Cheukting/mathqa huggingface dataset:
Question (geometry): the area of the square formed on the diagonal of a rectangle as its side is 108 1 / 3 % more than the area of the rectangle . if the perimeter of the rectangle is 28 units , find the difference between the sides of the rectangle ?
Options: a ) 5
b ) 4
c ) 7
d ) 2
e ) 1
Rationale: let the sides of the rectangle be l and b respectively . from the given data , ( √ l 2 + b 2 ) = ( 1 + 108 1 / 3 % ) lb = > l 2 + b 2 = ( 1 + 325 / 3 * 1 / 100 ) lb = ( 1 + 13 / 12 ) lb = 25 / 12 lb = > ( l 2 + b 2 ) / lb = 25 / 12 12 ( l 2 + b 2 ) = 25 lb adding 24 lb on both sides 12 l 2 + 12 b 2 + 24 lb = 49 lb 12 ( l 2 + b 2 + 2 lb ) = 49 lb but 2 ( l + b ) = 28 = > l + b = 14 12 ( l + b ) 2 = 49 lb = > 12 ( 14 ) 2 = 49 lb = > lb = 48 since l + b = 14 , l = 8 and b = 6 l - b = 8 - 6 = 2 m . answer : d
Answer: d
Question (general): for what value of x between − 9 and 9 , inclusive , is the value of x ^ 2 − 10 x + 16 the greatest ?
Options: a ) − 9 , b ) − 2 , c ) 0 , d ) 2 , e ) 9
Rationale: "we can see from the statement that two terms containing x , x ^ 2 will always be positive and - 10 x will be positive if x is - ive . . so the equation will have greatest value if x is - ive , and lower the value of x , greater is the equation . so - 9 will give the greatest value . . ans a"
Answer: a
Question (gain): the owner of a furniture shop charges his customer 10 % more than the cost price . if a customer paid rs . 8800 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6725 , b ) rs . 6727 , c ) rs . 8000 , d ) rs . 6725 , e ) rs . 6728
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8800 ( 100 / 110 ) = rs . 8000 . answer : c"
Answer: c
Question (general): if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 15 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 382 , c ) $ 345 , d ) $ 392 , e ) $ 399
Rationale: "( 348 / 116 ) 115 = 345 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 115 = 345 ( 300 + 45 ) answer c"
Answer: c
Question (general): the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 440 per month . the salary of the new supervisor is :
Options: a ) 233 , b ) 960 , c ) 287 , d ) 771 , e ) 191
Rationale: explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 440 = 3960 salary of the new supervisor = 3960 â ˆ ’ 3000 = 960 answer : b
Answer: b
Question (general): if ( m - 8 ) is a factor of m ^ 2 - hm - 24 , then h =
Options: a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16
Rationale: ( m - 8 ) ( m - a ) = m ^ 2 - hm - 24 a = - 3 h = 8 + a = 5 = b
Answer: b
Question (general): if the average of 5 x and 8 y is greater than 90 , and x is twice y , what is the least integer value of x ?
Options: a ) 4 , b ) 5 , c ) 20 , d ) 21 , e ) 23
Rationale: "if y is greater than 110 percent of x , is y greater than 75 ? ( 1 ) x > 75 x > 75 ( 2 ) y − x = 10 y − x = 10 pls verify . 1 ) sufficient . y > 1.1 x and x > 75 . min ( x ) = 75 y > 1.1 * 75 y > 82.5 2 ) insufficient . substituting ( x = y - 10 ) in y > 1.1 x y > 1.1 ( y - 10 ) y < 110 hence a ."
Answer: a
Question (general): how many three - element subsets of { 1,2 , 3,4 } are there that do not contain the pair of elements 2 and 4 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "required subsets are = { 1 , 2,3 } , { 1 , 3,4 } = 2 answer : b"
Answer: b
Question (physics): the length of the bridge , which a train 500 metres long and travelling at 42 km / hr can cross in 60 seconds , is ?
Options: a ) 100 m , b ) 200 m , c ) 300 m , d ) 250 m , e ) 350 m
Rationale: "speed = [ 42 x 5 / 18 ] m / sec = [ 35 / 3 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 60 35 / 3 = ( 130 + x ) / 60 500 + x = 700 = > x = 200 m answer : b"
Answer: b
Question (general): a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 20 % of the original number . what percent of the red candies remain ?
Options: a ) 5 % , b ) 7.5 % , c ) 10 % , d ) 12.5 % , e ) 15 %
Rationale: "let x be the original number of each color . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = x red + yellow = 0.25 x red = 0.125 x , since red = yellow . the answer is d ."
Answer: d
Question (gain): there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 12,000 after 3 years at the same rate ?
Options: a ) 2372 , b ) 2572 , c ) 4542 , d ) 2343 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 12000 . t = 3 years and r = 10 % p . a . c . i . = rs . 12000 x 1 + 10 3 - 1 100 = rs . 12000 x 331 1000 = 3972 . e"
Answer: e
Question (gain): a man bought 40 shares of rs . 80 at 5 discount , the rate of dividend being 12 1 / 2 % the rate of interest obtained is
Options: a ) 13.33 % , b ) 15.5 % , c ) 14 % , d ) 14.25 % , e ) 14.95 %
Rationale: "explanation : face value of a share = rs . 80 he bought each share at rs . 80 - rs . 5 = rs . 75 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 80 × 25 / 2 / 100 = rs . 10 total dividend = ( 40 × 10 ) ie , he got a dividend of ( 40 × 10 ) for an investment of rs . ( 40 × 75 ) interest obtained = 40 × 10 × 100 / 40 × 75 = 13.33 % answer : option a"
Answer: a
Question (general): the average of 2 , 76 and x is 5 . find the value of x ?
Options: a ) 10 , b ) 8 , c ) 12 , d ) 15 , e ) 5
Rationale: average = ( 2 + 7 + 6 + x ) / 4 = 5 x = 5 answer is e
Answer: e
Question (general): a car averages 65 mph for the first 5 hours of a trip and averages 75 mph for each additional hour . the average speed for the entire trip was 60 mph . how many hours long is the trip ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: "let the time for which car averages 75 mph = t 60 * ( t + 5 ) = 65 * 4 + 70 t = > 10 t = 40 = > t = 4 total duration of the trip = 5 + 4 = 9 answer a"
Answer: a
Question (general): if y > 0 , ( 6 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to 3 y / 10 + 3 y / 10 = 3 y / 5 = 60 % c"
Answer: c
Question (general): if the number is divided by 3 , it reduced by 36 . the number is
Options: a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 54 , e ) e ) 36
Rationale: "explanation : let the number be x . then , x - ( x / 3 ) = 36 = > 2 x / 3 = 36 = > x = 54 answer : option d"
Answer: d
Question (physics): 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 10 men , 4 women and 30 children together complete the piece of work ?
Options: a ) 5 days , b ) 15 days , c ) 28 days , d ) 4 days , e ) 7 days
Rationale: "explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 10 men ’ s 1 day ’ s work = 1 × 10 / 96 = 5 / 48 1 woman ’ s 1 day ’ s work = 1 / 192 4 women ’ s 1 day ’ s work = 1 / 192 × 4 = 1 / 48 1 child ’ s 1 day ’ s work = 1 / 240 30 children ’ s 1 day ’ s work = 1 / 8 therefore , ( 10 men + 4 women + 30 children ) ’ s 1 day ’ s work = 5 / 48 + 1 / 48 + 1 / 8 = 1 / 4 the required no . of days = 4 days answer : option d"
Answer: d
Question (other): in a group of 150 readers who read science fiction or literacy works or both , 120 read science fiction and 90 read literacy works . how many read both science fiction and literacy works ?
Options: a ) 70 , b ) 60 , c ) 90 , d ) 100 , e ) 110
Rationale: consider total number of reader n ( s u l ) = 150 people who read science fiction n ( s ) = 120 people who read literacy works n ( l ) = 90 both science fiction and literacy n ( s â ˆ © l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s â ˆ © l ) 150 = 120 + 90 - n ( s â ˆ © l ) n ( s â ˆ © l ) = 210 - 150 n ( s â ˆ © l ) = 60 so people read both science fiction and literacy works are 160 answer : b
Answer: b
Question (physics): the speed of a boat in still water in 30 km / hr and the rate of current is 7 km / hr . the distance travelled downstream in 36 minutes is :
Options: a ) 18.4 km , b ) 20.6 km , c ) 21.4 km , d ) 1111 km , e ) 22.2 km
Rationale: "explanation : speed downstream = ( 30 + 7 ) = 37 kmph time = 36 minutes = 36 / 60 hour = 3 / 5 hour distance travelled = time × speed = ( 3 / 5 ) × 37 = 22.2 km answer : option e"
Answer: e
Question (physics): 39 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 3 hours a day , complete the work ?
Options: a ) 10 , b ) 26 , c ) 14 , d ) 15 , e ) 16
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 39 : : 12 : x working hours / day 3 : 5 30 x 3 x x = 39 x 5 x 12 x = ( 39 x 5 x 12 ) / ( 30 x 3 ) x = 26 . answer : b"
Answer: b
Question (physics): in what time will two trains cross each other completely , which are running on the same parallel lines in opposite directions , each train running with a speed of 90 kmph being 160 m and 140 m in length respectively ?
Options: a ) 5.6 sec , b ) 6.2 sec , c ) 6.0 sec , d ) 7.2 sec , e ) 6.8 sec
Rationale: "d = 160 m + 140 m = 300 m * 1 / 1000 = 0.3 kms rs = 90 + 90 = 180 kmph t = ( 0.3 / 180 ) * 3600 = 6.0 sec answer : c"
Answer: c
Question (physics): cole drove from home to work at an average speed of 80 kmh . he then returned home at an average speed of 120 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78
Rationale: "first round distance travelled ( say ) = d speed = 80 k / h time taken , t 2 = d / 80 hr second round distance traveled = d ( same distance ) speed = 120 k / h time taken , t 2 = d / 120 hr total time taken = 2 hrs therefore , 2 = d / 80 + d / 120 lcm of 80 and 120 = 240 2 = d / 80 + d / 120 = > 2 = 3 d / 240 + 2 d / 240 = > d = 240 * 2 / 5 km therefore , t 1 = d / 80 = > t 1 = ( 240 * 2 ) / ( 5 x 80 ) = > t 1 = ( 6 x 60 ) / 5 - - in minutes = > t 1 = 72 minutes . c"
Answer: c
Question (general): the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 2 nd year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 48
Rationale: "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 thus for the 2 nd year = 50 , 3 rd year = 50 - 2 = 48 4 th year = 48 - 3 = 45 5 th year = 45 - 4 = 41 . 6 th year = 41 - 5 = 36 the correct answer is a ."
Answer: a
Question (gain): a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 25 % , what should be the sale price of the mixed tea ?
Options: a ) 23.75 , b ) 22 , c ) 20 , d ) 19.20 , e ) none of these
Rationale: "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 25 ) / 100 × 16 = 20 answer c"
Answer: c
Question (physics): pipe a fills a tank of capacity 800 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 48 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: "in one cycle they fill 40 + 30 - 20 = 50 liters 800 = 50 * n = > n = 16 here n = number of cycles . total time = 16 * 3 = 48 as in one cycle there are 3 minutes . thus 48 minutes answer : a"
Answer: a
Question (physics): in a dairy farm , 20 cows eat 10 bags of husk in 40 days . in how many days one cow will eat one bag of husk ?
Options: a ) 20 , b ) 40 , c ) 80 , d ) 30 , e ) 60
Rationale: "one cow eats 10 / 20 = 0.5 bags of husk in 40 days . then , it eats 1 bag in 40 / 0.5 = 80 days answer : c"
Answer: c
Question (general): if w / x = 1 / 3 and w / y = 3 / 4 , then ( x + y ) / y =
Options: a ) 13 / 4 , b ) 6 / 5 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5
Rationale: "w / x = 1 / 3 = > x = 3 w and w / y = 3 / 4 = > y = ( 4 / 3 ) w ( x + y ) / y = ( 3 w + 4 / 3 w ) / ( 4 / 3 w ) = ( 13 / 3 w ) / ( 4 / 3 w ) = 13 / 4 correct option : a"
Answer: a
Question (physics): the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 24 minutes is
Options: a ) 17.2 km , b ) 7.2 km , c ) 7.6 km , d ) 17.6 km , e ) 27.2 km
Rationale: "speed of a boat in still water = 15 km / hr speed of the current = 3 km / hr speed downstream = ( 15 + 3 ) = 18 km / hr distance travelled downstream in 24 minutes = ( 24 / 60 ) × 18 = ( 2 × 18 ) / 5 = 7.2 km answer is b"
Answer: b
Question (general): a man is 20 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 11 , b ) 25 , c ) 27 , d ) 18 , e ) 91
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 20 ) years . ( x + 20 ) + 2 = 2 ( x + 2 ) x + 22 = 2 x + 4 = > x = 18 . answer : d"
Answer: d
Question (geometry): a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 193 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 8,208 , b ) 9,409 , c ) 11,424 , d ) 12,586 , e ) can not be determined
Rationale: "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 193 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 193 ( x + y ) ( x - y ) = 193 193 is a prime number and thus it will be ( 97 + 96 ) * ( 97 - 96 ) . thus x = 97 and y = 96 x ^ 2 = 97 ^ 2 = 9409 the answer is b ."
Answer: b
Question (gain): a shopkeeper sold an article for rs 2564.36 . approximately what was his profit percent if the cost price of the article was rs 2400
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: "explanation : gain % = ( 164.36 * 100 / 2400 ) = 6.84 % = 7 % approx option d"
Answer: d
Question (geometry): if d is the smallest positive integer such that 3150 multiplied by d is the square of an integer , then d must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let ’ s start by prime factorizing 3150 . 3150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3150 itself is not a perfect square . ) we also are given that 3150 multiplied by d is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x d = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , d = 7 x 2 = 14 answer is e .
Answer: e
Question (other): at garage sale , all of the prices of the items sold were different . if the price of a radio sold at the garage sale was both the 9 th highest price and the 35 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 43 , b ) 28 , c ) 44 , d ) 49 , e ) 46
Rationale: 8 + 34 + 1 = 43 answer : a
Answer: a
Question (physics): excluding the stoppages , the speed of a bus is 12 km / hr and including the stoppages the speed of the bus is 6 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 30 min , c ) 12 min , d ) 20 min , e ) 18 min
Rationale: "speed of the bus without stoppage = 12 km / hr speed of the bus with stoppage = 6 km / hr difference in speed = 6 km / hr so , the time taken in the stoppages = time taken to cover 6 km = ( 6 / 12 ) hr = 1 / 2 hr = 30 min answer : b"
Answer: b
Question (physics): the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 14 kmph ?
Options: a ) 53.03 , b ) 50.01 , c ) 23.23 , d ) 24.23 , e ) 41.23
Rationale: "distance covered in 1 min = ( 14 * 1000 ) / 60 = 233.33 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 233.33 / 4.4 = 53.03 answer : a"
Answer: a
Question (gain): in a park there are two ponds with both brown ducks and green ducks . in the smaller pond there are 45 ducks and in the larger pond there are 55 ducks . if 20 % of the ducks in the smaller pond are green and 40 % of the ducks in the larger pond are green , then what percentage of ducks are green ?
Options: a ) 25 % , b ) 27 % , c ) 29 % , d ) 31 % , e ) 33 %
Rationale: "number of ducks in small pond = 45 green ducks in small pond = 20 % of 45 = 9 ducks number of ducks in large pond = 55 green ducks in large pond = 40 % of 55 = 22 ducks total number of ducks = 45 + 55 = 100 total number of green ducks = 9 + 22 = 31 ducks percentage of green ducks = 31 / 100 * 100 = 31 % answer : d"
Answer: d
Question (general): rice weighing 35 / 2 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: 35 / 2 ÷ 4 = 35 / 8 pounds in each container 35 / 8 pounds * 16 ounces / pound = 70 ounces in each container the answer is d .
Answer: d
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 12 and 48 ?
Options: a ) 20 , b ) 60 , c ) 40 , d ) 56 , e ) 20
Rationale: "prime factorization of 12 = 2 x 2 x 3 prime factorization of 48 = 2 x 2 x 2 x 2 x 3 gcf = 12 lcm = 48 sum = 60 ans : b"
Answer: b
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 $ 10 . 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 ) $ 3000 , b ) $ 1,350 , c ) $ 1,725 , 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 10 $ then total value is 300 * 10 = 3000 . imo option a is correct answer . ."
Answer: a
Question (general): ashok secured average of 74 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 66 , b ) 74 , c ) 78 , d ) 80 , e ) none of these
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 74 therefore total marks in 6 subjects = 74 * 6 = 444 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 444 – 370 = 74 answer b"
Answer: b
Question (geometry): susan made a block with small cubes of 5 cubic cm volume to make a block 7 small cubes long , 7 small cubes wide and 6 small cubes deep . she realise that she has used more small cubes than she really needed . she realised that she could have glued a fewer number of cubes together ot look like a block with same dimensions , if it were made
Options: a ) 194
b ) 195
c ) 196
d ) 197
e ) 198
Rationale: volume of cube of dimensions 7 7 6 is 7 * 7 * 6 = 294 if it were to look hollow the imaginary inside cube volume is to be deducted which is ( 7 - 2 ) * ( 7 - 2 ) * ( 6 - 2 ) = 100 ( here 2 is deducted because the inside cube which has to be hollow is 2 cubes more on every dimension ) so minimum number of cubes required to make hollow cube is 294 - 100 = 194 cubes answer : a
Answer: a
Question (physics): in a dairy farm , 55 cows eat 55 bags of husk in 55 days . in how many days one cow will eat one bag of husk ?
Options: a ) 34 days , b ) 40 days , c ) 46 days , d ) 50 days , e ) 55 days
Rationale: "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 55 bags 55 1 ] : : 55 : x = > x ∗ 55 ∗ 1 = 55 ∗ 1 ∗ 55 = > x = 55 option e"
Answer: e
Question (gain): today joelle opened an interest - bearing savings account and deposited $ 10,000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
Options: a ) $ 12025 , b ) $ 11075 , c ) $ 11025 , d ) $ 11095 , e ) $ 11015
Rationale: "interest for 1 st year = 10000 * 5 / 100 = 500 interest for 2 nd year = 10500 * 5 / 100 = 525 total = 10000 + 500 + 525 = 11025 answer : c"
Answer: c
Question (other): what is the prime factors ’ number of 18 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "prime factors ’ number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 1 * 3 ^ 2 prime factors ’ number will be 1 + 2 = 3 . hence , answer is b ."
Answer: b
Question (gain): a sum of money at simple interest amounts to $ 645 in 3 years and to $ 690 in 4 years . the sum is :
Options: a ) $ 153 , b ) $ 510 , c ) $ 598 , d ) $ 549 , e ) $ 675
Rationale: "b $ 510 s . i . for 1 year = $ ( 690 - 645 ) = $ 45 . s . i . for 3 years = $ ( 45 x 3 ) = $ 135 . principal = $ ( 645 - 135 ) = $ 510 ."
Answer: b
Question (gain): john and david can finish a job together in 4 hours . if john can do the job by himself in 5 hours , what percent of the job does david do ?
Options: a ) 20 % , b ) 25 % , c ) 24 % , d ) 23 % , e ) 22 %
Rationale: "you can also plug in numbers . for example , bob and alice work at a donut factory and make 20 donuts which is the job ( i picked this as a smart number ) . john on his own works 20 / 5 = 4 donuts per hour . john and david work 20 / 4 = 5 donuts per hour so david works 1 donuts / hour to find out the percentage , david works 1 donuts / hr x 4 hours = 4 donuts per hour . therefore 4 donuts / 20 donuts = 1 / 5 = 20 % answer : a"
Answer: a