Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
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ratio of two numbers x and y is 5 : 7 . if x is increased by 20 % and y is increased by 2 then the new ratio becomes 2 : 3 . what is the ratio 3 y : ( x + 6 ) | "let : x = 5 n y = 7 n 6 n / ( 7 n + 2 ) = 2 / 3 18 n = 2 * ( 7 n + 2 ) n = 1 so , x = 5 ; y = 7 y / ( x + 3 ) = 7 / 8 answer = a" | a ) 7 : 8 , b ) 8 : 7 , c ) 6 : 7 , d ) 7 : 6 , e ) 2 : 7 | a | divide(multiply(3, multiply(divide(2, subtract(multiply(divide(add(const_100, 20), const_100), 3), divide(7, 5))), divide(7, 5))), add(divide(2, subtract(multiply(divide(add(const_100, 20), const_100), 3), divide(7, 5))), 6)) | add(n2,const_100)|divide(n1,n0)|divide(#0,const_100)|multiply(n5,#2)|subtract(#3,#1)|divide(n3,#4)|add(n7,#5)|multiply(#5,#1)|multiply(#7,n6)|divide(#8,#6)| | general |
if a = { 9 , 17 , 25 , 28 , 29 , 30 } , how much less is the mean of the numbers in a than the median of the numbers in s ? | "this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number o... | a ) 1.0 , b ) 9.6 , c ) 3.5 , d ) 3.2 , e ) 5.1 | c | add(divide(add(add(add(add(9, 17), 25), 28), 29), add(const_4, const_1)), 25) | add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)|add(n2,#5)| | general |
a , b and c have rs . 1000 between them , a and c together have rs . 700 and b and c rs . 600 . how much does c have ? | "a + b + c = 1000 a + c = 700 b + c = 600 - - - - - - - - - - - - - - a + b + 2 c = 1300 a + b + c = 1000 - - - - - - - - - - - - - - - - c = 300 answer : c" | a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500 | c | subtract(add(700, 600), 1000) | add(n1,n2)|subtract(#0,n0)| | general |
sam β s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 10 more than 1 / 4 of the fine and peter paid $ 10 less than 1 / 3 of the fine , leaving pay $ 25 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ? | "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f β 4 , leaving ( 1 / 2 ) f β 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 10 ] + [ ( 1 / 3 ) f β 10 ] + [ ( 1 / 2 ) f β 25 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f β 25 multiply all terms by 12 to clear the f... | a ) $ 120 , b ) $ 125 , c ) $ 130 , d ) $ 135 , e ) $ 140 | b | add(multiply(add(multiply(add(divide(1, 2), add(divide(1, 4), divide(1, 3))), 25), 25), 2), const_10) | divide(n1,n2)|divide(n1,n5)|divide(n1,n8)|add(#0,#1)|add(#3,#2)|multiply(n6,#4)|add(n6,#5)|multiply(n8,#6)|add(#7,const_10)| | general |
from a pack of 52 cards , 1 card is drawn at random . what is the probability that a king is drawn ? | "the total number of cards is 52 . the number of kings is 4 . p ( king ) = 4 / 52 = 1 / 13 the answer is c ." | a ) 1 / 4 , b ) 4 / 13 , c ) 1 / 13 , d ) 3 / 26 , e ) 7 / 52 | c | divide(multiply(const_4, const_3), 52) | multiply(const_3,const_4)|divide(#0,n0)| | probability |
if ( 1 / 2 ) ^ 18 ( 1 / 81 ) ^ k = 1 / 18 ^ 18 , then k = | "i ' m going to focus on denominator only . . ( 2 ^ 18 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 18 hence 4 k = 36 k = 9 answer a i hope it ' s quite clear" | a ) 9 , b ) 12 , c ) 16 , d ) 24 , e ) 36 | a | divide(multiply(18, 2), const_4) | multiply(n1,n2)|divide(#0,const_4)| | general |
in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 300 girls , the total number of students in the college is | "explanation : let the boy are 8 x and girls are 5 x = > 5 x = 300 = > x = 60 total students = 8 x + 5 x = 13 x = 13 ( 60 ) = 780 option d" | a ) 420 , b ) 520 , c ) 620 , d ) 780 , e ) 820 | d | add(300, multiply(divide(300, 5), 8)) | divide(n2,n1)|multiply(n0,#0)|add(n2,#1)| | other |
the sale price sarees listed for rs . 390 after successive discount is 15 % and 25 % is ? | "390 * ( 85 / 100 ) * ( 75 / 100 ) = 248 answer : c" | a ) 298 , b ) 237 , c ) 248 , d ) 876 , e ) 291 | c | subtract(subtract(390, divide(multiply(390, 15), const_100)), divide(multiply(subtract(390, divide(multiply(390, 15), const_100)), 25), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | gain |
a student finds the average of 9 positive integers . each integer contains two digits . by mistake , the boy interchanges the digits of one number say pq for qp . due to this , the average becomes 1 less than the previous one . what was the difference of the two digits p and q ? | explanation : let the original number be pq i . e . , ( 10 p + q ) . after interchanging the digits , the new number becomes qp i . e . , ( 10 q + p ) . the question states that the average of 9 numbers has become 1 less than the original average . therefore , the sum of the original 9 numbers will be 9 * 1 more than t... | a ) 8 , b ) 6 , c ) 1 , d ) 4 , e ) 2 | c | multiply(divide(1, 9), 9) | divide(n1,n0)|multiply(n0,#0) | general |
a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 25 km in 10 hours . how much time he would have saved if the direction of tide has not changed ? | "explanation : he covered 5 km in 1 hour , so he might cover 25 km in 5 hours . but he took 10 hours . he would have saved 10 Γ’ β¬ β 5 = 5 hours . answer : b" | a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7 | b | subtract(10, divide(25, 5)) | divide(n2,n0)|subtract(n3,#0)| | physics |
a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7000 ? | "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 7000 * 6 ) - 34009 ] = rs . ( 42000 - 34009 ) = rs . 7991 . answer : e" | a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6991 , e ) s . 7991 | e | subtract(multiply(add(5, const_1), 7000), add(add(add(add(6435, 6927), 6855), 7230), 6562)) | add(n5,const_1)|add(n0,n1)|add(n2,#1)|multiply(n6,#0)|add(n3,#2)|add(n4,#4)|subtract(#3,#5)| | general |
during the first two weeks of january , the total rainfall in springdale was 30 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ? | "total rainfall in 2 weeks = 18 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 18 inches x = 12 and 1.5 x = 18 rainfall during second week = 18 inches option e" | a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 18 inches | e | multiply(30, divide(1.5, add(const_1, 1.5))) | add(n1,const_1)|divide(n1,#0)|multiply(n0,#1)| | general |
let f ( x , y ) be defined as the remainder when ( x β y ) ! is divided by x . if x = 45 , what is the maximum value of y for which f ( x , y ) = 0 ? | "the question is finding y such that ( 45 - y ) ! is a multiple of 45 . that means we need to have 5 * 3 ^ 2 in ( 45 - y ) ! 6 ! is the smallest factorial number with 5 * 3 ^ 2 as a factor . 45 - y = 6 y = 39 the answer is c ." | a ) 32 , b ) 35 , c ) 39 , d ) 40 , e ) 42 | c | subtract(45, multiply(const_2, divide(divide(45, const_2), add(const_1, const_4)))) | add(const_1,const_4)|divide(n0,const_2)|divide(#1,#0)|multiply(#2,const_2)|subtract(n0,#3)| | general |
what is the minimum value of | x - 4 | + | x + 2 | + | x - 5 | ? | "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 2 | > = 0 - - > minimum occurs at x = - 2 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 2 - - > result = 6 + 0 + 7 = 13 . also any negative value will push... | a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 8 | d | add(2, 5) | add(n1,n2)| | general |
the average weight of 8 persons increases by 4 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? | "total weight increased = ( 8 x 4 ) kg = 32 kg . weight of new person = ( 65 + 32 ) kg = 97 kg . answer : d" | a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 97 kg , e ) 25 kg | d | add(65, multiply(8, 4)) | multiply(n0,n1)|add(n2,#0)| | general |
a train 120 m in length crosses a telegraph post in 16 seconds . the speed of the train is ? | "s = 120 / 16 * 18 / 5 = 27 kmph answer : e" | a ) 16 kmph , b ) 88 kmph , c ) 54 kmph , d ) 18 kmph , e ) 27 kmph | e | multiply(const_3_6, divide(120, 16)) | divide(n0,n1)|multiply(#0,const_3_6)| | physics |
subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 25 pages . | "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 25 / 2.5 ) = 10 hrs answer : b" | a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16 | b | floor(subtract(divide(300, 40), divide(50, 10))) | divide(n2,n3)|divide(n0,n1)|subtract(#0,#1)|floor(#2)| | general |
if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 25 ( q + 1 ) , what is the least possible value of p + q ? | "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 25 , so the least value of p is 24 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 24 + 16 = 40 . answer : c ." | a ) 36 , b ) 42 , c ) 40 , d ) 46 , e ) none | c | subtract(add(25, 17), const_2) | add(n1,n3)|subtract(#0,const_2)| | general |
what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 54 ? | "explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 54 = rs . 3672 . answer : option a" | a ) 3672 , b ) 920 , c ) 7290 , d ) 6928 , e ) 3729 | a | multiply(square_perimeter(sqrt(289)), 54) | sqrt(n0)|square_perimeter(#0)|multiply(n1,#1)| | geometry |
excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 33 kmph . of how many minutes does the train stop per hour ? | "explanation : t = 12 / 45 * 60 = 16 answer : option c" | a ) 73 , b ) 83 , c ) 16 , d ) 83 , e ) 28 | c | subtract(const_60, multiply(const_60, divide(33, 45))) | divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)| | physics |
worker a takes 8 hours to do a job . worker b takes 10 hours to do the same job . how long should it take both a and b , working together but independently , to do the same job ? | "a β s 1 hour ' s work = 1 / 8 b ' s 1 hour ' s work = 1 / 10 ( a + b ) ' s 1 hour ' s work = ( 1 / 8 ) + ( 1 / 10 ) = 9 / 40 both a and b will finish the work in 40 / 9 days . answer b 40 / 9 hours" | a ) 70 hours , b ) 40 / 9 hours , c ) 9 hours , d ) 16 hours , e ) 20 hours | b | divide(const_1, add(divide(const_1, 8), divide(const_1, 10))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)| | physics |
rectangle dimensions were given , 2 doors dimensions given , 2 windows dimensions given . 70 cm wide wallpaper to be covered on the walls of this room . cost of wallpaper is 60 per meter . . calculate total cost | area of room = ( l * b ) m ^ 2 area of door + window = ( d + w ) m ^ 2 remaining area = ( ( l * b ) - ( d + w ) ) m ^ 2 so length = remaining area / 0.70 m total cost = length * 60 - - - ans and total cost = 60 answer : d | a ) 20 , b ) 25 , c ) 30 , d ) 60 , e ) 70 | d | multiply(60, const_1) | multiply(n3,const_1) | physics |
set s consists of integers { 12 , 34 } . if two numbers are chosen from set s at random , what is the probability that the sum of 2 numbers is more than 6 ? | number of ways you can choose 2 from 4 = 4 c 2 = 6 e = event of getting the 2 numbers is more than 6 = ( 3,4 ) = 1 probability = 1 / 6 answer is b | a ) 1 / 3 , b ) 1 / 6 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7 | b | inverse(6) | inverse(n3) | general |
in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 23 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ? | 200 are sophomores . the number of freshmen is 600 - 160 - 0.23 ( 800 ) = 256 the answer is c . | a ) 42 , b ) 48 , c ) 56 , d ) 64 , e ) 72 | c | subtract(divide(multiply(subtract(subtract(subtract(const_100, multiply(divide(160, 800), const_100)), 23), subtract(const_100, 75)), 800), const_100), divide(multiply(subtract(const_100, 75), 800), const_100)) | divide(n3,n0)|subtract(const_100,n2)|multiply(#0,const_100)|multiply(n0,#1)|divide(#3,const_100)|subtract(const_100,#2)|subtract(#5,n1)|subtract(#6,#1)|multiply(n0,#7)|divide(#8,const_100)|subtract(#9,#4) | gain |
the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal ... | "assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.09 * 80 90 x - 80 = 7.2 90 x = 87.2 x = 87.2 / 90 = 0.968 x is slightly under 0.9688 = 0.97 answer : b" | a ) $ 0.94 , b ) $ 0.97 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.20 | b | multiply(add(const_1, divide(9, const_100)), divide(0.80, divide(subtract(const_100, 10), const_100))) | divide(n2,const_100)|subtract(const_100,n1)|add(#0,const_1)|divide(#1,const_100)|divide(n0,#3)|multiply(#2,#4)| | gain |
if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly once in 3 consecutive flips ? | "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 h thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : d" | a ) 0.125 , b ) 0.25 , c ) 0.75 , d ) 0.375 , e ) 0.666 | d | multiply(power(divide(const_1, const_2), 3), 3) | divide(const_1,const_2)|power(#0,n0)|multiply(n0,#1)| | probability |
the average weight of 10 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what might be the weight of the new person ? | "explanation : total weight increased = ( 10 x 2.5 ) kg = 25 kg . weight of new person = ( 50 + 25 ) kg = 75 kg . answer : c" | a ) 76 kg , b ) 76.5 kg , c ) 75 kg , d ) data inadequate , e ) none of these | c | add(multiply(10, 2.5), 50) | multiply(n0,n1)|add(n2,#0)| | general |
the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hourr . the distance travelled downstream in 24 mins is ? | "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 = 2460 Γ 18 = 2 Γ 185 = 7.2 km c" | a ) 6 km , b ) 7 km , c ) 7.2 km , d ) 8 km , e ) 8.4 km | c | multiply(divide(24, const_60), add(15, 3)) | add(n0,n1)|divide(n2,const_60)|multiply(#0,#1)| | physics |
if 1 tic equals 4 tacs and 5 tacs equal 8 tocs , what is the ratio of one tic to one toc ? | "tic = 4 * tac and 5 * tac = 8 * toc ; 5 * tic = 20 * tac and 20 * tac = 32 * toc - - > 5 * tic = 32 * toc - - > tic / toc = 32 / 5 . answer : d ." | a ) 15 / 2 , b ) 6 / 5 , c ) 5 / 6 , d ) 32 / 5 , e ) 1 / 15 | d | add(divide(8, 1), divide(4, 1)) | divide(n3,n0)|divide(n1,n0)|add(#0,#1)| | other |
a man can row upstream at 22 kmph and downstream at 42 kmph , and then find the speed of the man in still water ? | "us = 22 ds = 42 m = ( 42 + 22 ) / 2 = 32 answer : d" | a ) 29 , b ) 92 , c ) 30 , d ) 32 , e ) 23 | d | divide(add(22, 42), const_2) | add(n0,n1)|divide(#0,const_2)| | physics |
if the side length of square b is five times that of square a , the area of square b is how many times the area of square a ? | "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 5 x ) ^ 2 = 25 x ^ 2 . the answer is c ." | a ) 5 , b ) 15 , c ) 25 , d ) 35 , e ) 45 | c | multiply(const_4, const_4) | multiply(const_4,const_4)| | geometry |
the average weight of 20 oarsmen in a boat is increased by 2 kg when one of the crew , who weight 40 kg is replaced by a new man . find the weight of the new man . | total weight increased = 2 * 20 = 40 kg weight of the new man = 40 + 40 = 80 kg answer is d | a ) 60 kg , b ) 50 kg , c ) 92 kg , d ) 80 kg , e ) 70 kg | d | add(multiply(2, 20), 40) | multiply(n0,n1)|add(n2,#0) | general |
in a club with 310 peopl , 138 play tennis , 255 play baseball , and 94 people play both sports . how many people do not pla a sport ? | take 94 off the baseball players - - > 161 then 161 + 138 = 299 play either baseball or tennis 310 - 299 = 11 answer is e | ['a ) 9', 'b ) 8', 'c ) 4', 'd ) 10', 'e ) 11'] | e | subtract(subtract(310, 138), subtract(255, 94)) | subtract(n0,n1)|subtract(n2,n3)|subtract(#0,#1) | other |
a 14 % stock yielding 8 % is quoted at ? | "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 14 , money invested = 100 Γ 14 / 8 = rs . 175 ie , market value of the stock = rs . 175 answer is c ." | a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 185 | c | multiply(divide(const_100, 8), 14) | divide(const_100,n1)|multiply(n0,#0)| | gain |
at present the ratio between the ages of arun and deepak is 4 : 3 . after 6 years , arun ' s age will be 26 years . what is the age of deepak at present ? | let the present ages of arun and deepak be 4 x years and 3 x years respectively 4 x + 6 = 26 4 x = 20 x = 5 deepak ' s age = 3 x = 15 years answer is a | a ) 15 , b ) 21 , c ) 23 , d ) 12 , e ) 25 | a | divide(multiply(subtract(26, 6), 3), 4) | subtract(n3,n2)|multiply(n1,#0)|divide(#1,n0) | other |
working together , jose and jane can complete an assigned task in 5 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 15 days . how long will jose take to complete the task if he worked alone ? ass... | "assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 5 5 ( x + y ) = xy next , we ' re told 1 job takes 15 days to complete if jose and jane ... | a ) 26 days , b ) 15 days , c ) 60 days , d ) 65 days , e ) 36 days | b | multiply(const_3, 5) | multiply(n0,const_3)| | physics |
two years ago , ram put $ 1,000 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 1,100 . the next year , his account balance increased by 20 % . at the end of the two years , by what percent has sam ' s account balance increased from his i... | "investment 1000 dollars 1 st year total gained = 100 total amount end of first year = 1100 second year account increased by 20 % = 1100 * 0.2 = 220 therefore total amount by second year end = 1320 so total percentage increase in money = ( 1320 - 1000 ) * 100 / 1000 = 32 % correct answer e = 32 %" | a ) 40 % , b ) 25 % , c ) 35 % , d ) 30 % , e ) 32 % | e | multiply(divide(add(multiply(divide(20, 100), 1,100), 100), 1,000), 100) | divide(n3,n1)|multiply(n2,#0)|add(n1,#1)|divide(#2,n0)|multiply(#3,n1)| | gain |
a gets 3 times as much money as b gets , b gets only rs . 25 more then what c gets . the 3 gets rs . 645 in all . find the share of b ? | a + b + c = 645 a = 3 b 3 b + b + b - 25 = 645 5 b = 670 b = 134 answer : a | a ) 134 , b ) 120 , c ) 218 , d ) 140 , e ) 145 | a | divide(add(645, 25), add(add(3, const_1), const_1)) | add(n1,n3)|add(n0,const_1)|add(#1,const_1)|divide(#0,#2) | general |
if ( a - b - c + d = 13 ) and ( a + b - c - d = 3 ) , what is the value of ( b - d ) ^ 2 ? | "eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 3 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 3 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 10 ( 2 ) simplify - b + d = 5 b - d = - 5 ( b - d ) ^ 2 = ( - 5 ) ^ 2 = 25 my answer : d" | a ) 4 . , b ) 8 . , c ) 12 . , d ) 25 . , e ) 64 . | d | power(subtract(3, divide(add(13, 3), 2)), 2) | add(n0,n1)|divide(#0,n2)|subtract(n1,#1)|power(#2,n2)| | general |
dhoni spent 20 percent of his earning last month on rent and 5 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ? | say dhoni ' s earning last month was $ 100 . dhoni spent 20 percent of his earning last month on rent - - > $ 20 on rent ; 5 percent less than what he spent on rent to purchase a new dishwasher - - > $ 20 * 0.95 = $ 19 on the dishwasher . left over amount 100 - ( 20 + 19 ) = $ 61 answer : a | a ) 61 % , b ) 62 % , c ) 65 % , d ) 64 % , e ) 50 % | a | subtract(const_100, add(20, multiply(20, subtract(const_1, divide(5, const_100))))) | divide(n1,const_100)|subtract(const_1,#0)|multiply(n0,#1)|add(n0,#2)|subtract(const_100,#3) | gain |
if a ' s height is 20 % less than that of b , how much percent b ' s height is more than that of a ? | "excess of b ' s height over a ' s = [ ( 20 / ( 100 - 20 ) ] x 100 % = 25 % answer : e )" | a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 25 % | e | multiply(divide(20, subtract(const_100, 20)), const_100) | subtract(const_100,n0)|divide(n0,#0)|multiply(#1,const_100)| | general |
a set of football matches is to be organized in a ` ` round - robin ' ' fashion , i . e . , every participating team plays a match against every other team once and only once . if 15 matches are totally played , how many teams participated ? | 2 ways to solve this problem . . summation ( x ) = n ( n - 1 ) / 2 n ( n - 1 ) / 2 = 15 ; n ^ 2 - n - 30 = 0 ans : 6 answer : c | a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | c | add(subtract(15, const_10), const_1) | subtract(n0,const_10)|add(#0,const_1) | general |
the average weight of 8 sailors in a boat is increased by 1 kg if one of them weighing 56 kg is replaced by a new sailor . the weight of the new sailor is ? | the sailor weighing 56 kg is replaced and the average is increased by 1 kg . hence , the weight of the new sailor is ( 56 + increase in total weight ) = 56 + 1 x 8 = 56 + 8 = 64 kg . answer : c | a ) 57 kg , b ) 60 kg , c ) 64 kg , d ) 62 kg , e ) 66 kg | c | add(56, 8) | add(n0,n2) | general |
there are some sweets in party , 1 / 3 rd eaten by kids . then 2 / 5 th of the remaining by men , then 2 / 3 rd of the remaining by women . at last 2 were remaining . how many sweets were in total ? | sol : if x sweets were there in total , then x Γ ( 1 β 1 / 3 ) Γ ( 1 β 2 / 5 ) Γ ( 1 β 2 / 3 ) = 2 x Γ 2 / 3 Γ 3 / 5 Γ 1 / 3 = 2 x = 15 answer : c | a ) 45 , b ) 27 , c ) 15 , d ) 26 , e ) 91 | c | divide(2, subtract(subtract(subtract(const_1, divide(1, 3)), multiply(divide(2, 5), subtract(const_1, divide(1, 3)))), multiply(divide(2, 3), subtract(subtract(const_1, divide(1, 3)), multiply(divide(2, 5), subtract(const_1, divide(1, 3))))))) | divide(n0,n1)|divide(n2,n3)|divide(n2,n1)|subtract(const_1,#0)|multiply(#1,#3)|subtract(#3,#4)|multiply(#2,#5)|subtract(#5,#6)|divide(n2,#7) | general |
the cost of 100 articles is equal to selling price of 90 . find the gain or loss percent ? | "c . p . of each article be $ 1 c . p . of 90 articles = 100 gain % = 10 / 90 * 100 = 11 % approximately answer is a" | a ) 11 % , b ) 20 % , c ) 27 % , d ) 32 % , e ) 49 % | a | multiply(divide(90, 90), const_100) | divide(n1,n1)|multiply(#0,const_100)| | gain |
a bag contains 5 green balls and 9 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ? | "the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 5 c 2 = 10 the number of ways to draw two white balls is 9 c 2 = 36 p ( two balls of the same colour ) = 46 / 91 the answer is d ." | a ) 11 / 21 , b ) 17 / 42 , c ) 23 / 42 , d ) 46 / 91 , e ) 51 / 91 | d | add(multiply(divide(9, add(5, 9)), divide(subtract(9, const_1), subtract(add(5, 9), const_1))), multiply(divide(subtract(5, const_1), subtract(add(5, 9), const_1)), divide(5, add(5, 9)))) | add(n0,n1)|subtract(n1,const_1)|subtract(n0,const_1)|divide(n1,#0)|divide(n0,#0)|subtract(#0,const_1)|divide(#1,#5)|divide(#2,#5)|multiply(#3,#6)|multiply(#7,#4)|add(#8,#9)| | other |
a no . when divided by 223 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ? | "223 + 43 = 266 / 17 = 11 ( remainder ) d" | a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 15 | d | divide(add(223, 43), 17) | add(n0,n1)|divide(#0,n2)| | general |
find the 25 % of rs . 400 . | "explanation : 25 % of 400 = > 25 / 100 * 400 = rs . 100 answer : c" | a ) s . 50 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 60 | c | multiply(400, divide(25, const_100)) | divide(n0,const_100)|multiply(n1,#0)| | gain |
a shop owner sells 40 mtr of cloth and gains sp of 10 mtrs . find the gain % ? | "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 40 m cloth ) β ( c . p . of 40 m cloth ) selling price of 30 m cloth = selling price of 40 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 30 m cloth = rs . 3000 and s . p . of 30 m cloth = rs . rs ... | a ) 33.33 % , b ) 40 % , c ) 50 % , d ) 66.67 % , e ) 70 % | a | multiply(divide(10, subtract(40, 10)), const_100) | subtract(n0,n1)|divide(n1,#0)|multiply(#1,const_100)| | gain |
ajay spends 50 % of his monthly income on household items , 25 % of his monthly income on buying cloths , 15 % of his monthly income on medicines and saves the remaining amount which is rs . 9000 . find his monthly income . | savings 10 % - 9000 expenditure 90 % - 81000 total - 90000 answer : a | a ) rs . 90000 , b ) rs . 36000 , c ) rs . 50000 , d ) rs . 45000 , e ) none of these | a | divide(9000, divide(subtract(const_100, add(add(50, 25), 15)), const_100)) | add(n0,n1)|add(n2,#0)|subtract(const_100,#1)|divide(#2,const_100)|divide(n3,#3) | gain |
the measurement of a rectangular box with lid is 50 cmx 30 cmx 38 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of Ο cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere ) | "d = 30 , r = 15 ; volume of the largest sphere = 4 / 3 Ο r 3 = 4 / 3 * Ο * 15 * 15 * 15 = 4500 Ο cm 3 answer : b" | a ) 288 , b ) 4500 , c ) 7200 , d ) 864 , e ) 9640 | b | multiply(divide(const_4, 3), power(3, 3)) | divide(const_4,n3)|power(n3,n3)|multiply(#0,#1)| | geometry |
if an article is sold at 12 % profit instead of 16 % profit , then the profit would be rs . 105 less . what is the cost price ? | "explanation : let the cost price of an article be rs . x . ( 16 % of x ) - ( 12 % of x ) = 105 16 x / 100 - 12 x / 100 = 105 = > 4 x = 160 * 100 = > x = 1500 cost price = rs . 4000 answer : b" | a ) rs . 3000 , b ) rs . 4000 , c ) rs . 3500 , d ) rs . 4500 , e ) rs . 6000 | b | multiply(divide(105, 16), const_100) | divide(n2,n1)|multiply(#0,const_100)| | gain |
gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 16 times as heavy as water ? | "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 16 w 19 + 9 x = 16 ( x + 1 ) x = 3 / 7 ratio of gold with copper = 1 : 3 / 7 = 7 : 3 answer is b" | a ) 1 : 2 , b ) 7 : 3 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5 | b | divide(subtract(16, 9), subtract(19, 16)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)| | general |
a question paper has 2 parts , a & b , each containing 7 questions . if a student has to choose 5 from part a & 4 from part b , in how many ways can he choose the questions ? | "there 7 questions in part a out of which 5 question can be chosen as = 7 c 5 . similarly , 4 questions can be chosen from 7 questions of part b as = 7 c 4 . hence , total number of ways , = 7 c 5 * 7 c 4 = [ 7 ! / ( 2 ! 5 ! ) ] * [ 7 ! / ( 3 ! * 4 ! ) ] = { 21 } * { 7 * 6 * 5 * 4 / ( 4 * 3 * 2 * 1 ) } = 735 . e" | a ) 1100 , b ) 1200 , c ) 1235 , d ) 1354 , e ) 735 | e | divide(multiply(choose(7, 5), choose(7, 4)), 7) | choose(n1,n2)|choose(n1,n3)|multiply(#0,#1)|divide(#2,n1)| | probability |
a man has some hens and cows . if the number of heads be 60 and the number of feet equals 200 , then the number of hens will be : | "explanation : let the number of hens be x and the number of cows be y . then , x + y = 60 . . . . ( i ) and 2 x + 4 y = 200 x + 2 y = 100 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 40 . the required answer = 20 . answer : d" | a ) 22 , b ) 25 , c ) 24 , d ) 20 , e ) 28 | d | divide(subtract(multiply(60, const_4), 200), const_2) | multiply(n0,const_4)|subtract(#0,n1)|divide(#1,const_2)| | general |
what is the difference between 62 % of 150 nd 20 % of 250 . | ( 62 / 100 ) * 150 Γ’ β¬ β ( 20 / 100 ) * 250 93 - 50 = 43 answer : c | a ) 16 , b ) 17 , c ) 43 , d ) 19 , e ) 20 | c | subtract(divide(multiply(62, 150), const_100), divide(multiply(20, 250), const_100)) | multiply(n0,n1)|multiply(n2,n3)|divide(#0,const_100)|divide(#1,const_100)|subtract(#2,#3) | gain |
of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 25 percent on food , and 25 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 20 percent tax on all other items , then the total tax that she paid was what per... | "assume she has $ 200 to spend . tax clothing = 50 % = $ 100 = $ 10.00 food = 25 % = $ 50 = $ 0.00 items = 25 % = $ 50 = $ 10.00 total tax = $ 20.00 % of total amount = 20 / 200 * 100 = 10 % answer b" | a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25 | b | multiply(divide(add(multiply(50, divide(10, const_100)), multiply(25, divide(20, const_100))), const_100), const_100) | divide(n3,const_100)|divide(n4,const_100)|multiply(n0,#0)|multiply(n2,#1)|add(#2,#3)|divide(#4,const_100)|multiply(#5,const_100)| | general |
if a 2 - b 2 = 11 and a * b = 5 , find a 4 + b 4 . | "a 2 - b 2 = 11 : given a 4 + b 4 - 2 a 2 b 2 = 112 : square both sides and expand . a * b = 2 : given a 2 b 2 = 52 : square both sides . a 4 + b 4 - 2 ( 25 ) = 121 : substitute a 4 + b 4 = 171 correct answer d" | a ) 62 , b ) 181 , c ) 170 , d ) 171 , e ) 50 | d | add(power(11, 2), multiply(power(5, 2), 2)) | power(n3,n0)|power(n2,n0)|multiply(#0,n0)|add(#2,#1)| | general |
on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salar... | "let the number of employees before jul 1 be 100 then av sal 1 = total 1 / 100 after jul 1 employees = 90 av sal 2 = total 2 / 90 now from the question av 2 = av 1 + 10 % total 2 / 90 = total 1 / 100 + 1 / 10 * total 1 / 100 total 2 / 90 = 11 total 1 / 1000 total 2 = 99 total 1 / 100 now percent = total 2 / total 1 * 1... | a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 % | b | multiply(10, 10) | multiply(n1,n1)| | general |
if q and d are both integers , q > d , and - 3 q > 19 , then the largest value of d would be ? | no , your thinking is incorrect . when we know that q > d and q < - 6.33 , the largest value of q can be - 7 while if q = - 7 , then largest value of d < - 7 will be - 8 . for negative numbers , - 7 > - 8 and - 8 > - 10 . you are right in saying that d can take any value less than - 7 - - - > d could be - 8 , - 9 , - 1... | a ) - 5 , b ) - 6 , c ) - 7 , d ) - 8 , e ) - 10 | d | floor(divide(19, negate(3))) | negate(n0)|divide(n1,#0)|floor(#1) | other |
a small company reduced its faculty by approximately 15 percent to 195 employees . what was the original number of employees ? | "if x is the original number of employees , then after 15 % reduction in employees number is . 85 x but we are given . 85 x = 195 x = 229 so the original number of employees is 229 correct answer - d" | a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 229 , e ) e ) 302 | d | divide(195, divide(subtract(const_100, 15), const_100)) | subtract(const_100,n0)|divide(#0,const_100)|divide(n1,#1)| | gain |
a man is 30 years older than his son . in three years , his age will be twice the age of his son . the present age of his son is : | "let the son ' s present age be x years . then , man ' s present age = ( x + 30 ) years . ( x + 30 ) + 3 = 2 ( x + 3 ) x + 33 = 2 x + 6 x = 27 . answer : c" | a ) 20 , b ) 21 , c ) 27 , d ) 23 , e ) 24 | c | divide(subtract(30, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | general |
henry earns $ 120 a week from his job . his income increased and now makes $ 180 a week . what is the percent increase ? | increase = ( 60 / 120 ) * 100 = ( 1 / 2 ) * 100 = 50 % . c | a ) 70 % , b ) 60 % , c ) 50 % , d ) 40 % , e ) 30 % | c | multiply(divide(subtract(180, 120), 120), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100) | gain |
a train 120 m long crosses a platform 120 m long in 6 sec ; find the speed of the train ? | "d = 120 + 120 = 240 t = 6 s = 240 / 6 * 18 / 5 = 144 kmph answer : a" | a ) 144 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 59 kmph | a | subtract(multiply(6, multiply(120, const_0_2778)), 120) | multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)| | physics |
an investor can sell her microtron stock for 36 $ per share and her dynaco stock for 48 $ per share , if she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of dynaco stock has she sold ? | "w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) = ( 48 - 40 ) / ( 40 - 36 ) = 8 / 4 = 2 / 1 = number of microtron stocks / number of dynaco stocks so for every 2 microtron stock , she sold 1 dynaco stock . so out of 300 total stocks , ( 1 / 3 ) th i . e . 300 / 3 = 100 must be dynaco stock . answer ( d )" | a ) 52 , b ) 75 , c ) 92 , d ) 100 , e ) 184 | d | divide(multiply(300, divide(40, subtract(48, 36))), divide(add(36, 48), subtract(48, 36))) | add(n0,n1)|subtract(n1,n0)|divide(n3,#1)|divide(#0,#1)|multiply(n2,#2)|divide(#4,#3)| | general |
working at constant rate , pump x pumped out half of the water in a flooded basement in 3 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constan... | "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 20 hours a" | a ) a . 20 , b ) b . 12 , c ) c . 14 , d ) d . 18 , e ) e . 24 | a | add(add(add(add(add(add(add(add(add(add(add(add(const_1, add(3, 3)), const_1), const_1), const_1), const_1), 3), const_1), const_1), const_1), const_1), const_1), const_1) | add(n0,n1)|add(#0,const_1)|add(#1,const_1)|add(#2,const_1)|add(#3,const_1)|add(#4,const_1)|add(#5,n0)|add(#6,const_1)|add(#7,const_1)|add(#8,const_1)|add(#9,const_1)|add(#10,const_1)|add(#11,const_1)| | physics |
two spherical balls lie on the ground touching . if one of the balls has a radius of 10 cm , and the point of contact is 12 cm above the ground , what is the radius of the other ball ? | "similar triangle properties . . 2 / r + 10 = 10 / r - 10 giving r = 15 / 2 . answer : d" | a ) 2 cm , b ) 5 / 2 cm , c ) 5 cm , d ) 15 / 2 cm , e ) none of the these | d | add(add(10, 12), 10) | add(n0,n1)|add(#0,n0)| | physics |
( 753 x 753 + 247 x 247 - 753 x 247 ) / ( 753 x 753 x 753 + 247 x 247 x 247 ) = ? | given exp . = ( a ^ 2 + b ^ 2 - ab ) / ( a ^ 3 + b ^ 3 ) = 1 / ( a + b ) = 1 / ( 753 + 247 ) = 1 / 1000 answer : a | a ) 1 / 1000 , b ) 1 / 506 , c ) 253 / 500 , d ) 253 / 1000 , e ) none of these | a | divide(subtract(add(multiply(753, 753), multiply(247, 247)), multiply(753, 247)), add(multiply(multiply(753, 753), 753), multiply(multiply(247, 247), 247))) | multiply(n0,n0)|multiply(n2,n2)|multiply(n0,n2)|add(#0,#1)|multiply(n0,#0)|multiply(n2,#1)|add(#4,#5)|subtract(#3,#2)|divide(#7,#6) | general |
the area of a square field is 7201 sq m . how long will a lady take to cross the field diagonally at the rate of 1.2 km / hr ? | "area of a square field = 7201 sq m let the side of square = a a ^ 2 = 7201 = > a = 84.86 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 84.86 = 120 speed of lady = 1.2 km / hour = 1200 m / hour = 20 m / min time taken by lady to cross the field diagonally = 120 / 20 = 6 min answer a" | a ) 6 min , b ) 5 min , c ) 5.5 min , d ) 4 min , e ) 3 min | a | divide(7201, multiply(1.2, const_1000)) | multiply(n1,const_1000)|divide(n0,#0)| | geometry |
one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in : | "slower pipe alone fill the tank = x faster pipe will fill in x / 3 min 1 / x + 3 / x = 1 / 36 x = 144 min answer a" | a ) 144 min , b ) 145 min , c ) 150 min , d ) 200 min , e ) 250 min | a | multiply(add(const_1, const_4), 36) | add(const_1,const_4)|multiply(n0,#0)| | physics |
the tax on a commodity is diminished by 22 % but its consumption is increased by 9 % . find the decrease percent in the revenue derived from it ? | "100 * 100 = 10000 78 * 109 = 8502 10000 - - - - - - - 1200 100 - - - - - - - ? = 15 % answer : c" | a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 % | c | subtract(const_100, divide(multiply(add(const_100, 9), subtract(const_100, 22)), const_100)) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(const_100,#3)| | general |
each of the three people individually can complete a certain job in 4 , 6 , and 8 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ? | "the two slowest people work at rates of 1 / 6 and 1 / 8 of the job per hour . the sum of these rates is 1 / 6 + 1 / 8 = 7 / 24 of the job per hour . the answer is c ." | a ) 3 / 8 , b ) 5 / 12 , c ) 7 / 24 , d ) 11 / 36 , e ) 13 / 48 | c | add(divide(1, 6), divide(1, 8)) | divide(n3,n1)|divide(n3,n2)|add(#0,#1)| | physics |
a man can row at 4 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ? | "explanation : speed in still water = 4 kmph speed of the current = 1 kmph speed downstream = ( 4 + 1 ) = 5 kmph speed upstream = ( 4 - 1 ) = 3 kmph let the required distance be x km total time taken = 1 hour Γ’ β‘ β x / 5 + x / 3 = 1 Γ’ β‘ β 3 x + 5 x = 15 Γ’ β‘ β 8 x = 15 Γ’ β‘ β x = 1.9 km answer : option d" | a ) 2.4 km , b ) 2.9 km , c ) 3.4 km , d ) 1.9 km , e ) 5.6 km | d | divide(multiply(subtract(4, 1), const_3), 4) | subtract(n0,n1)|multiply(#0,const_3)|divide(#1,n0)| | physics |
two numbers are respectively 20 % and 25 % more than a third number . the percentage that is first of the second is ? | "explanation : i ii iii 120 125 100 125 - - - - - - - - - - 120 100 - - - - - - - - - - - ? = > 96 % answer is c" | a ) 80 % , b ) 85 % , c ) 96 % , d ) 125 % , e ) 150 % | c | subtract(const_100, multiply(divide(add(20, const_100), add(25, const_100)), const_100)) | add(n0,const_100)|add(n1,const_100)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)| | gain |
if 5 % more is gained by selling an article for rs . 360 than by selling it for rs . 340 , the cost of the article is | "explanation : let c . p . be rs . x . then , 5 % of x = 360 - 340 = 20 x / 20 = 20 = > x = 400 answer : b" | a ) 289 , b ) 400 , c ) 200 , d ) 288 , e ) 111 | b | divide(subtract(360, 340), divide(5, const_100)) | divide(n0,const_100)|subtract(n1,n2)|divide(#1,#0)| | gain |
weights of two friends ram and shyam are in the ratio 6 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ? | "solution : given ratio of ram and shayam ' s weight = 6 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 6 / 5 or , x = 21 % . answer : option c" | a ) 19 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none | c | add(15, multiply(subtract(15, 10), divide(6, 5))) | divide(n0,n1)|subtract(n4,n2)|multiply(#0,#1)|add(n4,#2)| | gain |
how many of the positive factors of 36 , 84 and how many common factors are there in numbers ? | "factors of 36 - 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36 factors of 84 - 1 , 2 , 3 , 4 , 6 , 7 , 12 , 14 , 21 , 28 , 42 , 84 comparing both , we have six common factors of 36 and 84 - 1,2 , 3,4 , 6,12 , answer ( e )" | a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6 | e | divide(84, 36) | divide(n1,n0)| | other |
jaclyn buys $ 20 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter | "explanation : i = ( p x r x t ) / 100 = 30000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 475 answer : a" | a ) 475 , b ) 234 , c ) 289 , d ) 345 , e ) none of these | a | divide(divide(multiply(multiply(const_100, const_100), 9.5), const_100), const_4) | multiply(const_100,const_100)|multiply(n2,#0)|divide(#1,const_100)|divide(#2,const_4)| | gain |
if 5 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ? | parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 5 c 2 for vertical 8 c 2 total parallelogram is 5 c 2 * 8 c 2 = 10 * 28 = 280 answer : a | a ) 280 , b ) 63 , c ) 120 , d ) 160 , e ) 1260 | a | multiply(divide(multiply(5, subtract(5, const_1)), const_2), divide(multiply(8, subtract(8, const_1)), const_2)) | subtract(n0,const_1)|subtract(n1,const_1)|multiply(n0,#0)|multiply(n1,#1)|divide(#2,const_2)|divide(#3,const_2)|multiply(#4,#5) | physics |
in a group of buffaloes and ducks , the number of legs are 24 more than twice the number of heads . what is the number of buffaloes in the group ? | let no . of buffaloes be x & no . of ducks be y buffaloes have 4 legs while ducks have 2 4 x + 2 y = 2 * ( x + y ) + 24 = > 4 x + 2 y - 2 x - 2 y = 24 = > x = 12 number of buffaloes in the group = 12 answer : a | a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16 | a | divide(24, const_2) | divide(n0,const_2) | general |
a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 24 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = ... | the distance the sound traveled to the man is 24 * 330 = 7920 meters the answer is b . | a ) 6810 , b ) 7920 , c ) 9030 , d ) 10,140 , e ) 11,250 | b | multiply(330, 24) | multiply(n1,n3) | physics |
what is the thousandths digit in the decimal equivalent of 57 / 5000 ? | 57 / 5000 = 57 / ( 5 * 10 ^ 3 ) = ( 57 / 5 ) * 10 ^ - 3 = 11.4 * 10 ^ - 3 = . 0114 thousandths digit = 1 answer b | a ) 0 , b ) 1 , c ) 3 , d ) 5 , e ) 6 | b | floor(multiply(const_100, divide(57, 5000))) | divide(n0,n1)|multiply(#0,const_100)|floor(#1) | general |
6 / 8 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded... | "total population = 80 ( assume ) . 6 / 8 * 80 = 60 people from montague . 2 / 8 * 80 = 20 people from capulet . 0.2 * 60 = 12 people from montague support juliet . 0.7 * 20 = 14 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 14 / ( 12 + 14 ) = ~ 54 a... | a ) 28 % , b ) 54 % , c ) 45 % , d ) 72 % , e ) 78 % | b | multiply(divide(multiply(divide(70, const_100), divide(subtract(8, 6), 8)), add(multiply(divide(subtract(const_100, 80), const_100), divide(6, 8)), multiply(divide(70, const_100), divide(subtract(8, 6), 8)))), const_100) | divide(n3,const_100)|divide(n0,n1)|subtract(n1,n0)|subtract(const_100,n2)|divide(#2,n1)|divide(#3,const_100)|multiply(#0,#4)|multiply(#5,#1)|add(#7,#6)|divide(#6,#8)|multiply(#9,const_100)| | gain |
45 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ? | "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 : 45 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 45 x 5 x 12 x = ( 45 x 5 x 12 ) / ( 30 x 6 ) x = 15 answer b" | a ) 10 , b ) 15 , c ) 13 , d ) 18 , e ) 19 | b | divide(multiply(multiply(45, 12), 5), multiply(30, 6)) | multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|divide(#2,#1)| | physics |
the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ? | "total increase in weight = 8 Γ 2.5 = 20 if x is the weight of the new person , total increase in weight = x β 65 = > 20 = x - 65 = > x = 20 + 65 = 85 answer is c ." | a ) 75 , b ) 65 , c ) 85 , d ) 95 , e ) 80 | c | add(multiply(8, 2.5), 65) | multiply(n0,n1)|add(n2,#0)| | general |
it takes 60 identical printing machines 4 hours to print 200,000 cards . how long would it take 50 of these machines to print the same total ? | "50 % of 60 = 40 % or 0.30 4 hr x 60 min = 240 min 240 min x 0.30 = 72 min or 1 hr and 12 min 1 hr and 12 min + 4 hr = 5 hr and 12 min answer is e" | a ) 10 hr , b ) 5 hr , c ) 6 hr , d ) 4 hr 30 min , e ) 5 hr 12 min | e | add(divide(60, 4), divide(200,000, 50)) | divide(n0,n1)|divide(n2,n3)|add(#0,#1)| | probability |
in a party , there are rows arranged with 1220 and 30 chairs and there were 3 left in all the cases . when there were 11 rows . there were no chair left . if 30 chairs were added . then what will be the reminder ? | lcm of 12 , 2030 is 120 . so the number is in the form of 120 x + 3 which is divisible by 11 , by placing x = 3 , we get 363 which is divisible by 11 and the multiple of 120 when 3 is subtracted from 363 . so the no . is 363 . so when 30 is added to it and is divided by 11 we get remainder as 8 answer : a | a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | a | subtract(11, 3) | subtract(n3,n2) | general |
for every integer n β₯ 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 106 ) β g ( 103 ) ? | "g ( 106 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 * 105 g ( 103 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 g ( 106 ) - g ( 103 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 * 105 - 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 = 1 * 3 * 5 * 7 * 9 * . . . * 103 * ( 105 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 10... | a ) 100 , b ) 99 , c ) 98 , d ) 102 , e ) 104 | e | subtract(106, 1) | subtract(n2,n1)| | general |
if x is 11 percent greater than 90 , then x = | "11 % of 90 = ( 90 * 0.11 ) = 9.9 11 % greater than 90 = 90 + 9.9 = 99.9 answer is clearly a ." | a ) 99.9 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2 | a | add(90, multiply(divide(11, const_100), 90)) | divide(n0,const_100)|multiply(n1,#0)|add(n1,#1)| | general |
the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 240 m , its area is ? | "5 x + 12 x + 13 x = 240 = > x = 8 a = 40 , b = 96 , c = 104 s = ( 40 + 96 + 104 ) / 2 = 120 answer : e" | a ) 150 , b ) 882 , c ) 277 , d ) 261 , e ) 120 | e | multiply(240, divide(240, add(add(5, 12), 13))) | add(n0,n1)|add(n2,#0)|divide(n3,#1)|multiply(n3,#2)| | geometry |
total 22 matches are conducted in knockout match type . how many players will be participated in that tournament ? | "21 players answer : c" | a ) 24 , b ) 26 , c ) 21 , d ) 20 , e ) 19 | c | add(22, const_1) | add(n0,const_1)| | general |
in an intercollegiate competition that lasted for 3 days , 150 students took part on day 1 , 110 on day 2 and 140 on day 3 . if 75 took part on day 1 and day 2 and 25 took part on day 2 and day 3 and 15 took part on all three days , how many students took part only on day 2 ? | "day 1 & 2 = 75 ; only day 1 & 2 ( 75 - 15 ) = 60 , day 2 & 3 = 25 ; only day 2 & 3 ( 25 - 15 ) = 10 , only day 2 = 110 - ( 60 + 10 + 15 ) = 25 answer : d" | a ) 50 , b ) 35 , c ) 45 , d ) 25 , e ) 60 | d | subtract(150, add(add(15, 75), divide(add(15, subtract(110, add(add(75, 25), 15))), 2))) | add(n7,n13)|add(n7,n10)|add(n13,#1)|subtract(n3,#2)|add(n13,#3)|divide(#4,n4)|add(#0,#5)|subtract(n1,#6)| | physics |
what is the remainder when you divide 2 ^ 200 + 2 by 7 ? | answer is d . this is very similar to the 32 ^ 32 ^ 32 + 2 divided by 7 question . | a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 5 | d | reminder(multiply(200, 2), 2) | multiply(n0,n1)|reminder(#0,n2)| | general |
jim drove 923 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ? | the number of miles to drive to finish his journey is given by 1200 - 923 = 277 miles correct answer b | a ) 113 miles , b ) 277 miles , c ) 456 miles , d ) 887 miles , e ) 767 miles | b | subtract(1200, 923) | subtract(n1,n0) | physics |
on increasing the price of t . v . sets by 70 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ? | "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 Γ 100 ) = rs . 10000 new sale value = rs . ( 170 Γ 80 ) = rs . 13600 increase % = 3600 / 10000 Γ 100 = 36 % answer : c" | a ) 4 , b ) 5 , c ) 36 , d ) 2 , e ) 7 | c | subtract(add(const_100, 70), add(divide(multiply(add(const_100, 70), 20), const_100), const_100)) | add(n0,const_100)|multiply(n1,#0)|divide(#1,const_100)|add(#2,const_100)|subtract(#0,#3)| | gain |
how many cubes of 10 cm edge can be put in a cubic box of 1 m edge ? | "( 110 Γ 100 Γ 100 ) / 10 Γ 10 Γ 10 = 1000 answer is e ." | a ) 4000 , b ) 2000 , c ) 3000 , d ) 5000 , e ) 1000 | e | divide(volume_cube(1), volume_cube(divide(10, const_100))) | divide(n0,const_100)|volume_cube(n1)|volume_cube(#0)|divide(#1,#2)| | physics |
what is the remainder when you divide 2 ^ 200 + 1 by 7 ? | answer is e . this is very similar to the 32 ^ 32 ^ 32 + 1 divided by 7 question . | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | e | reminder(multiply(200, 2), 1) | multiply(n0,n1)|reminder(#0,n2)| | general |
a train running at the speed of 60 km / hr crosses a pole in 36 seconds . find the length of the train ? | "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 36 = 600 meter answer : b" | a ) 150 meter , b ) 600 meter , c ) 167 meter , d ) 719 meter , e ) 169 meter | b | multiply(divide(multiply(60, const_1000), const_3600), 36) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
the area of a parallelogram is 128 sq m and its altitude is twice the corresponding base . then the length of the base is ? | 2 x * x = 128 = > x = 8 answer : a | ['a ) 8', 'b ) 7', 'c ) 6', 'd ) 5', 'e ) 2'] | a | sqrt(divide(128, const_2)) | divide(n0,const_2)|sqrt(#0) | geometry |
the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together ? | "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 20 ) / 2 = 40 . answer : a" | a ) 40 , b ) 99 , c ) 88 , d ) 77 , e ) 66 | a | divide(add(60, 20), const_2) | add(n0,n1)|divide(#0,const_2)| | general |
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