.4 sec . answer c"
Answer: c
Question (general): a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number e of tickets sold by the male members of the association
Options: a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66
Rationale: given that , total average e sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c .
Answer: c
Question (gain): uncle bruce is baking chocolate chip cookies . he has 72 ounces of dough ( with no chocolate ) and 50 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 40 % chocolate ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 2 , e ) 10
Rationale: "first , you must find the total weight of the mixture given that 80 % of it will be dough . 60 % * total = 72 = > ( 6 / 10 ) total = 72 = > total = 720 / 6 = > total = 120 oz , from there , you must find 10 % of the total 40 oz of the mixture . 40 % * total = > ( 4 / 10 ) ( 120 ) = 48 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 50 - 48 oz = 2 oz chocolate left over . answer : d"
Answer: d
Question (general): 107 ã — 107 + 93 ã — 93 = ?
Options: a ) 20198 , b ) 20098 , c ) 20000 , d ) 20088 , e ) 20085
Rationale: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1072 + 932 = ( 100 + 7 ) 2 + ( 100 â ˆ ’ 7 ) 2 = 2 ( 1002 + 72 ) = 2 ( 10000 + 49 ) = 20098 . answer : option b"
Answer: b
Question (general): how many integers from 100 to 800 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 80 , d ) 70 , e ) 90
Rationale: "question is asking for palindrome first digit possibilities - 1 through 7 = 7 8 is not possible here because it would result in a number greater than 8 ( i . e 808 , 818 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 7 * 10 = 70 answer is d ."
Answer: d
Question (general): a part - time employee whose hourly wage was increased by 50 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 ) 17 , d ) 20 , e ) 33.33
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 = 1.5 x now we need to find number of hours worked so that x * y = 1.5 x * z i . e z = 1 / 1.5 y = 2 / 3 y % decrease = ( y - 2 / 3 y ) / y * 100 = 100 / 3 = 33.33 % . thus my answer is e ."
Answer: e
Question (physics): pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed w ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16
Rationale: "let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this w we get x = 8 . b ."
Answer: b
Question (general): 653 ã — 1001 = ?
Options: a ) 649011 , b ) 540041 , c ) 654321 , d ) 653001 , e ) 643001
Rationale: "653 ã — ( 1000 + 1 ) 653000 + 1 653001 answer d"
Answer: d
Question (physics): pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed x ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16
Rationale: "let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this x we get x = 8 . b ."
Answer: b
Question (general): at a certain college , 50 percent of the total number of students are freshmen . if 40 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 20 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?
Options: a ) 14 % , b ) 4 % , c ) 15 % , d ) 5 % , e ) 25 %
Rationale: "let ' s say there is a total of 100 students at this college . 50 percent of the total number of students are freshmen . # of freshmen = 50 % of 100 = 50 40 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 40 % of 50 = 20 . . . and , of these , 20 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 20 % of 20 = 4 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 4 / 100 = 4 % answer : b"
Answer: b
Question (gain): what will be the difference between simple and compound interest at 10 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) rs . 31 , b ) rs . 32.10 , c ) rs . 40.40 , d ) rs . 64.10 , e ) rs . 74.10
Rationale: "s . i . = ( 1000 * 10 * 4 ) / 100 = rs . 400 c . i . = [ 1000 * ( 1 + 10 / 100 ) 4 - 1000 ] = rs . 464.10 difference = ( 464.10 - 400 ) = rs . 64.10 answer : d"
Answer: d
Question (general): 60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 50 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 100 worth of popcorn per day ?
Options: a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44
Rationale: lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 12 ( 44 - 12 ) must be those with four screens or more a is the answer
Answer: a
Question (physics): a train 200 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 28 , b ) 50 , c ) 77 , d ) 22 , e ) 12
Rationale: "speed of the train relative to man = ( 200 / 10 ) m / sec = ( 20 ) m / sec . [ ( 20 ) * ( 18 / 5 ) ] km / hr = 72 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 72 = = > x = 77 km / hr . answer : c"
Answer: c
Question (physics): if there are 156 laborers in a crew , and on a certain day , 70 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
Options: a ) 45.9 % , b ) 43.9 % , c ) 42.9 % , d ) 41.9 % , e ) 44.9 %
Rationale: "70 / 156 * 100 = 44.87 44.9 % correct answer e"
Answer: e
Question (physics): a work can be finished in 16 days by 30 women . the same work can be finished in 10 days by sixteen men . the ratio between the capacity of a man and a woman is
Options: a ) 3 : 1 , b ) 4 : 3 , c ) 2 : 3 , d ) 2 : 1 , e ) 2 : 4
Rationale: "work done by 30 women in 1 day = 1 / 16 work done by 1 woman in 1 day = 1 / ( 16 × 30 ) work done by 16 men in 1 day = 1 / 10 work done by 1 man in 1 day = 1 / ( 10 × 16 ) ratio of the capacity of a man and woman = 1 / ( 10 × 16 ) : 1 / ( 16 × 30 ) = 1 / 10 : 1 / 30 = 1 / 1 : 1 / 3 = 3 : 1 option a"
Answer: a
Question (other): the ratio of numbers is 4 : 5 and their h . c . f is 4 . their l . c . m is :
Options: a ) 80 , b ) 16 , c ) 24 , d ) 48 , e ) 98
Rationale: "let the numbers be 4 x and 5 x . then their h . c . f = x . so , x = 4 . so , the numbers are 16 and 20 . l . c . m of 16 and 20 = 80 . answer : a"
Answer: a
Question (physics): length of a rectangular plot is 12 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 56 m
b ) 60 m
c ) 80 m
d ) 82 m
e ) 84 m
Rationale: let breadth = x metres . then , length = ( x + 12 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 12 ) + x ] = 200 2 x + 12 = 100 2 x = 88 x = 44 hence , length = x + 12 = 56 m a
Answer: a
Question (general): two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 65 km more than the other . what is the distance between the two stations ?
Options: a ) 585 km , b ) 767 km , c ) 276 km , d ) 178 km , e ) 176 km
Rationale: "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 65 km more than the other , 25 x â € “ 20 x = 65 5 x = 65 x = 13 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 13 = 585 km . answer : a"
Answer: a
Question (physics): what is the length of a bridge ( in meters ) , which a train 140 meters long and travelling at 45 km / h can cross in 30 seconds ?
Options: a ) 205 , b ) 220 , c ) 235 , d ) 250 , e ) 265
Rationale: "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 30 seconds , the train can travel 25 / 2 * 30 = 375 meters 375 = length of train + length of bridge length of bridge = 375 - 140 = 235 meters the answer is c ."
Answer: c
Question (physics): a train crosses a platform of 140 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 190 , b ) 88 , c ) 77 , d ) 62 , e ) 52
Rationale: length of the train be â € ˜ x â € ™ x + 140 / 15 = x + 250 / 20 4 x + 560 = 3 x + 750 x = 190 m answer : a
Answer: a
Question (general): what is the sum of the integers from - 170 to 171 , inclusive ?
Options: a ) 181 , b ) 171 , c ) 191 , d ) 201 , e ) 202
Rationale: "in an arithmetic progression , the nth term is given by tn = a + ( n - 1 ) d here tn = 171 , a = - 170 , d = 1 hence , 171 = - 170 + ( n - 1 ) or n = 342 sum of n terms can be calculated by sn = n / 2 ( a + l ) a = first term , l = last term , n = no . of terms sn = 342 * ( - 170 + 171 ) / 2 sn = 342 * 1 / 2 sn = 171 answer : b"
Answer: b
Question (general): if 7 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 21 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 7 * 6 / 2 = 21 answer : a"
Answer: a
Question (gain): a sum was put a simple interest at a certain rate for 3 years . had it been put at 3 % higher rate , it would have fetched rs . 90 more . the sum is :
Options: a ) s . 750 , b ) s . 900 , c ) s . 1000 , d ) s . 1200 , e ) s . 1500
Rationale: "explanation : let the sub be rs . x and the initial rate be r % . then x ã — ( r + 3 ) ã — 3 / 100 â ˆ ’ x ã — r ã — 3 / 100 = 90 â ‡ ’ x ã — 3 ã — 3 / 100 = 90 â ‡ ’ x ã — 3 / 100 = 30 â ‡ ’ 3 x = 3000 â ‡ ’ x = 1000 answer : option c"
Answer: c
Question (general): at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 8.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: oa is definitely wrong . the answer should be a .
Answer: a
Question (other): find the ratio in which rice at rs . 7.00 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 6 : 7 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 8
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 70 = 6 : 7 answer : a"
Answer: a
Question (physics): if the lcm and hcf of 4 and another number is 36 and 2 respectively . find the other number ?
Options: a ) 18 , b ) 16 , c ) 14 , d ) 13 , e ) 15
Rationale: hcf x lcm = product of numbers 2 x 36 = 4 x the other number other number = ( 2 x 36 ) / 4 other number = 18 answer : a
Answer: a
Question (general): a certain car uses one gallon of gasoline every 40 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?
Options: a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 50 %
Rationale: "4 miles on the highway = 4 / 40 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 40 + 4 / 20 = 3 / 10 gallons . 8 miles on the highway = 8 / 40 gallons . the % change = ( 3 / 10 - 8 / 40 ) / ( 8 / 40 ) = 1 / 2 = 0.50 . answer : e ."
Answer: e
Question (gain): a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 864 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 668 , d ) s . 700 , e ) s . 760
Rationale: "s . i . for 1 year = rs . ( 864 - 815 ) = rs . 49 . s . i . for 3 years = rs . ( 49 x 3 ) = rs . 147 . principal = rs . ( 815 - 147 ) = rs . 668 . answer : option c"
Answer: c
Question (geometry): the breadth of a rectangular hall is two - thirds of its length . if the area of the hall is 2400 sq metres , what is the length in metres ?
Options: a ) 120
b ) 80
c ) 60
d ) 40
e ) none of these
Rationale: let the length of the rectangular hall be ‘ x ’ m , then the breadth of the rectangular hall = 2 x ⁄ 3 m . area of hall = 2 x ⁄ 3 × x = 2 x 2 ⁄ 3 or , 2 x 2 ⁄ 3 = 2400 or x = 60 m answer c
Answer: c
Question (geometry): if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 166 m , what is its area ?
Options: a ) 1590 , b ) 2535 , c ) 2530 , d ) 2515 , e ) 2520
Rationale: "length = breadth + 23 . therefore , 4 × breadth + 2 × 23 = 166 m ⇒ breadth = 30 m length = 30 + 23 = 53 m area = 53 × 30 = 1590 m 2 answer is a ."
Answer: a
Question (general): a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 5.50 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,650 , d ) $ 2,050 , e ) $ 2,250
Rationale: "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 5.5 $ then total value is 300 * 5.5 = 1650 . imo option c is correct answer . ."
Answer: c
Question (general): find √ ? / 18 = 4 ?
Options: a ) 76 , b ) 5776 , c ) 304 , d ) 5184 , e ) none
Rationale: "answer let √ n / 18 = 4 then √ n = 18 x 4 = 72 ∴ n = 72 x 72 = 5184 . correct option : d"
Answer: d
Question (general): the population of a city increases by 6 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.27 % , c ) 27 % , d ) 15.76 % , e ) none of these
Rationale: actual increase in population = 5 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 5 / 100 ) ^ 3 = 115.7625 ∴ required percentage = 15.7625 % answer : d
Answer: d
Question (general): find the average of all the numbers between 6 and 34 which are divisible by 6 .
Options: a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 21
Rationale: "solution average = ( ( 12 + 18 + 24 + 30 ) / 5 ) = 84 / 4 = 21 . answer e"
Answer: e