Cheukting/mathqa huggingface dataset:
Question (physics): calculate the l . c . m of 7 / 10 , 8 / 9 , 3 / 8 , 5 / 12 is :
Options: a ) 840 , b ) 70 , c ) 740 , d ) 140 , e ) 940
Rationale: required l . c . m = l . c . m . of 7 , 8 , 3 , 5 / h . c . f . of 10 , 9 , 8 , 12 = 840 / 1 = 840 answer is a
Answer: a
Question (geometry): a circular mat with diameter 18 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ?
Options: a ) 5 / 12
b ) 3 / 5
c ) 1 / 2
d ) 3 / 8
e ) 5 / 6
Rationale: so we are looking for the area of the cloth over the area of the table area of the cloth = ( pi ) ( r ) ^ 2 which is about ( 3 ) ( 9 ) ( 9 ) area of the table = ( 24 ) ( 24 ) so the quick way to estimate is looking at the fraction like this : ( 3 / 24 ) ( 81 / 24 ) i hope this is easy to follow , so with some simplification i get ( 1 / 8 ) ( 3 ) = ( 3 / 8 ) answer is d
Answer: d
Question (physics): a man swims downstream 36 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 2 , e ) 4
Rationale: "36 - - - 3 ds = 12 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 12 + 6 ) / 2 = 9 answer : c"
Answer: c
Question (general): the cash realised on selling a 14 % stock is rs . 109.25 , brokerage being 1 / 4 % is ?
Options: a ) 366 , b ) 106 , c ) 102 , d ) 109 , e ) 122
Rationale: "cash realised = rs . ( 109.25 - 0.25 ) = rs . 109 . answer : d"
Answer: d
Question (gain): the price of maruti car rises by 30 percent while the sales of the car come down by 20 % . what is the percentage change in the total revenue ?
Options: a ) - 4 % , b ) - 2 % , c ) + 4 % , d ) + 2 % , e ) none of these
Rationale: solution : let initial price of maruti car be rs . 100 . as price increases 30 % , price of car will become , ( 100 + 30 % of 100 ) = rs . 130 . due to increase in price , sales is down by 20 % . it means , it is going make 20 % less revenue as expected after increment of price . so , new revenue = ( 130 - 20 % of 130 ) = rs . 104 . the initial revenue was rs . 100 which becomes rs . 104 at the end . it means there is 4 % increment in the total revenue . mind calculation method : 100 = = 30 % ↑ ( price effect ) = = > 130 = = 20 % ↓ ( sales effects ) = = > 104 . hence , 4 % rises . answer : option c
Answer: c
Question (general): if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 21 ( q + 1 ) , what is the least possible value of p + q ?
Options: a ) 36 , b ) 42 , c ) 44 , d ) 46 , e ) none
Rationale: "17 ( p + 1 ) = 21 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 21 / 17 - - > the least positive value of p + 1 is 21 , so the least value of p is 20 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 20 + 16 = 36 . answer : a ."
Answer: a
Question (general): the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 60 percent of b , what is the value of m / x ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 4 , d ) 3 / 2 , e ) 2 / 3
Rationale: "a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 5 / 4 ) * 4 = 2 / 5 the answer is b ."
Answer: b
Question (other): two numbers are in the ratio 3 : 4 . if their l . c . m . is 84 . what is sum of the numbers ?
Options: a ) 49 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 84 = > 12 x = 84 = > x = 84 / 12 = 7 sum of the numbers = 3 x + 4 x = 7 x = 7 x 7 = 49 answer : option a"
Answer: a
Question (geometry): three rugs have a combined area of 212 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?
Options: a ) 18 square meters , b ) 20 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters
Rationale: "total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 212 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 24 . answer : c ."
Answer: c
Question (general): when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction q of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?
Options: a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14
Rationale: "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus q = 11 / 14 of the remaining votes must be against . answer : a ."
Answer: a
Question (general): for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 20000 , my total savings for the two - year is
Options: a ) s . 8000 , b ) s . 9000 , c ) s . 9900 , d ) s . 9990 , e ) s . 11000
Rationale: "sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 20000 + 35000 ) = 66000 - 55000 = rs . 11000 e"
Answer: e
Question (physics): tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 12 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 156 , b ) 146 , c ) 158 , d ) 187 , e ) 160
Rationale: "a 156 sum = ( n x n ) + n hence , 12 x 12 = 144 + 12 = 156"
Answer: a
Question (gain): during a certain season , a team won 70 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 180 , b ) 170 , c ) 156 , d ) 150 , e ) 100
Rationale: "we are first given that a team won 70 percent of its first 100 games . this means the team won 0.7 x 100 = 70 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 70 + 0.5 t – 50 = 0.7 t 20 = 0.2 t 200 = 2 t 100 = t answer is e ."
Answer: e
Question (general): a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is six times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 54 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 18 : 2 = > for 18 soap , salt = 2 = > for 2 soap , salt = ( 2 / 18 ) * 2 = 2 / 9 so , water : soap : salt = 3 : 2 : 2 / 9 = 54 : 36 : 4 after open container , water : soap : salt = 27 : 36 : 4 so , water : salt = 27 : 4 = 54 : 8 e"
Answer: e
Question (general): if x 2 + kx - 3 , is divisible by ( x - 1 ) , what is the value of k
Options: a ) - 1 , b ) 1 , c ) 2 , d ) - 1 , e ) 0
Rationale: explanation : if x 2 + kx - 3 is divisible by ( x - 1 ) then x = 1 ( 1 ) 2 + 1 ( k ) - 3 = 0 1 + k - 3 = 0 k = 2 answer : option c
Answer: c
Question (general): if ( x - 10 ) ( y - 5 ) ( z - 2 ) = 1000 then what is the least value of x + y + z ? if x , y , z are all integer no .
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: ( x - 10 ) ( y - 5 ) ( z - 2 ) = 1000 put x = 0 y = - 5 z = 12 then ( 0 - 10 ) ( - 5 - 5 ) ( 12 - 2 ) = 1000 ( - 10 ) ( - 10 ) ( 10 ) = 1000 1000 = 1000 answer : a
Answer: a
Question (general): 0.002 x 0.4 = ?
Options: a ) 8.0 , b ) 0.008 , c ) 0.08 , d ) 0.8 , e ) 0.0008
Rationale: "2 x 4 = 8 . sum of decimal places = 4 0.002 x 0.4 = 0.0008 answer : option e"
Answer: e
Question (general): for what value of x , is | x – 2 | + | x + 5 | + | x | = 17 ?
Options: a ) 0 , b ) 3 , c ) - 3 , d ) 5 , e ) - 5
Rationale: "for what value of x , is | x – 2 | + | x + 5 | + | x | = 17 ? it ' s easiest just to plug in answer choices : ( d ) : 5 | x – 2 | + | x + 5 | + | x | = 17 ? | 5 - 3 | + | 5 + 5 | + | 5 | = 17 ? | 2 | + | 10 | + | 5 | = 17 ( d )"
Answer: d
Question (physics): a can run 4 times as fast as b and gives b a start of 60 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 75 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 60 m he gains 60 * ( 4 / 3 ) i . e 80 m answer : c"
Answer: c
Question (physics): a train 175 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 22 sec , b ) 16 sec , c ) 17 sec , d ) 88 sec , e ) 10 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 175 * 2 / 35 = 10 sec answer : e"
Answer: e
Question (gain): an 80 - liter solution of cool - drink is made from 10 % jasmine water . if 8 liters of jasmine and 12 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 12 % , b ) 14 % , c ) 16 % , d ) 18 % , e ) 20 %
Rationale: "the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.1 ( 80 ) + 8 ) / 100 = 16 / 100 = 16 % the answer is c ."
Answer: c
Question (general): what is the sum of all the multiples of 10 between 0 and 99 ?
Options: a ) 500 , b ) 620 , c ) 450 , d ) 340 , e ) 440
Rationale: "the multiples of 10 between 0 and 99 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , and 90 . if these are all added together , the result is 450 . final answer : c"
Answer: c
Question (geometry): the length of rectangle is thrice its breadth and its perimeter is 120 m , find the area of the rectangle ?
Options: a ) 432 sq m , b ) 356 sq m , c ) 452 sq m , d ) 428 sq m , e ) 675 sq m
Rationale: "2 ( 3 x + x ) = 120 l = 45 b = 15 lb = 45 * 15 = 675 answer : e"
Answer: e
Question (gain): an article is bought for rs . 805 and sold for rs . 900 , find the gain percent ?
Options: a ) 12.8 % , b ) 17.8 % , c ) 15.8 % , d ) 11.8 % , e ) 14.8 %
Rationale: "805 - - - - 95 100 - - - - ? = > 11.8 % answer : d"
Answer: d
Question (general): at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 164.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 21 , b ) $ 27 , c ) $ 31 , d ) $ 41 , e ) it can not be determined
Rationale: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 44.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 31 . in any case , there is no necessity to know each item ' s price , just the sum . answer : c"
Answer: c
Question (general): 65 % of x = 20 % of 682.50 . find the value of x ?
Options: a ) 100 , b ) 210 , c ) 150 , d ) 180 , e ) 199
Rationale: "65 % of x = 20 % of 682.50 then , 65 / 100 * x = 20 / 100 * 6825 / 10 x = 210 answer is b"
Answer: b
Question (general): a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 200 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "given that p is smallest integer greater than 200 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 answer : e"
Answer: e
Question (physics): a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 120 kilometers ?
Options: a ) 4.5 , b ) 5.5 , c ) 6.5 , d ) 3 , e ) 8.5
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 120 kilometers ? 120 ÷ 40 = 3 × 1 gallon = 3 gallons correct answer d"
Answer: d
Question (general): a ranch has both horses and ponies . exactly 5 / 7 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
Options: a ) 34 , b ) 38 , c ) 42 , d ) 46 , e ) 50
Rationale: "5 / 7 * p are ponies with horseshoes , so p is a multiple of 7 . 2 / 3 * 5 / 7 * p = 10 / 21 * p are icelandic ponies with horseshoes , so p is a multiple of 21 . the minimum value of p is 21 . then h = p + 4 = 25 . the minimum number of horses and ponies is 46 . the answer is d ."
Answer: d
Question (gain): a fruit seller had some oranges . he sells 40 % oranges and still has 420 oranges . how many oranges he had originally ?
Options: a ) 420 , b ) 700 , c ) 220 , d ) 400 , e ) none of these
Rationale: "explanation : he sells 40 % of oranges and still there are 420 oranges remaining = > 60 % of oranges = 420 ⇒ ( 60 × total oranges ) / 100 = 420 ⇒ total oranges / 100 = 7 ⇒ total oranges = 7 × 100 = 700 answer : option b"
Answer: b
Question (general): if x ^ 2 + y ^ 2 = 16 and xy = 3 , then ( x − y ) ^ 2 =
Options: a ) 8 , b ) 11 , c ) 10 , d ) 17 , e ) 20
Rationale: "but you can not take xy + 3 to mean xy = - 3 . . only if xy + 3 = 0 , it will mean xy = - 3 . . rest your solution is perfect and you will get your correct answer as 16 - 2 * 3 = 10 . . answer c"
Answer: c
Question (physics): on the first day of her vacation , louisa traveled 160 miles . on the second day , traveling at the same average speed , she traveled 280 miles . if the 160 - mile trip took 3 hours less than the 280 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 40 , b ) 45 , c ) 46 , d ) 48 , e ) 50
Rationale: ( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 160 / t = 280 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 160 / 4 = 40 answer : a
Answer: a
Question (general): evaluate : | 5 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 71 , e ) 80
Rationale: "according to order of operations , inner brackets first . hence | 5 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 5 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 5 + 72 | - | 5 - 11 | = | 77 | - | - 6 | = 77 - 6 = 71 correct answer d ) 71"
Answer: d
Question (gain): a 10 % stock yielding 8 % is quoted at ?
Options: a ) 125 , b ) 170 , c ) 175 , d ) 180 , e ) 185
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 10 , money invested = 100 × 10 / 8 = rs . 125 ie , market value of the stock = rs . 125 answer is a ."
Answer: a
Question (general): what is the sum of natural numbers between 30 and 100
Options: a ) 4615 , b ) 4860 , c ) 5000 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 30 and 100 numbers = 71 = > 100 - 30 = 70 + 1 = 71 sn = 71 / 2 ã — 130 = 71 ã — 65 = 4615 answer : a"
Answer: a
Question (general): what is the least value of x . so that 4 x 569 is divisible by 3 ?
Options: a ) 2 , b ) 5 , c ) 1 , d ) 0 , e ) 7
Rationale: "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 4 + x + 5 + 6 + 9 = 24 + x least value of x may be 0 therefore 24 + 0 = 24 is divisible by 3 . d"
Answer: d
Question (gain): if a trader sold two cars each at rs . 325475 and gains 12 % on the first and loses 12 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.44 % , b ) 1.43 % , c ) 1.34 % , d ) 4.44 % , e ) 1.74 %
Rationale: sp of each car is rs . 325475 , he gains 12 % on first car and losses 12 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 12 ) ( 12 ) / 100 % = 1.44 % answer : a
Answer: a
Question (physics): i flew my tiny seaplane to visit my mother . on the flight up , i flew at 96 mph . on the way home , i flew 88 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 110 mph , c ) 92 mph , d ) 100 mph , e ) 99 mph
Rationale: "( 96 mph + 88 mph ) / 2 = 92 mph correct answer is : c"
Answer: c
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 20 cm ?
Options: a ) 827 cm 2 , b ) 380 cm 2 , c ) 285 cm 2 , d ) 178 cm 2 , e ) 176 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 20 ) = 380 cm 2 answer : b"
Answer: b
Question (general): if x < y < z and y - x > 11 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 15
Rationale: "we have : 1 ) x < y < z 2 ) y - x > 11 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 11 , the least value for y - x must be 13 , the least value for x must be 2 , and , thus , the least possible value for y must be 15 ( y - 2 = 13 , y = 15 ) 2 < 15 < z , since z is odd , the least possible value for z is 17 z - x = 17 - 2 = 15 answer e"
Answer: e
Question (general): find k if 24 / k = 4 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3
Rationale: "since 24 / k = 4 and 24 / 6 = 4 , then k = 6 correct answer a"
Answer: a
Question (general): a merchandise feedback online portal accords ‘ ratings ’ to a product by recording the percentage of customers who have reported their views as either ‘ satisfied ’ or ‘ unsatisfied ’ only . the portal rounds off the exact percentage value calculated to the closest integral value . if the percentage of unsatisfied customers as recorded by the portal is 57 % , what is the least possible number of people that could have reported their views as ‘ satisfied ’ ?
Options: a ) 2 , b ) 3 , c ) 12 , d ) 43 , e ) 57
Rationale: 57 % unsatisfied . so ~ 43 % satisfied but 100 % should be an integer only and since the above percentages are approximations 100 % should be as close as possible to an integer . now substitute value [ 1 ] if 43 % is 2 what is 100 % - > 200 / 43 is not giving a number which is closest to an integer . [ 2 ] if 43 % is 3 what is 100 % - > 300 / 43 [ 43 * 7 = 301 ] . . . therefore closest possible to an integer . [ it also satisfies the least possible and hence we need not check for other choices which are greater than 3 ] therefore ans is b .
Answer: b
Question (probability): a bag consists of 30 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 5 / 6 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "bag consists of 20 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 30 - 5 - 9 = 16 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 30 + 16 / 30 = 25 / 30 = 5 / 6 hence , answer will be a ."
Answer: a
Question (geometry): the sides of a cube are in the ratio of 1 : 2 the ratio of their volumes is ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 8 , d ) 2 : 1 , e ) 2 : 4
Rationale: 1 : 8 answer : c
Answer: c
Question (general): what is the least value of x , so that 23 x 57 is divisible by 3
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : 23257 is not divisible by 3 23057 is not divisible by 3 23157 is divisible by 3 23357 is not divisible by 3 2 + 3 + 1 + 5 + 7 = 18 18 / 3 = 6 . x = 1 answer : option c"
Answer: c
Question (gain): a present value of a machine is $ 1000 . its value depletiation rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 900 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 795
Rationale: "p = $ 1000 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 1000 * 9 / 10 * 9 / 10 = $ 810 answer is b"
Answer: b
Question (general): in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 48 . what is the total number of students in the school ?
Options: a ) 72 , b ) 80 , c ) 120 , d ) 100 , e ) 150
Rationale: "let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 48 + 2 / 3 of 48 ( 80 / 100 ) x = 80 x = 100 . answer d"
Answer: d
Question (gain): to produce an annual income of rs . 1200 from a 15 % stock at 90 , the amount of stock needed is :
Options: a ) s . 10,000 , b ) s . 10,800 , c ) s . 14,400 , d ) s . 16,000 , e ) s . 46,000
Rationale: "solution for an income of rs . 15 , stock needed = rs . 100 . for an income of rs . 1500 , stock needed = rs . 10 / 12 x 15000 = 10,000 answer a"
Answer: a
Question (gain): a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 756 find the share of a .
Options: a ) 240 , b ) 388 , c ) 288 , d ) 277 , e ) 122
Rationale: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 756 = 288 answer : c"
Answer: c
Question (general): what is 2 2 / 3 - 1 1 / 4 divided by 1 / 2 - 1 / 3 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 17 / 2 , e ) 51 / 4
Rationale: "2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 3 - 1 / 6 = ( 2 - 1 ) / 6 = 1 / 6 so 17 / 12 / 1 / 6 = 17 / 12 * 6 = 17 / 2 answer - d"
Answer: d