regisss/math_qa huggingface dataset:
Problem: the difference between simple interest and compound interest on $ 1200 for one year at 10 % per annum reckoned half - yearly is :
Options: a ) $ 5 , b ) $ 8 , c ) $ 9 , d ) $ 3 , e ) $ 7
Rationale: "s . i = $ [ ( 1200 * 10 * 1 ) / 100 ] = $ 120 . c . i = $ [ 1200 * ( 1 + ( 5 / 100 ) ^ 2 ) - 1200 ] = $ 123 . difference = $ ( 123 - 120 ) = $ 3 . answer ( d )"
Answer: d
Problem: a train 110 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 61 kmph , e ) 70 kmph
Rationale: explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 110 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 1980 < = > x = 61 speed of the train is 61 kmph . answer : option d
Answer: d
Problem: the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 5.80 . the price of corn is increasing at a constant rate of 5 x 5 x cents per day while the price of wheat is decreasing at a constant rate of 2 √ ∗ x − x 2 ∗ x − x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 5.60
Rationale: "let yy be the # of days when these two bushels will have the same price . first let ' s simplify the formula given for the rate of decrease of the price of wheat : 2 √ ∗ x − x = 1.41 x − x = 0.41 x 2 ∗ x − x = 1.41 x − x = 0.41 x , this means that the price of wheat decreases by 0.41 x 0.41 x cents per day , in yy days it ' ll decrease by 0.41 xy 0.41 xy cents ; as price of corn increases 5 x 5 x cents per day , in yy days it ' ll will increase by 5 xy 5 xy cents ; set the equation : 320 + 5 xy = 580 − 0.41 xy 320 + 5 xy = 580 − 0.41 xy , solve for xyxy - - > xy = 48 xy = 48 ; the cost of a bushel of corn in yy days ( the # of days when these two bushels will have the same price ) will be 320 + 5 xy = 320 + 5 ∗ 48 = 560320 + 5 xy = 320 + 5 ∗ 48 = 560 or $ 5.6 . answer : e ."
Answer: e
Problem: find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number
Options: a ) 17 , b ) 15 , c ) 12 , d ) 8 , e ) 3
Rationale: "f the number is x , then , x + 17 = 60 / x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 , - 20 , so x = 3 ( as 3 is positive ) answer : e"
Answer: e
Problem: the length of a rectangular garden is three times its width . if the area of the rectangular garden is 588 square meters , then what is the width of the rectangular garden ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "let x be the width of the garden . 3 x ^ 2 = 588 x ^ 2 = 196 x = 14 the answer is c ."
Answer: c
Problem: a train 360 m long is running at a speed of 72 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 29 sec , c ) 25 sec , d ) 27 sec , e ) 34 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 20 = 25 sec answer : c"
Answer: c
Problem: if 20 typists can type 48 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 63 , b ) 72 , c ) 144 , d ) 216 , e ) 400
Rationale: "20 typists can type 48 letters , so 30 typists can type = 48 * 30 / 20 48 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 48 * 30 * 60 / 20 * 20 = 216 d is the answer"
Answer: d
Problem: a car traveling at a certain constant speed takes 15 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 60 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 48 , b ) 50 , c ) 52 , d ) 54 , e ) 56
Rationale: "60 * t = 1 km = > t = 1 / 60 km / h v * ( t + 15 / 3600 ) = 1 v ( 1 / 60 + 15 / 3600 ) = 1 v ( 75 / 3600 ) = 1 v = 48 km / h the answer is a ."
Answer: a
Problem: p and q started a business investing rs . 96,000 and rs . 28,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 24 : 7 , c ) 25 : 6 , d ) 21 : 3 , e ) 17 : 4
Rationale: "p : q = 96000 : 28000 = 24 : 7 answer : b"
Answer: b
Problem: a train 90 m long running at 56 kmph crosses a platform in 18 sec . what is the length of the platform ?
Options: a ) 190 , b ) 200 , c ) 180 , d ) 881 , e ) 271
Rationale: "d = 56 * 5 / 18 = 25 = 280 – 90 = 190 answer : a"
Answer: a
Problem: a card is drawn from a pack of 52 cards . the probability of ge ƫ ng a queen of club or a king of heart is
Options: a ) 1 / 13 , b ) 2 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) none of these
Rationale: "explanation : total number of cases = 52 favourable cases = 2 probability = 2 / 56 = 1 / 26 answer : c"
Answer: c
Problem: this topic is locked . if you want to discuss this question please re - post it in the respective forum . matt and peter can do together a piece of work in 20 days . after they have worked together for 12 days matt stops and peter completes the remaining work in 14 days . in how many days peter complete the work separately .
Options: a ) 26 days , b ) 27 days , c ) 23 days , d ) 35 days , e ) 24 days
Rationale: together they complete the job in 20 days means they complete 12 / 20 of the job after 12 days . peter completes the remaining ( 8 / 20 ) of the job in 14 days which means that the whole job ( 1 ) can be completed in x days . < = > 8 / 20 - > 14 < = > x = 14 / ( 8 / 20 ) = 35 thus the answer is d .
Answer: d
Problem: we bought a total of 80 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 373 . how many math books did we buy ?
Options: a ) 23 , b ) 27 , c ) 31 , d ) 35 , e ) 39
Rationale: "m + h = 80 h = 80 - m 4 m + 5 h = 373 4 m + 5 * ( 80 - m ) = 373 m = 27 the answer is b ."
Answer: b
Problem: if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number s of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning s = 5 out of 6 also possible as you will see 5 or 1 will give you same equation . . ans d"
Answer: d
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: a can do a piece of work in 3 hours ; b and c together can do it in 2 hours , which a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 6 hours , b ) 3 hours , c ) 2 hours , d ) 5 hours , e ) 4 hours
Rationale: "a ' s 1 hour work = 1 / 3 ; ( b + c ) ' s 1 hour work = 1 / 2 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 3 + 1 / 2 ) = 5 / 6 b ' s 1 hour work = ( 5 / 6 - 1 / 2 ) = 1 / 3 b alone will take 3 hours to do the work . answer : b"
Answer: b
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively . the ratio of their speeds is ?
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) 5 : 2
Rationale: "answer : option b let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 16 : â ˆ š 9 = 4 : 3"
Answer: b
Problem: at what rate percent on simple interest will rs . 650 amount to rs . 950 in 5 years ?
Options: a ) 3.33 % , b ) 5.93 % , c ) 4.33 % , d ) 5.33 % , e ) 9.23 %
Rationale: "300 = ( 650 * 5 * r ) / 100 r = 9.23 % answer : e"
Answer: e
Problem: a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 98 are wrong and the other digits are correct , then the correct answer would be :
Options: a ) 288889 , b ) 556677 , c ) 555681 , d ) 267788 , e ) 268811
Rationale: "explanation : 987 = 3 * 7 * 47 . so , the required number must be divisible by each one of 3 , 7 , 47 553681 = > ( sum of digits = 28 , not divisible by 3 ) 555181 = > ( sum of digits = 25 , not divisible by 3 ) 555681 is divisible by each one of 3 , 7 , 47 . answer : c ) 555681"
Answer: c
Problem: when leo imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that leo paid was $ 87.50 , what was the total value of the item ?
Options: a ) $ 1600 , b ) $ 1850 , c ) $ 2250 , d ) $ 2400 , e ) $ 2750
Rationale: let the value of the item be $ x , then 0.07 ( x − 1000 ) = 87.5 - - > x − 1000 = 1250 x − 1000 = 1250 - - > x = 2250 . answer : c .
Answer: c
Problem: the annual interest rate earned by an investment increased by 6 percent from last year to this year . if the annual interest rate earned by the investment this year was 15.90 percent , what was the annual interest rate last year ?
Options: a ) 20 % , b ) 18 % , c ) 16 % , d ) 25 % , e ) 15 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.06 i ( last year ) = 1.06 i ( last year ) 15.90 = 1.06 x i ( last year ) i ( last year ) = 15.90 / 1.06 = 1590 / 106 = 15 % answer : e"
Answer: e
Problem: john and steve are speed walkers in a race . john is 12 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 26 seconds , d ) 34 seconds , e ) 28 seconds
Rationale: let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 12 + 2 - - - > 0.5 t = 14 - - - > t = 28 seconds . e is the correct answer .
Answer: e
Problem: i chose a number and divide it by 6 . then i subtracted 189 from the result and got 3 . what was the number i chose ?
Options: a ) 1200 , b ) 1152 , c ) 1189 , d ) 1190 , e ) 100
Rationale: "let x be the number i chose , then x / 6 − 189 = 3 x / 6 = 192 x = 1152 answer is b ."
Answer: b
Problem: a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 400 more . what was the sum ?
Options: a ) s . 1200 , b ) s . 800 , c ) s . 1400 , d ) s . 1000 , e ) s . 920
Rationale: "at 5 % more rate , the increase in s . i for 10 years = rs . 400 ( given ) so , at 5 % more rate , the increase in si for 1 year = 400 / 10 = rs . 40 / - i . e . rs . 40 is 5 % of the invested sum so , 1 % of the invested sum = 40 / 5 therefore , the invested sum = 40 × 100 / 5 = rs . 800 answer : b"
Answer: b
Problem: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 26 m * 2 m * 0.75 m ?
Options: a ) 29798 , b ) 27908 , c ) 78902 , d ) 26000 , e ) 27991
Rationale: "26 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 26 = 1 / 1000 * x = > x = 26000 answer : d"
Answer: d
Problem: the product of two successive numbers is 462 . which is the smaller of the two numbers ?
Options: a ) 21 , b ) 23 , c ) 26 , d ) 27 , e ) 29
Rationale: a 21 from the given alternatives , 21 × 22 = 462 ∴ smaller number = 21
Answer: a
Problem: in a group of ducks and cows , the total number of legs are 30 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 28 more than twice the number of heads = > 2 ( d + 2 c ) = 30 + 2 ( c + d ) = > d + 2 c = 15 + c + d = > 2 c = 15 + c = > c = 15 i . e . , total number of cows = 15 answer is b ."
Answer: b
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36 seconds . the length of each train is ?
Options: a ) 40 meter , b ) 45 meter , c ) 50 meter , d ) 55 meter , e ) none of these
Rationale: "explanation : let the length of each train is x meter distance will be x + x = 2 x relative speed = 46 - 36 = 10 km / hr = 10 * ( 5 / 18 ) = 25 / 9 m / sec distance = speed * time 2 x = 25 / 9 ∗ 36 2 x = 100 = > x = 50 so length of both the trains are 50 meters option c"
Answer: c
Problem: if a ' s height is 25 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 33.33 % , e ) 66.65 %
Rationale: "excess of b ' s height over a ' s = [ ( 25 / ( 100 - 25 ) ] x 100 % = 33.33 % answer : d )"
Answer: d
Problem: the tax on a commodity is diminished by 24 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 %
Rationale: "100 * 100 = 10000 76 * 112 = 8512 10000 - - - - - - - 1488 100 - - - - - - - ? = 15 % answer : c"
Answer: c
Problem: a and b can do a piece of work in 6 2 / 3 days and 5 days respectively . they work together for 2 days and then a leaves . in how many days after that b will complete the work alone .
Options: a ) 6 â ½ days , b ) 1 â ½ days , c ) 8 â ½ days , d ) 5 â ½ days , e ) 2 â ½ days
Rationale: "explanation : 3 / 20 * 2 + ( 2 + x ) / 5 = 1 x = 1 â ½ days answer : b"
Answer: b
Problem: convert the 13 / 48 m / s into kilometers per hour ?
Options: a ) 1.5 kmph . , b ) 0.91 kmph . , c ) 1.2 kmph . , d ) 1.5 kmph . , e ) 0.98 kmph .
Rationale: "13 / 48 m / s = 13 / 48 * 18 / 5 = 49 / 50 = 0.98 kmph . answer : e"
Answer: e
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle ?
Options: a ) 18 cm , b ) 16 cm , c ) 40 cm , d ) 20 cm , e ) 50 cm
Rationale: "let bresdth x cm length = 2 x cm new l = ( 2 x - 5 ) cm new breadth = ( x + 5 ) new area = ( 2 x - 5 ) sq cm = ( 2 x - 5 ) ( x + 5 ) = 2 x 2 + 75 x = 20 cm l = 2 x - 2 = 2 * 20 = 40 cm answer c"
Answer: c
Problem: there is a total of 90 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 6 and the probability that it will be green is 1 / 5 . what is the probability that the marble will be either red or blue ?
Options: a ) 3 / 5 , b ) 7 / 15 , c ) 11 / 15 , d ) 19 / 30 , e ) 23 / 30
Rationale: "p ( red or blue ) = 1 - p ( white ) - p ( green ) = 30 / 30 - 5 / 30 - 6 / 30 = 19 / 30 the answer is d ."
Answer: d
Problem: what is the average of first 21 multiples of 7 ?
Options: a ) 67 , b ) 69 , c ) 77 , d ) 79 , e ) 81
Rationale: "required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 7 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 77 c"
Answer: c
Problem: uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 14 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 3 , b ) 6 , c ) 7.2 , d ) 5 , e ) 9
Rationale: "answer is d . x / x + 36 = 1 / 5 x = 9 14 - 9 = 5"
Answer: d
Problem: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 25 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 55 , c ) 28 , d ) 66 , e ) 11
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 25 / 5 = 5 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 5 = 55 secs . answer : b"
Answer: b
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of q is less than the square root of q . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "q 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Problem: two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 2 ½ hours if they are walking in the same direction ?
Options: a ) 7 km , b ) 6 km , c ) 3 1 / 8 km , d ) 9 km , e ) 5 km
Rationale: "rs = 5 ¾ - 4 ½ = 1 ¼ t = 2 ½ h . d = 5 / 4 * 5 / 2 = 25 / 8 = 3 1 / 8 km answer : c"
Answer: c
Problem: if an object travels at 85 feet per second , how many feet does it travel in 30 minutes ?
Options: a ) 3000 , b ) 1500 , c ) 1800 , d ) 9000 , e ) 2500
Rationale: "if an object travels at 85 feet per second it covers 85 x 60 feet in one minute , and 5 x 60 x 30 feet in 30 minutes . answer = 9000 answer : d"
Answer: d
Problem: if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 50 km , b ) 56 km , c ) 60 km , d ) 70 km , e ) 80 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a"
Answer: a
Problem: in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 53900 . how many times did he participate in the competition ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "53900 = 2 * 2 * 5 * 5 * 7 * 7 * 11 john participated 7 times . the answer is a ."
Answer: a
Problem: 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 15 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
Options: a ) 31 , b ) 25 , c ) 35 , d ) 45 , e ) 75
Rationale: "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 15 % = 27 responded as satisfied , so remaining satisfied are 120 - 27 = 93 so 93 is what percentage of 300 - 31 % so the answer should be a"
Answer: a
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 62 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.85 kgs , c ) 58.7 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 62 ) = 1174 kgs actual average weight is 1174 / 20 = 58.7 kgs c"
Answer: c
Problem: 34 men can complete a piece of work in 18 days . in how many days will 17 men complete the same work ?
Options: a ) 36 , b ) 26 , c ) 97 , d ) 26 , e ) 19
Rationale: "explanation : let the required number of days be a . then , less men , more days ( indirect proportion ) 17 : 34 : : 18 : a 17 x a = 34 x 18 a = ( 34 x 18 ) / 17 a = 36 answer : a"
Answer: a
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg . what might be the weight of the new person ?
Options: a ) 56 kg , b ) 80 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "b 80 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 60 + 20 ) kg = 80 kg ."
Answer: b
Problem: the perimeter of one square is 48 cm and that of another is 24 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 13 √ 4 , b ) 13 √ 2 , c ) 13.4 √ 2 , d ) 12 √ 4 , e ) 13 √ 9
Rationale: "4 a = 48 4 a = 24 a = 12 a = 6 a 2 = 144 a 2 = 36 combined area = a 2 = 180 = > a = 13.4 d = 13.4 √ 2 answer : c"
Answer: c
Problem: if a certain number when divided by the numbers 5 , 32 one after other successively , leaves a remainder 0 , 21 then what will be the remainders if it is divided by the numbers 2 , 35
Options: a ) 1 , 20 , b ) 1 , 21 , c ) 1 , 22 , d ) 1 , 23 , e ) 1 , 24
Rationale: the number is 35 , when divided by 5 , 32 leaves remainder 0 , 21 respectively . so if 35 is divided by 2 , 35 leaves remainder 1 , 20 respectively . answer : a
Answer: a
Problem: p and q invested in a business . the profit earned was divided in the ratio 2 : 3 . if p invested rs 30000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 45000 , d ) 20000 , e ) 60000
Rationale: "let the amount invested by q = q 30000 : q = 2 : 3 ⇒ 30000 × 3 = 2 q ⇒ q = ( 30000 × 3 ) / 2 = 45000 answer is c ."
Answer: c
Problem: the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number q ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: ( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = q answer : b
Answer: b
Problem: a man is 30 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 28 years , c ) 21 years , d ) 20 years , e ) 19 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 30 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 30 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 28 answer : b"
Answer: b
Problem: what is the value of ( 4 ) ^ - 6 ?
Options: a ) 1 / 1008 , b ) 1 / 6400 , c ) 1 / 6550 , d ) 1 / 6660 , e ) 1 / 4096
Rationale: "4 ^ - 6 = 1 / ( 4 ) ^ 6 = 1 / 4096 answer : e"
Answer: e
Problem: machine x takes 60 hours longer than machine y to produce 1080 widgets . machine y produces 20 percent more widgets in an hour than machine x does in an hour . how many widgets per hour does machine x produce
Options: a ) 100 , b ) 65 , c ) 25 , d ) 11 , e ) 3
Rationale: machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 60 so , x = 60 . hence 6 x = 6 * 60 = 360 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 360 = 3 hence option ( e ) .
Answer: e
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 22 , b ) 35 , c ) 25 , d ) 99 , e ) 21
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 20 ) = 90 ( x - 5 ) 350 = 10 x = > x = 35 . answer : b"
Answer: b
Problem: a train running at the speed of 52 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 130 , b ) 272 , c ) 278 , d ) 277 , e ) 112
Rationale: "speed = 52 * ( 5 / 18 ) m / sec = 130 / 9 m / sec length of train ( distance ) = speed * time ( 130 / 9 ) * 9 = 130 meter answer : a"
Answer: a
Problem: what is the remainder when 1234 * 6789 * 1111 is divided by 19
Options: a ) 15 , b ) 23 , c ) 7 , d ) 10 , e ) 43
Rationale: "12345 / 19 = = > remainder = 14 678910 / 19 = = > remainder = 2 111111 / 19 = = > remainder = 18 = 14 * 2 * 18 = 504 / 19 = = > remainder = 10 answer : d"
Answer: d
Problem: how many 1 / 4 s are there in 37 1 / 2 ?
Options: a ) 150 , b ) 450 , c ) 500 , d ) 650 , e ) 700
Rationale: "required number = ( 75 / 2 ) / ( 1 / 4 ) = ( 75 / 2 x 4 / 1 ) = 150 . answer : a"
Answer: a
Problem: if x : y = 2 : 9 , find the value of ( 2 x + 2 y ) : ( 5 x – y )
Options: a ) 22 : 1 , b ) 22 : 3 , c ) 7 : 1 , d ) 5 : 3 , e ) 8 : 1
Rationale: "explanation : given : x / y = 2 / 9 ( 2 x + 2 y ) : ( 5 x – y ) = ( 2 * 2 + 2 * 9 ) : ( 5 * 2 – 9 ) = 22 : 1 answer : a"
Answer: a