Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
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the salary of a worker is first increased by 25 % and afterwards reduced by 25 % . what is the net change in the worker ' s salary ? | "let x be the original salary . the final salary is 0.75 ( 1.25 x ) = 0.9375 x the answer is d ." | a ) 3.25 % increase , b ) 3.25 % decrease , c ) 6.25 % increase , d ) 6.25 % decrease , e ) no change | d | subtract(const_100, subtract(add(25, const_100), divide(multiply(add(25, const_100), 25), const_100))) | add(n0,const_100)|multiply(n0,#0)|divide(#1,const_100)|subtract(#0,#2)|subtract(const_100,#3)| | gain |
a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 13 brown mice in the experiment , how many mice in total are in the experiment ? | "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 13 = > m = 39 answer a" | a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 10 | a | subtract(divide(13, divide(2, 3)), 13) | divide(n0,n1)|divide(n2,#0)|subtract(#1,n2)| | general |
perimeter of front wheel = 30 , back wheel = 20 . if front wheel revolves 240 times . how many revolutions will the back wheel take ? | sice the distance covered by both the wheels should be same so let x be the no . of revolutions by the back wheel so 240 * 2 * pie * 30 = x * 2 * pie * 20 so x = 360 . answer : d | a ) 120 , b ) 180 , c ) 240 , d ) 360 , e ) 480 | d | divide(multiply(30, 240), 20) | multiply(n0,n2)|divide(#0,n1) | general |
15 litres of mixture contains 25 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ? | alcohol in the 15 litres of mix . = 25 % of 15 litres = ( 25 * 15 / 100 ) = 3.75 litres water in it = 15 - 3.75 = 11.25 litres new quantity of mix . = 15 + 3 = 18 litres quantity of alcohol in it = 3.75 litres percentage of alcohol in new mix . = 3.75 * 100 / 18 = 20.83 % answer is a | a ) 20.83 % , b ) 23 % , c ) 18.3 % , d ) 19.75 % , e ) 21.23 % | a | multiply(divide(subtract(add(15, 3), add(multiply(divide(subtract(const_100, 25), const_100), 15), 3)), add(15, 3)), const_100) | add(n0,n2)|subtract(const_100,n1)|divide(#1,const_100)|multiply(n0,#2)|add(n2,#3)|subtract(#0,#4)|divide(#5,#0)|multiply(#6,const_100) | gain |
rs . 800 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 800 become in 3 years ? | "solution s . i . = rs . ( 956 - 800 ) = rs . 156 rate = ( 100 x 156 / 800 x 3 ) = 6 1 / 2 % new rate = ( 6 1 / 2 + 4 ) % = 10 1 / 2 % new s . i . = rs . ( 800 x 21 / 2 x 3 / 100 ) rs . 252 . ∴ new amount = rs . ( 800 + 252 ) = rs . 1052 . answer c" | a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1052 , d ) data inadequate , e ) none of these | c | add(800, divide(multiply(multiply(800, add(divide(multiply(subtract(956, 800), const_100), multiply(800, 3)), 4)), 3), const_100)) | multiply(n0,n2)|subtract(n1,n0)|multiply(#1,const_100)|divide(#2,#0)|add(n3,#3)|multiply(n0,#4)|multiply(n2,#5)|divide(#6,const_100)|add(n0,#7)| | gain |
a certain college ' s enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollme... | "suppose enrollment in 1991 was 100 then enrollment in 1992 will be 120 and enrollment in 1993 will be 120 * 1.15 = 138 increase in 1993 from 1991 = 138 - 100 = 38 answer : e" | a ) 17.5 % , b ) 24 % , c ) 30 % , d ) 35 % , e ) 38 % | e | subtract(multiply(add(const_100, 20), divide(add(const_100, 15), const_100)), const_100) | add(n1,const_100)|add(n4,const_100)|divide(#1,const_100)|multiply(#0,#2)|subtract(#3,const_100)| | gain |
sonika deposited rs . 6200 which amounted to rs . 7200 after 5 years at simple interest . had the interest been 3 % more . she would get how much ? | "( 6200 * 5 * 3 ) / 100 = 930 7200 - - - - - - - - 8130 answer : b" | a ) 9680 , b ) 8130 , c ) 8134 , d ) 8556 , e ) 9808 | b | add(multiply(multiply(add(divide(3, const_100), divide(divide(subtract(7200, 6200), 5), 6200)), 6200), 5), 6200) | divide(n3,const_100)|subtract(n1,n0)|divide(#1,n2)|divide(#2,n0)|add(#0,#3)|multiply(n0,#4)|multiply(n2,#5)|add(n0,#6)| | gain |
a bag of potatoes weighs 50 lbs divided by half of its weight . how much does the bag of potatoes weight ? | "sol . 50 ÷ 5 = 10 . answer : c" | a ) 20 lb , b ) 30 lb , c ) 10 lb , d ) 15 lb , e ) 5 lb | c | divide(50, const_1) | divide(n0,const_1)| | general |
if x is a positive integer , then the least value of x for which x ! is divisible by 100,000 is ? can someone please explain intuitively what the question is asking ? | in order x ! to be divisible by 1,000 , it should have at least 3 trailing zeros . a trailing 0 in factorial of a number is produced by 2 and 5 in it : 2 * 5 = 10 . so , we need 10 to be in x ! at least in power of 3 . 5 ! = 120 has 1 trailing zeros . 10 ! will have 2 trailing zeros . 15 ! will have 3 trailing zeros . ... | a ) 5 , b ) 9 , c ) 12 , d ) 20 , e ) 30 | d | multiply(divide(const_10, const_2), const_4) | divide(const_10,const_2)|multiply(#0,const_4) | general |
there is enough provisions for 600 men in an army camp for 25 days . if there were 200 men less , how long will the provision last ? | exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 200 * d 2 d 2 = 600 * 25 / 200 = 75 days . answer : d | a ) 50 days , b ) 60 days , c ) 70 days , d ) 75 days , e ) 90 days | d | divide(multiply(600, 25), 200) | multiply(n0,n1)|divide(#0,n2) | physics |
a person spent rs . 8,550 from his salary on food and 8,640 on house rent . after that he was left with 40 % of his monthly salary . what is his monthly salary ? | "total money spent on food and house rent = 8,550 + 8,640 = 17,190 which is 100 - 40 = 60 % of his monthly salary ∴ his salary = 17190 x 100 / 60 = 28650 answer : b" | a ) 38,650 , b ) 28,650 , c ) 48,650 , d ) 68,650 , e ) 18,650 | b | divide(add(multiply(add(const_4, const_1), const_100), 40), sqrt(const_100)) | add(const_1,const_4)|sqrt(const_100)|multiply(#0,const_100)|add(n2,#2)|divide(#3,#1)| | gain |
when x is multiplied by 3 , the result is 26 more than the result of subtracting x from 62 . what is the value of x ? | "the equation that can be formed is : 3 x - 26 = 62 - x or , 4 x = 88 or , x = 22 . answer : e" | a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22 | e | divide(add(62, 26), add(3, const_1)) | add(n1,n2)|add(const_1,n0)|divide(#0,#1)| | general |
find the principle on a certain sum of money at 6 % per annum for 2 2 / 5 years if the amount being rs . 1120 ? | "1120 = p [ 1 + ( 6 * 12 / 5 ) / 100 ] p = 979 answer : a" | a ) 979 , b ) 1288 , c ) 2778 , d ) 2682 , e ) 1021 | a | divide(1120, add(divide(multiply(divide(add(multiply(2, 5), 2), 5), 6), const_100), const_1)) | multiply(n1,n3)|add(n1,#0)|divide(#1,n3)|multiply(n0,#2)|divide(#3,const_100)|add(#4,const_1)|divide(n4,#5)| | general |
my watch gains 5 min every hour . how many degrees the second hand moves in every min ? | gain 5 min every 1 hr degrees moves = = > 390 answer c | a ) 300 , b ) 350 , c ) 390 , d ) 400 , e ) 450 | c | divide(multiply(divide(const_3600, const_10), add(5, const_60)), const_60) | add(n0,const_60)|divide(const_3600,const_10)|multiply(#0,#1)|divide(#2,const_60) | physics |
if 5 cats can kill 5 rats in 5 minutes , how long will it take 100 cats to kill 100 rats ? | "it will take 5 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 5 minutes , so 100 cats can kill 100 rats in 5 minutes answer e" | a ) 1 minutes , b ) 2 minutes , c ) 3 minutes , d ) 4 minutes , e ) 5 minutes | e | multiply(5, const_1) | multiply(n0,const_1)| | physics |
4.2 x 4.2 - 1.9 x 1.9 / 2.3 x 6.1 is equal to : | "given expression = ( a 2 - b 2 ) / ( a + b ) ( a - b ) = ( a 2 - b 2 ) / ( a 2 - b 2 ) = 1 . answer is b ." | a ) 2 , b ) 1 , c ) 3 , d ) 4 , e ) 8 | b | divide(subtract(multiply(4.2, 4.2), multiply(1.9, 1.9)), 2.3) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n4)| | general |
a collection of books went on sale , and 2 / 3 of them were sold for $ 4 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ? | "since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 4 ) or $ 288 . the best answer is therefore a . answ... | a ) $ 288 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54 | a | multiply(const_2.0, divide(multiply(36, divide(2, 3)), divide(const_1, 3))) | divide(n2,n1)|divide(const_1,n1)|multiply(n3,#0)|divide(#2,#1)|multiply(n0,#3)| | general |
calculate the number of bricks , each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 m x 5 m when 10 % of its volume is occupied by concrete ? | "explanation : let ' b ' be the nuber of bricks . = > 10 x 4 / 100 x 5 x 90 / 100 = 25 / 100 x 15 / 100 x 8 / 100 x b = > 10 x 20 x 90 = 15 x 2 x b = > b = 6000 answer is a" | a ) 6000 , b ) 5400 , c ) 3800 , d ) 4700 , e ) 2500 | a | divide(multiply(multiply(multiply(10, divide(4, const_100)), 5), subtract(const_1, divide(10, const_100))), multiply(multiply(divide(25, const_100), divide(15, const_100)), divide(8, const_100))) | divide(n4,const_100)|divide(n3,const_100)|divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|multiply(n3,#0)|multiply(#3,#4)|subtract(const_1,#1)|multiply(n5,#5)|multiply(#2,#6)|multiply(#8,#7)|divide(#10,#9)| | physics |
in how many ways 5 boys and 5 girls can be seated in a row so that boys and girls are alternate ? | "number of ways = 2 * 5 ! * 5 ! = 28800 answer is e" | a ) 28400 , b ) 28500 , c ) 28600 , d ) 28700 , e ) 28800 | e | multiply(factorial(5), factorial(5)) | factorial(n0)|factorial(n1)|multiply(#0,#1)| | probability |
the average monthly salary of laborers and supervisors in a factory is rs . 1250 per month ; where as the average monthly salary of 6 supervisors is rs . 2450 . if the average monthly salary of the laborers is rs . 850 find the number of laborers ? | "2450 850 \ / 1250 / \ 400 1200 1 : 3 1 - - > 6 3 - - > ? 18 answer : e" | a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | e | subtract(subtract(multiply(divide(subtract(multiply(2450, 6), multiply(1250, 6)), subtract(1250, 850)), const_2), const_4), const_2) | multiply(n1,n2)|multiply(n0,n1)|subtract(n0,n3)|subtract(#0,#1)|divide(#3,#2)|multiply(#4,const_2)|subtract(#5,const_4)|subtract(#6,const_2)| | general |
in a digital circuit which was to implement ( a b ) + ( a ) xor ( b ) , the designer implements ( a b ) ( a ) xor ( b ) what is the probability of error in it ? | a b ab a xor b ( ab ) + ( a xor b ) ( ab ) ( a xor b ) 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 so , we are getting 3 wrong answers out of 4 probability of error is 3 / 4 = 75 % answer : c | a ) 25 % , b ) 35 % , c ) 75 % , d ) 45 % , e ) 55 % | c | multiply(divide(const_3, const_4), const_100) | divide(const_3,const_4)|multiply(#0,const_100) | general |
if 4 men can colour 48 m long cloth in 2 days , then 5 men can colour 36 m long cloth in | the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 5 = 1.2 day . a | a ) 1.2 day , b ) 2.0 days , c ) 3 days , d ) 4.2 days , e ) 5 days | a | divide(36, multiply(divide(48, multiply(4, 2)), 5)) | multiply(n0,n2)|divide(n1,#0)|multiply(n3,#1)|divide(n4,#2) | physics |
a man gains 10 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be . | "explanation : let the c . p . = x , then s . p . = ( 110 / 100 ) x = 11 x / 10 new s . p . = 2 ( 11 x / 10 ) = 22 x / 10 profit = 22 x / 10 - x = 12 x / 10 profit % = ( profit / c . p . ) * 100 = > ( 12 x / 10 ) * ( 1 / x ) * 100 = 120 % option b" | a ) 130 % , b ) 120 % , c ) 150 % , d ) 160 % , e ) 170 % | b | add(multiply(subtract(multiply(add(const_1, divide(10, const_100)), const_2), const_1), const_100), const_100) | divide(n0,const_100)|add(#0,const_1)|multiply(#1,const_2)|subtract(#2,const_1)|multiply(#3,const_100)|add(#4,const_100)| | gain |
man 1 does a work in 10 days and man 2 does the same work in 15 days . in how many days they together will do the same work ? | man 1 day work = 1 / 10 man 2 day work = 1 / 15 both work = 1 / 10 + 1 / 15 = = = > 3 + 2 / 30 = = > 1 / 6 answer c | a ) 10 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days | c | divide(const_1, add(divide(const_1, 10), divide(const_1, 15))) | divide(const_1,n1)|divide(const_1,n3)|add(#0,#1)|divide(const_1,#2) | physics |
from a container having pure milk , 20 % is replaced by water and the process is repeated thrice . at the end of the third operation , the milk is | "solution let total quantity of original milk = 100 gm . milk after first operation = 80 % of 1000 ‹ = › 800 gm . milk after second operation = 80 % of 800 ‹ = › 640 gm . milk after third operation = 80 % of 640 ‹ = › 512 gm . strength of final mixtures = 51.2 % . answer c" | a ) 40 % pure , b ) 50 % pure , c ) 51.2 % pure , d ) 58.8 % pure , e ) none | c | multiply(power(divide(subtract(const_100, 20), const_100), const_3), const_100) | subtract(const_100,n0)|divide(#0,const_100)|power(#1,const_3)|multiply(#2,const_100)| | other |
what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 6 ? | "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 6 ? 9 ^ 6 = ( 3 ^ 2 ) ^ 6 = 3 ^ 12 b . 12" | a ) 5 , b ) 12 , c ) 10 , d ) 20 , e ) 30 | b | multiply(subtract(9, 6), 6) | subtract(n1,n2)|multiply(n2,#0)| | general |
1396 x 1396 | "1396 x 1396 = ( 1396 ) 2 = ( 1400 - 2 ) 2 = ( 1400 ) 2 + ( 4 ) 2 - ( 4 x 1400 x 4 ) = 1948816 . answer : option a" | a ) 1948816 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these | a | multiply(divide(1396, 1396), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
a man invested rs . 4940 in rs . 10 shares quoted at rs . 9.50 . if the rate of dividend be 14 % , his annual income is | "market value of a share = rs . 9.50 investment = rs . 4940 number of shares = 4940 / 9.50 = 520 face value of a share = rs . 10 dividend = 14 % dividend per share = ( 10 × 14 ) / 100 = rs . 1.4 his annual income = 520 × 1.4 = rs . 728 answer is e ." | a ) 708 , b ) 718 , c ) 738 , d ) 748 , e ) 728 | e | multiply(divide(14, const_100), multiply(divide(4940, 9.50), 10)) | divide(n3,const_100)|divide(n0,n2)|multiply(n1,#1)|multiply(#0,#2)| | gain |
if 20 gallons of grape juice are added to 40 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ? | "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 × 0.10 = 4 gallons of grape juice . 40 × 0.90 = 36 gallons of other components . if we add 20 gallons of grape juice , we will end up with 24 gallons of grape juice and 36 gallons of other components , and we will... | a ) 14 % , b ) 25 % , c ) 28 % , d ) 34 % , e ) 40 % | e | multiply(divide(add(multiply(divide(10, const_100), 40), 20), add(40, 20)), const_100) | add(n0,n1)|divide(n2,const_100)|multiply(n1,#1)|add(n0,#2)|divide(#3,#0)|multiply(#4,const_100)| | general |
the l . c . m . of two numbers is 30 . the numbers are in the ratio 2 : 3 . then sum of the number is : | "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 30 or x = 5 . the numbers are 10 and 15 . hence , required sum = ( 10 + 15 ) = 25 . answer : option a" | a ) 25 , b ) 32 , c ) 40 , d ) 53 , e ) 54 | a | add(multiply(divide(30, multiply(2, 3)), 3), multiply(divide(30, multiply(2, 3)), 2)) | multiply(n1,n2)|divide(n0,#0)|multiply(n2,#1)|multiply(n1,#1)|add(#2,#3)| | other |
a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 12 more blue balls than white balls , and twice as many red balls as blue balls , how many white balls does the box has ? | x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 12 more blue balls than white balls . . . equation # 2 : y = 12 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 2 y solve equa... | a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16 | e | divide(subtract(100, multiply(12, const_3)), const_4) | multiply(n1,const_3)|subtract(n0,#0)|divide(#1,const_4) | general |
bill and jane play a simple game involving two fair dice , each of which has 6 sides numbered from 1 to 6 ( with an equal chance of landing on any side ) . bill rolls the dice and his score is the total of the two dice . jane then rolls the dice and her score is the total of her two dice . if jane ’ s score is higher t... | there are three possible outcomes in the game : 1 . b wins 2 . j wins 3 . draw so , 1 = p ( j ) + p ( b ) + p ( draw ) 1 = p ( j ) + p ( b ) + p ( draw ) the probability of b winning or j winning the game is same . so , 1 = 2 ∗ p ( j ) + p ( draw ) 1 = 2 ∗ p ( j ) + p ( draw ) so , we need to calculate the probability ... | a ) 15 / 36 , b ) 175 / 432 , c ) 575 / 1296 , d ) 583 / 1296 , e ) 1 / 2 | c | divide(subtract(1, divide(add(multiply(divide(multiply(multiply(subtract(6, 1), 6), add(multiply(subtract(6, 1), const_2), 1)), 6), const_2), multiply(6, 6)), power(multiply(6, 6), const_2))), const_2) | multiply(n0,n0)|subtract(n0,n1)|multiply(#1,const_2)|multiply(n0,#1)|power(#0,const_2)|add(n1,#2)|multiply(#5,#3)|divide(#6,n0)|multiply(#7,const_2)|add(#8,#0)|divide(#9,#4)|subtract(n1,#10)|divide(#11,const_2) | probability |
the total age of a and b is 11 years more than the total age of b and c . c is how many year younger than a | "explanation : given that a + b = 11 + b + c = > a ? c = 11 + b ? b = 11 = > c is younger than a by 11 years answer : option a" | a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15 | a | multiply(11, const_1) | multiply(n0,const_1)| | general |
if the sides of a triangle are 30 cm , 40 cm and 50 cm , what is its area ? | "the triangle with sides 30 cm , 40 cm and 50 cm is right angled , where the hypotenuse is 50 cm . area of the triangle = 1 / 2 * 40 * 30 = 600 cm 2 answer : option d" | a ) 400 , b ) 500 , c ) 550 , d ) 600 , e ) 700 | d | divide(multiply(40, 50), const_2) | multiply(n1,n2)|divide(#0,const_2)| | geometry |
the area of an equilateral triangle is subtracted from its base , and the perimeter is then added to this total , the result is 4 . what is the height of the equilateral triangle if its base is 2 ? | an eqilateral triangle means all sides are equal ; therefore , base = side . the equation is ; base - area + perimeter = b - a + p = b - 1 / 2 bh + 3 b , and b = 2 . so , 2 - 2 / 2 h + 6 = 4 , and 8 - h = 4 . by plugging in the answers we can test the answers quickly ; then , 4 is the only possible answer . answer : c | ['a ) 2', 'b ) 3', 'c ) 4', 'd ) 5', 'e ) 6'] | c | add(subtract(2, 4), multiply(2, const_3)) | multiply(n1,const_3)|subtract(n1,n0)|add(#0,#1) | geometry |
( 6 ! - 4 ! ) / 5 ! = ? | ( 6 ! - 4 ! ) / 5 ! ( 4 ! * 5 * 6 - 4 ! ) / 5 ! 4 ! ( 5 * 6 - 1 ) / 4 ! * 5 29 / 5 answer a | a ) 29 / 5 , b ) 28 / 3 , c ) 27 / 6 , d ) 25 / 4 , e ) 29 / 6 | a | divide(subtract(factorial(6), factorial(4)), factorial(5)) | factorial(n0)|factorial(n1)|factorial(n2)|subtract(#0,#1)|divide(#3,#2) | general |
a sum of money is sufficient to pay p ' s wages for 24 days and q ' s wages for 40 days . the same money is sufficient to pay the wages of both for ? | let the total money be $ x p ' s 1 day work = $ x / 24 q ' s 1 day work = $ x / 40 p + q 1 day work = $ x / 15 money is sufficient to pay the wages of both for 15 days answer is d | a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16 | d | divide(const_1, add(divide(const_1, 24), divide(const_1, 40))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2) | general |
if i walk at 5 km / h , i miss the bus by 9 minutes . if i walk at 3 km / h , i reach 6 minutes before the arrival of the bus . how far i walk to reach the bus stand ? | "d = product of speed difference of time / difference of speed d = 5 x 3 / 60 [ 9 â ˆ ’ ( â ˆ ’ 6 ) / 5 - 3 ] [ here , â € “ ve sign indicates before the schedule time ] â ‡ ’ d = 1.87 km answer e" | a ) 1.99 km , b ) 1.55 km , c ) 1.82 km , d ) 2.87 km , e ) 1.87 km | e | multiply(divide(multiply(5, 3), subtract(3, 5)), divide(add(9, 6), const_60)) | add(n1,n3)|multiply(n0,n2)|subtract(n2,n0)|divide(#1,#2)|divide(#0,const_60)|multiply(#3,#4)| | physics |
tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 27000 after completion of one year . what will be jose ' s share of profit ? | "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 27000 = 15000 b" | a ) 20000 , b ) 15000 , c ) 25000 , d ) 34000 , e ) 30000 | b | multiply(27000, subtract(const_1, divide(multiply(30000, multiply(2, multiply(2, const_3))), add(multiply(45000, subtract(multiply(2, multiply(2, const_3)), 2)), multiply(30000, multiply(2, multiply(2, const_3))))))) | multiply(n1,const_3)|multiply(#0,n1)|multiply(n0,#1)|subtract(#1,n1)|multiply(n2,#3)|add(#4,#2)|divide(#2,#5)|subtract(const_1,#6)|multiply(n3,#7)| | gain |
how many numbers from 10 to 50 are exactly divisible by 9 ? | "10 / 9 = 1 and 50 / 9 = 5 = = > 5 - 1 = 4 . therefore 4 answer : e" | a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14 | e | add(divide(subtract(multiply(floor(divide(50, 9)), 9), multiply(add(floor(divide(10, 9)), const_1), 9)), 9), const_1) | divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)| | general |
a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 7 years ago ? | "let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e ... | a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 7 | e | subtract(add(6, 8), 7) | add(n1,n2)|subtract(#0,n4)| | general |
in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 84 more candidates got selected than a . what was the number of candidates appeared from each state ? | "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 84 more candidates got selected than state a from these , it is clear that 1 % of the... | a ) 7000 , b ) 8400 , c ) 6000 , d ) 5000 , e ) 4000 | b | divide(84, divide(subtract(7, 6), const_100)) | subtract(n1,n0)|divide(#0,const_100)|divide(n2,#1)| | general |
find the area of a parallelogram with base 34 cm and height 18 cm ? | "area of a parallelogram = base * height = 34 * 18 = 612 cm 2 answer : d" | a ) 198 cm 2 , b ) 384 cm 2 , c ) 510 cm 2 , d ) 612 cm 2 , e ) 680 cm 2 | d | multiply(34, 18) | multiply(n0,n1)| | geometry |
a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey ? | "the total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in ap whose first term is 30 and last term is 48 = 10 / 2 [ 30 + 48 ] = 390 km . answer : b" | a ) 288 , b ) 390 , c ) 287 , d ) 266 , e ) 161 | b | divide(add(add(30, multiply(2, 10)), 30), 2) | multiply(n1,n2)|add(n0,#0)|add(n0,#1)|divide(#2,n1)| | physics |
in a sports club with 35 members , 15 play badminton and 18 play tennis and 5 do not play either . how many members play both badminton and tennis ? | "15 + 18 = 33 but where as total number is 35 - 5 = 30 therefore answer is 33 - 30 = 3 hence answer is a" | a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | a | subtract(add(add(15, 18), 5), 35) | add(n1,n2)|add(n3,#0)|subtract(#1,n0)| | other |
on day one , a store sold 96 pens . on each of the next d days , the company sold 44 pens . if the average daily sales of pens over this time period ( including day one ) is 48 pens , what is the value of d ? | 96 + 44 d = 48 ( d + 1 ) . 4 d = 48 . d = 12 . the answer is d . | a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | d | divide(subtract(96, 48), subtract(48, 44)) | subtract(n0,n2)|subtract(n2,n1)|divide(#0,#1) | general |
walking 7 / 6 of his usual rate , a boy reaches his school 5 min early . find his usual time to reach the school ? | "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 5 - - - - - - - - - ? = 35 m answer : d" | a ) 22 , b ) 28 , c ) 99 , d ) 35 , e ) 66 | d | multiply(5, 7) | multiply(n0,n2)| | gain |
carrie likes to buy t - shirts at the local clothing store . they cost $ 9.15 each . one day , she bought 22 t - shirts . how much money did she spend ? | $ 9.15 * 22 = $ 201.3 . answer is d . | a ) $ 150 , b ) $ 248.75 , c ) $ 200 , d ) $ 201.3 , e ) $ 190 | d | floor(multiply(22, 9.15)) | multiply(n0,n1)|floor(#0)| | general |
there were two candidates in an election . winner candidate received 56 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ? | "w = 56 % l = 44 % 56 % - 44 % = 12 % 12 % - - - - - - - - 288 56 % - - - - - - - - ? = > 1344 answer : b" | a ) 776 , b ) 1344 , c ) 299 , d ) 257 , e ) 125 | b | divide(multiply(divide(288, divide(subtract(56, subtract(const_100, 56)), const_100)), 56), const_100) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)| | gain |
243 has been divided into 3 parts such that half of the first part , one - third of the second part and one - fourth of the third part are equal . the largest part is ? | explanation : ratio of their shares = ( 35000 * 8 ) : ( 42000 * 10 ) = 2 : 3 . reena ' s share rs . 31570 * ( 2 / 5 ) = rs . 12628 . answer : a ) 12628 | a ) 12628 , b ) 23488 , c ) 26688 , d ) 26667 , e ) 12672 | a | multiply(multiply(multiply(multiply(243, 3), 3), 3), const_2) | multiply(n0,n1)|multiply(n1,#0)|multiply(n1,#1)|multiply(#2,const_2) | general |
in the rectangular coordinate system , points ( 8 , 0 ) and ( – 8 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ? | the answer is c it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater... | ['a ) 2', 'b ) 4', 'c ) 8', 'd ) 16', 'e ) none of the above'] | c | sqrt(power(8, const_2)) | power(n0,const_2)|sqrt(#0) | geometry |
a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party e . if one registered voter has a favorable impression of both parties for ev... | "s = 100 not ( e and b ) = 35 only e = 20 ( e and b ) / b = 1 / 2 let ( e and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans" | a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45 | a | divide(subtract(const_100, add(35, 20)), const_3) | add(n0,n1)|subtract(const_100,#0)|divide(#1,const_3)| | gain |
if y ¤ w = y ^ ( 2 w ) for all positive integers , then ( 3 ¤ 4 ) ¤ 2 = | y ¤ w = y ^ ( 2 w ) 3 ¤ 4 = 3 ^ ( 8 ) ( 3 ¤ 4 ) ¤ 2 = ( 3 ^ 8 ) ¤ 2 = ( 3 ^ 8 ) ^ 4 = 3 ^ 32 correct option : e | a ) 3 ^ 8 , b ) 3 ^ 12 , c ) 3 ^ 16 , d ) 3 ^ 24 , e ) 3 ^ 32 | e | power(power(3, multiply(2, 4)), multiply(2, 2)) | multiply(n0,n2)|multiply(n0,n0)|power(n1,#0)|power(#2,#1) | general |
a circular rim a having a diameter of 45 inches is rotating at the rate of x inches / min . another circular rim b with a diameter of 30 inches is rotating at the rate of y inches / min . what is the value of y in terms of x , if both the rims reach their starting positions at the same time after every rotation . | t = s 1 / v 1 = s 2 / v 2 or , 45 / x = 30 / y or , y = 45 x / 30 = 3 x / 2 ( answer a ) | ['a ) 3 x / 2', 'b ) 4 x / 5', 'c ) 7 x / 5', 'd ) 5 x / 7', 'e ) 3 x / 4'] | a | divide(multiply(const_3, 45), const_2) | multiply(n0,const_3)|divide(#0,const_2) | geometry |
a typist uses a sheet measuring 20 cm by 30 cm lengthwise . if a margin of 2 cm is left on each side and a 3 cm margin on top and bottom , then percent of the page used for typing is | solution area of the sheet = ( 20 x 30 ) cm ² = 600 cm ² area used for typing = [ ( 20 - 4 ) x ( 30 - 6 ) ] cm ² = 384 cm ² required percentage = ( 384 / 600 x 100 ) % = 64 % . answer c | a ) 40 , b ) 60 , c ) 64 , d ) 72 , e ) none | c | multiply(divide(multiply(subtract(30, add(3, 3)), subtract(20, const_4)), multiply(20, 30)), const_100) | add(n3,n3)|multiply(n0,n1)|subtract(n0,const_4)|subtract(n1,#0)|multiply(#3,#2)|divide(#4,#1)|multiply(#5,const_100) | gain |
the h . c . f . of two numbers is 12 and their difference is 12 . the numbers are : | explanation : out of the given numbers , the two with h . c . f . 12 and difference 12 are 84 and 96 . answer is d | a ) 66 , 78 , b ) 70 , 82 , c ) 94 , 106 , d ) 84 , 96 , e ) none of these | d | multiply(12, add(const_3, const_4)) | add(const_3,const_4)|multiply(n0,#0) | general |
john , james and jim ' investment ratio in a business is 4 : 7 : 9 . if total total investment is 80000 . find jim ' s investment ? | let the investment of john james and jim is 4 x 7 x and 9 x 4 x + 7 x + 9 x = 80000 20 x = 80000 x = 4000 jim ' investment = 9 * 4000 = 36000 answer : d | a ) 35000 , b ) 40000 , c ) 16000 , d ) 36000 , e ) 60000 | d | multiply(divide(80000, add(add(4, 7), 9)), 9) | add(n0,n1)|add(n2,#0)|divide(n3,#1)|multiply(n2,#2) | other |
two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 3 days ? | "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 3 days = 3 ( 1 / 18 ) = 1 / 6 . answer : c" | a ) 1 / 5 , b ) 1 / 1 , c ) 1 / 6 , d ) 1 / 3 , e ) 1 / 7 | c | multiply(3, add(divide(const_1, 30), divide(const_1, 45))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)| | physics |
calculate how long it will take a swimmer to swim a distance of 8 km against the current of a river which flows at 1.4 km / hr , given that he can swim in still water at 3 km / h | swim in still water at = 3 speed of river = 1.4 us = 3 - 1.4 = 1.6 distance = 8 t = 8 / 1.6 = 5 answer : e | a ) 20 seconds , b ) 3 , c ) 4 , d ) 1 , e ) 5 | e | divide(8, subtract(3, 1.4)) | subtract(n2,n1)|divide(n0,#0) | gain |
if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 39 | "p ã · 44 = 432 = > p = 432 * 44 = 19008 p / 39 = 19008 / 39 = 487 , remainder = 15 c" | a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19 | c | reminder(multiply(432, 44), 39) | multiply(n0,n1)|reminder(#0,n3)| | general |
a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 8 the total number of upgraded sensors on the entire satellite , wh... | "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 8 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 8 ) = 3 x . the fraction of sensors which have been upgraded is x / ( x + 3 x ) = x / 4 x = 1 / 4 the answer is a ." | a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 8 , e ) 1 / 24 | a | divide(24, add(24, multiply(24, multiply(divide(1, 8), 24)))) | divide(n1,n2)|multiply(n0,#0)|multiply(n0,#1)|add(n0,#2)|divide(n0,#3)| | general |
if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 4 ø 2 ) ø 1 = ? | "4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 4 ø 1 = 2 ^ 4 / 2 = 8 the answer is c ." | a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32 | c | divide(power(2, divide(power(2, 4), power(2, 2))), power(2, 1)) | power(n0,n2)|power(n0,n0)|power(n0,n4)|divide(#0,#1)|power(n0,#3)|divide(#4,#2)| | general |
if 3 ^ x * 4 ^ y = 531,441 and x – y = 12 , then x = ? | "since 531,441 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 12 and y = 0 , then x = 12 . the answer is c ." | a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14 | c | multiply(12, const_1) | multiply(n3,const_1)| | general |
a man buys a cycle for rs . 2300 and sells it at a loss of 30 % . what is the selling price of the cycle ? | "s . p . = 70 % of rs . 2300 = rs . 70 x 2300 / 100 = rs . 1610 answer : option b" | a ) s . 1690 , b ) s . 1610 , c ) s . 1890 , d ) s . 1602 , e ) s . 1092 | b | divide(multiply(subtract(const_100, 30), 2300), const_100) | subtract(const_100,n1)|multiply(n0,#0)|divide(#1,const_100)| | gain |
how many hours are there in 660 minutes ? | "solution : number of minutes in 1 hour = 60 minutes so just divide 660 by 60 660 ã · 60 = 11 , so there are 11 hours in 660 minutes option d" | a ) 60 hours , b ) 6 hours , c ) 30 hours , d ) 11 hours , e ) 10 hours | d | divide(660, const_60) | divide(n0,const_60)| | physics |
a is twice as good a workman as b and they took 9 days together to do the work b alone can do it in ? | "wc = 2 : 1 2 x + x = 1 / 9 x = 1 / 27 = > 27 days answer : d" | a ) 25 days , b ) 88 days , c ) 21 days , d ) 27 days , e ) 13 days | d | multiply(divide(multiply(9, add(const_2, const_1)), const_2), const_2) | add(const_1,const_2)|multiply(n0,#0)|divide(#1,const_2)|multiply(#2,const_2)| | physics |
tom read a book containing 480 pages by reading the same number of pages each day . if he would have finished the book 5 days earlier by reading 16 pages a day more , how many days did tom spend reading the book ? | "say the number of days tom spent reading the book was dd . then : the number of pages he read per day would be 480 / d the number of pages he would read per day with an increased speed would be 480 / d − 5 e are told that the number of pages for the second case was 16 pages per day more , so 480 / d = 480 / d − 5 − 16... | a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 18 | c | divide(subtract(sqrt(add(multiply(multiply(16, 5), const_4), power(16, const_2))), 16), const_2) | multiply(n1,n2)|power(n2,const_2)|multiply(#0,const_4)|add(#2,#1)|sqrt(#3)|subtract(#4,n2)|divide(#5,const_2)| | general |
ajay and vijay have some marbles with them . ajay told vijay ` ` if you give me ' x ' marbles , both of us will have equal number of marbles ' ' . vijay then told ajay ` ` if you give me twice as many marbles , i will have 30 more marbles than you would ' ' . find ' x ' ? | if vijay gives ' x ' marbles to ajay then vijay and ajay would have v - x and a + x marbles . v - x = a + x - - - ( 1 ) if ajay gives 2 x marbles to vijay then ajay and vijay would have a - 2 x and v + 2 x marbles . v + 2 x - ( a - 2 x ) = 30 = > v - a + 4 x = 30 - - - ( 2 ) from ( 1 ) we have v - a = 2 x substituting ... | a ) 7 , b ) 5 , c ) 6 , d ) 4 , e ) 3 | b | divide(30, multiply(const_2, const_3)) | multiply(const_2,const_3)|divide(n0,#0) | general |
the average of temperatures at noontime from monday to friday is 45 ; the lowest one is 42 , what is the possible maximum range of the temperatures ? | "there are 5 days so the sum of temperature can be 45 * 5 = 225 lowest is 42 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 42 = 168 . on the fifth day it is 225 - 168 = 57 range is therefore 57 - 42 = 15 answer a" | a ) 15 , b ) 25 , c ) 40 , d ) 45 , e ) 75 | a | subtract(subtract(multiply(45, add(const_2, const_3)), multiply(42, const_4)), 42) | add(const_2,const_3)|multiply(n1,const_4)|multiply(n0,#0)|subtract(#2,#1)|subtract(#3,n1)| | general |
david is 12 years older than his daughter rosy . in 4 years david will be twice as old as rosy . what is rosy current age . | "now : rosy = x , david = x + 12 in 4 years rosy = x + 4 , david = x + 12 + 4 or 2 ( x + 4 ) x + 16 = 2 x + 8 x = 8 rosy is 8 years old answer : d" | a ) 9 , b ) 10 , c ) 11 , d ) 8 , e ) 12 | d | subtract(add(12, 4), multiply(const_2, 4)) | add(n0,n1)|multiply(n1,const_2)|subtract(#0,#1)| | general |
one - third of 1200 is what percent of 236 ? | "answer let one - third of 1200 is n % of 236 . ∵ 1200 / 3 = ( n x 236 ) / 100 ∴ n = ( 400 x 100 ) / 236 = 169.49 correct option : a" | a ) 169.49 , b ) 30 , c ) 120.32 , d ) 125.32 , e ) 15.152 | a | multiply(const_100, divide(divide(1200, const_3), 236)) | divide(n0,const_3)|divide(#0,n1)|multiply(#1,const_100)| | gain |
if 2 is the remainder when m is divided by 5 , what is the remainder when 3 m is divided by 5 ? | let ' s find a number which when divided by 5 leaves remainder 2 = 5 + 2 = 7 i . e . one possible value of m = 7 value of 3 m = 3 * 7 = 21 when em is divided by 5 then remainder = rem ( 21 / 5 ) = 1 answer : option b | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | b | reminder(5, 2) | reminder(n1,n0) | physics |
the population of a town is 8100 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ? | "formula : ( after = 100 denominator ago = 100 numerator ) 8100 × 100 / 90 × 100 / 90 = 10000 e )" | a ) 9000 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000 | e | subtract(subtract(8100, multiply(8100, divide(10, const_100))), multiply(subtract(8100, multiply(8100, divide(10, const_100))), divide(10, const_100))) | divide(n1,const_100)|multiply(n0,#0)|subtract(n0,#1)|multiply(#0,#2)|subtract(#2,#3)| | gain |
average age of students of an adult school is 48 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students . | explanation : let the original no . of students be x . according to situation , 48 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 40 so , required no . of students after joining the new students = x + 120 = 160 . answer : b | a ) 1200 , b ) 160 , c ) 360 , d ) 240 , e ) none of these | b | multiply(divide(subtract(multiply(add(32, 4), 120), multiply(120, 32)), subtract(48, add(32, 4))), 4) | add(n2,n3)|multiply(n1,n2)|multiply(n1,#0)|subtract(n0,#0)|subtract(#2,#1)|divide(#4,#3)|multiply(n3,#5) | general |
if 9 - 4 / x = 7 + 8 / x , then x = | we ' re given the equation 9 - 4 / x = 7 + 8 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we have to multiple 2 of the numbers to give them that denominator . . . 9 x - 4 x / x = 7 x + 8 x / x we can then eliminate that denominator , which gives us . . . . 9 x - 4 = 7 x... | a ) 15 , b ) 6 , c ) 1 , d ) 5 , e ) 12 | b | divide(add(8, const_4), subtract(9, 7)) | add(n3,const_4)|subtract(n0,n2)|divide(#0,#1) | general |
calculate the circumference of a circular field whose radius is 4 centimeters . | "circumference c is given by c = 2 ï € r = 2 ï € * 4 = 8 ï € cm correct answer d" | a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10 | d | circumface(4) | circumface(n0)| | physics |
it costs $ 4 for the first 1 / 4 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 12 per hour . if a certain customer uses the laundry machine for 3 hours and 25 minutes , how much will it cost him ? | "3 hrs 25 min = 205 min first 15 min - - - - - - > $ 4 time left is 190 min . . . now , 60 min costs $ 12 1 min costs $ 12 / 60 190 min costs $ 12 / 60 * 190 = > $ 38 so , total cost will be $ 38 + $ 4 = > $ 42 hene answer will be ( e ) $ 42" | a ) $ 25 , b ) $ 32 , c ) $ 36 , d ) $ 40 . , e ) $ 42 . | e | add(add(multiply(12, 3), 4), multiply(divide(12, const_60), divide(25, 4))) | divide(n3,const_60)|divide(n5,n2)|multiply(n3,n4)|add(n0,#2)|multiply(#0,#1)|add(#3,#4)| | physics |
the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 637 , krishan has ? | "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 637 : n & there n = 289 x 637 / 49 = rs . 3757 answer : c" | a ) s . 2890 , b ) s . 2330 , c ) s . 3757 , d ) s . 1620 , e ) s . 2680 | c | multiply(divide(multiply(divide(637, 7), 17), 7), 17) | divide(n4,n0)|multiply(n1,#0)|divide(#1,n0)|multiply(n1,#2)| | other |
last week david spent 40 percent of his wages on recreation . this week , his wages are 5 percent less than last week ʼ s wages and he spent 50 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week | say david ' s wages last week were $ 100 , so he spent 0.40 * 100 = $ 40 on recreation ; this week ' s wages is 0.95 * 100 = $ 95 , so he spends 0.5 * 95 = $ 47.5 on recreation ; 47.5 / 40 = 1.1875 , hence the amount he spends on recreation this week is 118.75 % of the amount he spent on recreation last week : 40 * 1.1... | a ) 118.75 % , b ) 128.75 % , c ) 116.75 % , d ) 117.75 % , e ) 114.75 % | a | multiply(divide(multiply(divide(50, const_100), subtract(const_1, divide(5, const_100))), divide(40, const_100)), const_100) | divide(n2,const_100)|divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#1)|multiply(#0,#3)|divide(#4,#2)|multiply(#5,const_100) | general |
the data a and b are equal to the data subtracted c ; the data b is 3 times the data a ; if the data a is equal to 12 what is the sum of the data a , b and c ? | the equations raised . a + b = c b = 3 a a = 12 then b = 36 and c = 48 a + b + c = 96 answer : e | a ) 86 , b ) 92 , c ) 84 , d ) 102 , e ) 96 | e | add(add(add(12, multiply(12, 3)), multiply(12, 3)), 12) | multiply(n0,n1)|add(n1,#0)|add(#1,#0)|add(n1,#2) | general |
the population of a town is 30000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ? | "30000 × 80 / 100 × 80 / 100 = 19200 answer ; b" | a ) 4300 , b ) 19200 , c ) 5120 , d ) 5230 , e ) 5366 | b | subtract(subtract(30000, multiply(30000, divide(20, const_100))), multiply(subtract(30000, multiply(30000, divide(20, const_100))), divide(20, const_100))) | divide(n1,const_100)|multiply(n0,#0)|subtract(n0,#1)|multiply(#0,#2)|subtract(#2,#3)| | gain |
a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 150 more than a : | "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 150 ... | a ) 2348 , b ) 7250 , c ) 4350 , d ) 1998 , e ) 2771 | c | multiply(add(add(multiply(3, 6), multiply(4, 5)), multiply(5, 4)), divide(150, subtract(multiply(4, 5), multiply(3, 6)))) | multiply(n0,n3)|multiply(n1,n2)|add(#0,#1)|subtract(#1,#0)|add(#2,#1)|divide(n6,#3)|multiply(#4,#5)| | general |
a man can row downstream at 18 kmph and upstream at 6 kmph . find the speed of the man in still water and the speed of stream respectively ? | let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 6 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 24 = > x = 12 , y = 6 . answer : c | a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9 | c | divide(divide(add(18, 6), const_2), const_2) | add(n0,n1)|divide(#0,const_2)|divide(#1,const_2) | physics |
the ratio of 3 numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ? | let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e | a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9 | e | sqrt(divide(1701, add(power(4, 2), add(power(1, 2), power(2, 2))))) | power(n1,n2)|power(n2,n2)|power(n3,n2)|add(#0,#1)|add(#3,#2)|divide(n4,#4)|sqrt(#5) | other |
a lady builds 10 cm length , 18 cm width , and 4 cm height box using 12 cubic cm cubes . what is the minimum number of cubes required to build the box ? | "number of cubes required = volume of box / volume of cube = 10 * 18 * 4 / 12 = 60 cubes answer : d" | a ) 107 , b ) 70 , c ) 78 , d ) 60 , e ) 111 | d | divide(multiply(multiply(10, 18), 4), 12) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,n3)| | geometry |
the sum of the first 80 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ? | "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 80 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 80 positive even integers = 2550 sum of 1 st 100 odd numbers = ... | a ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600 | c | multiply(divide(add(200, 101), const_2), add(divide(subtract(200, 101), const_2), const_1)) | add(n2,n3)|subtract(n3,n2)|divide(#1,const_2)|divide(#0,const_2)|add(#2,const_1)|multiply(#4,#3)| | general |
a 300 m long train crosses a platform in 45 sec while it crosses a signal pole in 18 sec . what is the length of the platform ? | "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 45 = 50 / 3 3 x + 900 = 2250 = > x = 450 m . answer : d" | a ) 287 , b ) 350 , c ) 828 , d ) 450 , e ) 122 | d | subtract(multiply(speed(300, 18), 45), 300) | speed(n0,n2)|multiply(n1,#0)|subtract(#1,n0)| | physics |
in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 3.5 . the factory holds a $ 45 worth stock of 11 modules . how many of the modules in the stock are of the cheaper kind ? | so the number of $ 3.50 modules must be 10 so that the leftover 1 modules are of $ 10 which will give a total value $ 45 . 10 * 3.50 + 1 * 10 = 35 + 10 = 45 answer : e | a ) 30 , b ) 28 , c ) 25 , d ) 20 , e ) 10 | e | divide(subtract(45, 10), 3.5) | subtract(n2,n0)|divide(#0,n1) | other |
the average salary of all the workers in a workshop is rs . 10000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 8000 . the total number of workers in the workshop is : | "explanation : lot the total number of workers be v then , 10000 v = ( 12000 * 7 ) + 8000 ( v - 7 ) < = > 2000 v = 28000 < = > v = 14 answer : a ) 14" | a ) 14 , b ) 21 , c ) 88 , d ) 37 , e ) 29 | a | add(7, divide(multiply(7, subtract(12000, 10000)), subtract(10000, 8000))) | subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)| | general |
a salt manufacturing company produced a total of 4000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ? | "total production of salt by the company in that year = 4000 + 4100 + 4200 + . . . . + 5100 = 54600 . average monthly production of salt for that year = 54600 / 365 â ‰ ˆ 149 answer : b" | a ) 140 , b ) 149 , c ) 156 , d ) 195 , e ) 100 | b | divide(divide(multiply(add(multiply(4000, const_2), multiply(subtract(const_12, const_1), 100)), const_12), const_2), add(add(multiply(const_3, 100), multiply(multiply(const_2, const_3), const_10)), add(const_2, const_3))) | add(const_2,const_3)|multiply(n0,const_2)|multiply(n1,const_3)|multiply(const_2,const_3)|subtract(const_12,const_1)|multiply(n1,#4)|multiply(#3,const_10)|add(#1,#5)|add(#2,#6)|add(#8,#0)|multiply(#7,const_12)|divide(#10,const_2)|divide(#11,#9)| | general |
a little girl is numbering her collection of butterflies by placing single - digit stickers under each specimen . if the girl has 330 butterflies , how many stickers does she need ? ( the numbers are consecutive and the number of the first butterfly is 1 ) . | for the first 9 butterflies we need 9 stickers . for the next 90 we need 2 stickers each or 180 stickers . for the next 900 butterflies we need 3 stickers each . the first 99 butterflies correspond to 189 stickers . subtract 99 from the total number of butterflies ( 330 ) . this leaves 231 butterflies that use 3 sticke... | a ) 882 , b ) 901 , c ) 1001 , d ) 1003 , e ) 1346 | a | add(multiply(add(subtract(330, const_100), const_1), const_3), add(multiply(const_3, const_3), multiply(multiply(multiply(const_3, const_3), const_10), const_2))) | multiply(const_3,const_3)|subtract(n0,const_100)|add(#1,const_1)|multiply(#0,const_10)|multiply(#3,const_2)|multiply(#2,const_3)|add(#0,#4)|add(#6,#5) | physics |
a batsman in his 17 th innings makes a score of 80 , and thereby increases his average by 2 . what is his average after the 17 th innings ? he had never been ’ not out ’ . | "average score before 17 th innings = 80 - 2 × 17 = 46 average score after 17 th innings = > 46 + 2 = 48 answer : a" | a ) 48 , b ) 37 , c ) 39 , d ) 43 , e ) 42 | a | add(subtract(80, multiply(2, 17)), 2) | multiply(n0,n2)|subtract(n1,#0)|add(n2,#1)| | general |
19 times a number gives 342 . the number is | "explanation : let the number be ' n ' 19 × n = 342 ⇒ n = 18 correct option : a" | a ) 18 , b ) 19 , c ) 16 , d ) none , e ) can not be determined | a | divide(342, divide(342, 19)) | divide(n1,n0)|divide(n1,#0)| | general |
1.45 , 2.56 , 4.78 , 8.11 , 12.55 , ( . . . . ) | "explanation : 1.11 , 2.22 , 3.33 , 4.44 , 5.55 , hence 5.55 = 18.1 answer : e" | a ) 17.3 , b ) 16.2 , c ) 15.3 , d ) 19.5 , e ) 18.1 | e | subtract(negate(8.11), multiply(subtract(2.56, 4.78), divide(subtract(2.56, 4.78), subtract(1.45, 2.56)))) | negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)| | general |
how many positive integers less than 1000 are multiples of 5 but not of 4 or 7 ? | "there are 1000 / 5 = 200 multiples of 5 . now we have to find the number of multiples of 5 and 4 that is 20 between 0 to 1000 and 5 and 7 that is 35 between 0 to 1000 . multiples of 20 = 1000 / 20 = 50 multiples . and multiples of 35 = 1000 / 35 = 28.5 so 28 multiples of 35 . so multiples of 5 between o to 1000 not in... | a ) 114 , b ) 121 , c ) 122 , d ) 129 , e ) 136 | c | divide(factorial(subtract(add(const_4, 5), const_1)), multiply(factorial(5), factorial(subtract(const_4, const_1)))) | add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)| | general |
a trader bought a car at 20 % discount on its original price . he sold it at a 45 % increase on the price he bought it . what percent of profit did he make on the original price ? | "original price = 100 cp = 80 s = 80 * ( 145 / 100 ) = 116 100 - 116 = 16 % c )" | a ) a ) 10 % , b ) b ) 12 % , c ) c ) 16 % , d ) d ) 20 % , e ) e ) 22 % | c | multiply(subtract(divide(divide(multiply(subtract(const_100, 20), add(const_100, 45)), const_100), const_100), const_1), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|divide(#3,const_100)|subtract(#4,const_1)|multiply(#5,const_100)| | gain |
the diagonal of the floor of a rectangular closet is 7 feet . the shorter side of the closet is 4 feet . what is the area of the closet in square feet ? | other side = 15 2 - 9 2 2 2 ft = 225 - 81 4 4 ft = 144 4 ft = 6 ft . area of closet = ( 6 x 4.5 ) sq . ft = 27 sq . ft . b ) | ['a ) 20 sq . ft', 'b ) 27 sq . ft', 'c ) 37 sq . ft', 'd ) 47 sq . ft', 'e ) 57 sq . ft'] | b | rectangle_area(sqrt(subtract(power(divide(add(multiply(7, const_2), const_1), const_2), const_2), power(divide(add(multiply(const_4, const_2), const_1), const_2), const_2))), divide(add(multiply(const_4, const_2), const_1), const_2)) | multiply(const_2,const_4)|multiply(n0,const_2)|add(#0,const_1)|add(#1,const_1)|divide(#2,const_2)|divide(#3,const_2)|power(#5,const_2)|power(#4,const_2)|subtract(#6,#7)|sqrt(#8)|rectangle_area(#4,#9) | geometry |
whats the reminder when 445876 , 985420 , 215546 , 656452 is divided by 8 | a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . a number ending in 3 zeroes is divisible by 8 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 445876 , 985420 , 215546 , 656452 = 445876 , 985420 , 215546 ... | a ) 1 , b ) 7 . , c ) 4 , d ) 3 , e ) 9 | c | reminder(445876, 8) | reminder(n0,n4) | general |
each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife ... | as they arrived 10 minutes earlier than usual , they saved 10 minutes on round trip from home to station ( home - station - home ) - - > 5 minutes in each direction ( home - station ) - - > wife meets husband 5 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he m... | a ) 45 minutes , b ) 50 minutes , c ) 55 minutes , d ) 52 minutes , e ) 35 minutes | c | subtract(const_60, divide(10, const_2)) | divide(n0,const_2)|subtract(const_60,#0) | physics |
in what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way ? | "t = 75 / 50 * 18 / 5 = 5.4 sec answer : b" | a ) 3 , b ) 5.4 , c ) 4.3 , d ) 6.5 , e ) 7 | b | divide(75, multiply(50, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics |
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