Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
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3 candidates in an election and received 1000 , 2000 and 4000 votes respectively . what % of the total votes did the winning candidate got in that election ? | "total number of votes polled = ( 1000 + 2000 + 4000 ) = 7000 so , required percentage = 4000 / 7000 * 100 = 57.14 % c" | a ) 45 % , b ) 50 % , c ) 57.14 % , d ) 60 % , e ) 65.12 % | c | multiply(divide(4000, add(add(1000, 2000), 4000)), const_100) | add(n1,n2)|add(n3,#0)|divide(n3,#1)|multiply(#2,const_100)| | gain |
two numbers are less than third number by 20 % and 37 % respectively . how much percent is the second number less than by the first | "let the third number is x . then first number = ( 100 - 20 ) % of x = 80 % of x = 80 x / 100 second number is ( 63 x / 100 ) difference = 80 x / 100 - 63 x / 100 = 17 x / 100 so required percentage is , difference is what percent of first number ( 17 x / 100 * 100 / 80 x * 100 ) % = 5 % answer : a" | a ) 5 % , b ) 10 % , c ) 9 % , d ) 11 % , e ) 12 % | a | subtract(multiply(divide(subtract(37, 20), subtract(const_100, 20)), const_100), const_10) | subtract(n1,n0)|subtract(const_100,n0)|divide(#0,#1)|multiply(#2,const_100)|subtract(#3,const_10)| | gain |
a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 45 % ? | "cost price = rs . 500 profit = 45 % of 500 = rs . 225 selling price = cost price + profit = 500 + 225 = 725 answer : e" | a ) 600 , b ) 887 , c ) 256 , d ) 654 , e ) 725 | e | add(500, multiply(500, divide(45, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | gain |
the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 3 : 2 . if the oil bill for february had been $ 20 more , the corresponding ratio would have been 5 : 3 . how much was the oil bill for january ? | "3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 20 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 20 ) = $ 120 . the answer is b ." | a ) $ 100 , b ) $ 120 , c ) $ 140 , d ) $ 160 , e ) $ 180 | b | divide(20, subtract(divide(5, 3), divide(3, 2))) | divide(n3,n4)|divide(n0,n1)|subtract(#0,#1)|divide(n2,#2)| | general |
salesperson a ' s compensation for any week is $ 240 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ? | "240 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 180 x = $ 9,000 the answer is b ." | a ) $ 7000 , b ) $ 9000 , c ) $ 11,000 , d ) $ 13,000 , e ) $ 15,000 | b | divide(add(divide(subtract(240, multiply(divide(6, const_100), 1,000)), subtract(divide(8, const_100), divide(6, const_100))), divide(subtract(240, multiply(divide(6, const_100), 1,000)), subtract(divide(8, const_100), divide(6, const_100)))), 1,000) | divide(n1,const_100)|divide(n3,const_100)|multiply(#0,n2)|subtract(#1,#0)|subtract(n0,#2)|divide(#4,#3)|add(#5,#5)|divide(#6,n2)| | general |
a shop produces sarongs . the daily average production is given by 5 n + 20 , where n is the number of workers aside from the owner . in the first k days , 500 units are produced , and then 5 workers are added to the team . after another k days , the cumulative total is 1300 . how many workers were part of the latter p... | "the daily average production is given by 5 n + 20 - given in the first k days , 500 units are produced = ( 5 n + 20 ) k = 500 k = 500 / 5 n + 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 workers were added = 5 ( n + 5 ) + 20 = 5 n + 45 cumulative is 1300 . . thus for the current period ... | a ) a ) 6 , b ) b ) 10 , c ) c ) 9 , d ) d ) 15 , e ) e ) 23.5 | c | add(20, 5) | add(n0,n1)| | general |
carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 15 inches by 20 inches and jordan ' s rectangle is 6 inches long , how wide is jordan ' s rectangle , in inches ? | "area of first rectangle is 15 * 20 = 300 hence area of second would be 6 x = 300 x x = 50 answer is d" | a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60 | d | divide(rectangle_area(15, 20), 6) | rectangle_area(n0,n1)|divide(#0,n2)| | geometry |
martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 18.00 , how many discounted tickets did he buy ? | "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 18 0.4 x = 2 = > x = 5 discounted tickets = 10 - x = 5 ans : c" | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | c | subtract(multiply(10, 2.00), multiply(1.60, 10)) | multiply(n0,n1)|multiply(n0,n2)|subtract(#0,#1)| | gain |
the purchase price of an article is $ 48 . in order to include 15 % of cost for overhead and to provide $ 12 of net profit , the markup should be | "cost price of article = 48 $ % of overhead cost = 15 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 15 = 40 % answer d" | a ) 15 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 45 % | d | add(multiply(divide(12, 48), const_100), 15) | divide(n2,n0)|multiply(#0,const_100)|add(n1,#1)| | gain |
in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 8 days , working 13.33 hours a day , the number of men required is : | "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 13.33 : 8 : : 12 : x = > 8 x 13.33 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 8 x 13.33 ) = > x = 9 answer : e" | a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9 | e | divide(divide(multiply(multiply(12, 8), 10), 13.33), 8) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,n4)|divide(#2,n1)| | physics |
papaya , a popular soft drink , contains only 4 ingredients . soda water comprise 4 / 7 of papaya and natural lemon juice makes 1 / 3 of papaya . the amounts of sugar and papaya puree in papaya are equal . due to a malfunction , the mixing machine mixes double the regular amount of lemon juice and 3 times the regular a... | soda water = 12 / 21 natural lemon juice = 7 / 21 the quantities of sugar and papaya puree are equal . total units are 21 of which 12 + 7 = 19 are used up by above two . remaining is 2 which is equally divided between sugar and papaya puree : sugar = 1 / 21 papaya puree = 1 / 21 thus ratio of soda : lemon : sugar : pur... | a ) 7 / 30 , b ) 7 / 21 , c ) 2 / 5 , d ) 12 / 29 , e ) 4 / 7 | c | divide(multiply(divide(4, 7), multiply(7, 3)), add(add(add(multiply(const_2, 7), multiply(divide(4, 7), multiply(7, 3))), multiply(3, 1)), 1)) | divide(n0,n2)|multiply(n2,n4)|multiply(n2,const_2)|multiply(n3,n4)|multiply(#0,#1)|add(#2,#4)|add(#5,#3)|add(n3,#6)|divide(#4,#7) | general |
how long does a train 130 m long running at the speed of 80 km / hr takes to cross a bridge 140 m length ? | "speed = 80 * 5 / 18 = 22 m / sec total distance covered = 130 + 140 = 270 m . required time = 270 / 22 = 12.3 sec . answer : b" | a ) 13.9 sec , b ) 12.3 sec , c ) 17.9 sec , d ) 61.9 sec , e ) 47.98 sec | b | divide(add(130, 140), multiply(80, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | physics |
ramesh , xyz and rajeev put a partnership . profit is 36000 , if ramesh and xyz ratio is 5 : 4 and xyz and rajeev 8 : 9 . find rajeev ' s share . | ramesh : xyz = 5 : 4 xyz : rajeev = 8 : 9 then ramesh : xyz / rajeev : xyz = 5 : 4 / 9 : 8 ramesh / rajeev = 10 / 9 therefore ramesh : xyz : rajeev = 10 : 8 : 9 then rajeev share = ( 9 / 27 ) * 36000 = 12000 answer : d | a ) 14000 , b ) 15000 , c ) 16000 , d ) 12000 , e ) 17000 | d | multiply(36000, divide(9, add(add(divide(multiply(5, 8), 4), 8), 9))) | multiply(n1,n3)|divide(#0,n2)|add(n3,#1)|add(n4,#2)|divide(n4,#3)|multiply(n0,#4) | other |
a trader cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 10 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 30 % of that is added to the weight , the weight claimed by the trader is obtained . if he cha... | anyways , one can infer that he ' steals ' 10 % from suppliers and then charges 30 % extra to customers so basically 1.1 * 1.3 = 1.43 given that 1 is start point , we get 43 % more hence answer is b | a ) 20 % , b ) 43 % , c ) 99.33 % , d ) 75.109 % , e ) 47 % | b | subtract(multiply(divide(add(const_100, 30), const_100), add(const_100, 10)), const_100) | add(n0,const_100)|add(n1,const_100)|divide(#1,const_100)|multiply(#0,#2)|subtract(#3,const_100) | gain |
in measuring the sides of a rectangle , one side is taken 14 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements . | "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 114 * 95 = 10,830 , which is 8.3 % greater than the actual area . answer : c ." | a ) 3.5 % , b ) 2.4 % , c ) 8.3 % , d ) 5 % , e ) 2.6 % | c | subtract(subtract(14, 5), divide(multiply(14, 5), const_100)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,const_100)|subtract(#1,#2)| | geometry |
in an office , totally there are 5200 employees and 45 % of the total employees are males . 50 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ? | "number of male employees = 5200 * 45 / 100 = 2340 required number of male employees who are less than 50 years old = 4160 * ( 100 - 50 ) % = 2340 * 50 / 100 = 1170 . answer : b" | a ) 1040 , b ) 1170 , c ) 1150 , d ) 4160 , e ) none of these | b | multiply(divide(multiply(5200, 45), const_100), divide(subtract(const_100, 50), const_100)) | multiply(n0,n1)|subtract(const_100,n2)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)| | general |
a lady builds 12 cm length , 16 cm width , and 6 cm height box using 3 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 = 12 * 16 * 6 / 3 = 384 cubes answer : b" | a ) 345 , b ) 384 , c ) 378 , d ) 398 , e ) 300 | b | divide(multiply(multiply(12, 16), 6), 3) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,n3)| | geometry |
oil cans x and y are right circular cylinders and the height and radius of y are each 10 times those of x . if the oil in can x filled to capacity sells for $ 1 , how much does the oil in y sell for if y is only half filled ? | "formula for vol of a cyl is pi * r ^ 2 * h so vy = 1000 * vy y when half filled will cost 500 times x so ans is c" | a ) $ 400 , b ) $ 450 , c ) $ 500 , d ) $ 550 , e ) $ 600 | c | multiply(power(10, 1), 10) | power(n0,n1)|multiply(n0,#0)| | general |
the perimeter of a semi circle is 121 cm then the radius is ? | "36 / 7 r = 121 = > r = 24 answer : c" | a ) 17 , b ) 28 , c ) 24 , d ) 26 , e ) 12 | c | divide(121, add(const_2, const_pi)) | add(const_2,const_pi)|divide(n0,#0)| | physics |
if you write down all the numbers from 1 to 100 , then how many multiples of 3 ? | division rule for 3 - sum of all digits is multiple of 3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 ans - e | a ) a ) 32 , b ) b ) 38 , c ) c ) 30 , d ) d ) 31 , e ) e ) 33 | e | divide(subtract(100, const_1), 3) | subtract(n1,const_1)|divide(#0,n2) | general |
if x + ( 1 / x ) = 5 , what is the value q of x ^ 2 + ( 1 / x ) ^ 2 ? | squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c | a ) q = 21 , b ) q = 22 , c ) q = 23 , d ) 24 , e ) 27 | c | subtract(power(5, 2), 2) | power(n1,n2)|subtract(#0,n2) | general |
if 2 ^ 4 , 3 ^ 3 , and 13 ^ 3 are factors of the product of 1452 and w , where w is a positive integer , what is the smallest possible value of w ? | i will go with e ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 13 ^ 1 = 468 | a ) 198 , b ) 288 , c ) 363 , d ) 396 , e ) 468 | e | multiply(multiply(power(2, 2), power(3, 2)), 13) | power(n0,n0)|power(n2,n0)|multiply(#0,#1)|multiply(n4,#2) | general |
a man is walking at a speed of 10 km per hour . after every kilometre , he takes rest for 7 minutes . how much time will be take to cover a distance of 7 kilometres ? | "rest time = number of rest Γ£ β time for each rest = 6 Γ£ β 7 = 42 minutes total time to cover 7 km = ( 7 Γ’ Β β 10 Γ£ β 60 ) minutes + 42 minutes = 84 minutes answer c" | a ) 80 min . , b ) 70 min . , c ) 84 min . , d ) 55 min . , e ) none of these | c | add(multiply(divide(7, 10), speed(const_60, const_1)), multiply(const_4, 7)) | divide(n1,n0)|multiply(n1,const_4)|speed(const_60,const_1)|multiply(#0,#2)|add(#3,#1)| | physics |
find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 20 is a prime number , when each of the given numbers is equally likely to be selected ? | "let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 } n ( x ) = 8 , n ( s ) = 20 hence , the required probability is 8 / 20 . answer : c" | a ) 10 / 20 , b ) 1 / 20 , c ) 8 / 20 , d ) 3 / 20 , e ) 7 / 20 | c | divide(multiply(3, const_5), 20) | multiply(n2,const_5)|divide(#0,n3)| | probability |
in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio o... | "straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if th... | a ) 100 , b ) 300 , c ) 400 , d ) 3,000 , e ) 4,000 | c | multiply(divide(12, subtract(99, 96)), const_100) | subtract(n3,n0)|divide(n2,#0)|multiply(#1,const_100)| | general |
if two painters can complete two rooms in two hours , how many rooms painted if 10 painters work for 6 hours ? | "explanation : two painters can complete two rooms in two hours . so 30 rooms can be painted in 6 hrs by 10 painters answer : d ) 10 painters" | a ) 35 , b ) 25 , c ) 20 , d ) 30 , e ) 15 | d | divide(multiply(multiply(6, const_3), const_3), multiply(const_3, const_3)) | multiply(n1,const_3)|multiply(const_3,const_3)|multiply(#0,const_3)|divide(#2,#1)| | physics |
what is the probability of getting exactly 2 heads in a single throw of five fair coins ? | "one possible case is hhttt . p ( hhttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 2 = 10 possible cases . p ( 2 heads ) = 10 * 1 / 32 = 5 / 16 the answer is d ." | a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 16 , e ) 11 / 32 | d | divide(const_2, choose(add(const_3, const_3), const_3)) | add(const_3,const_3)|choose(#0,const_3)|divide(const_2,#1)| | probability |
the compound ratio of 2 : 3 , 3 : 4 and 4 : 5 ? | 2 / 3 * 3 / 4 * 4 / 5 = 2 / 5 2 : 5 answer : b | a ) 1 : 2 , b ) 2 : 5 , c ) 3 : 4 , d ) 3 : 5 , e ) 3 : 9 | b | divide(divide(multiply(2, 3), multiply(3, 4)), divide(multiply(3, 4), multiply(const_2.0, 5))) | multiply(n0,n2)|multiply(n1,n3)|multiply(n2,n4)|multiply(const_2.0,n5)|divide(#0,#1)|divide(#2,#3)|divide(#4,#5)| | other |
a certain university will select 2 of 6 candidates eligible to fill a position in the mathematics department and 3 of 5 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidate... | "6 c 2 * 5 c 3 = 15 * 10 = 150 the answer is ( c )" | a ) 42 , b ) 70 , c ) 150 , d ) 165 , e ) 315 | c | multiply(multiply(5, 3), 6) | multiply(n3,n5)|multiply(n1,#0)| | other |
the probability that event b occurs is 0.4 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event a will occur ? | "p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.6 = 0.4 + p ( a ) - 0.25 p ( a ) = 0.45 ans : b" | a ) 0.05 , b ) 0.45 , c ) 0.15 , d ) 0.5 , e ) 0.55 | b | subtract(add(0.25, 0.6), 0.4) | add(n1,n2)|subtract(#0,n0)| | other |
when anunfaircoin is tossed twice , the probability of getting one tails and one heads is 1 / 2 . what is the probability of getting two heads and two tails if the coin is tossed 4 times ? | let the probability of heads be x and the probability of tails be 1 - x . so , we are given that p ( one tails and one heads ) = 2 * x * ( 1 - x ) = 1 / 2 . p ( two heads and two tails ) = 4 ! / ( 2 ! 2 ! ) * x ^ 2 * ( 1 - x ) ^ 2 = 6 * ( x * ( 1 - x ) ) ^ 2 . we are multiplying by 4 ! / ( 2 ! 2 ! ) because hhtt scenar... | a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 9 | e | divide(divide(1, const_1), multiply(add(multiply(1, const_1), 2), const_3)) | divide(n0,const_1)|multiply(n0,const_1)|add(n1,#1)|multiply(#2,const_3)|divide(#0,#3) | general |
amar takes as much time in running 15 meters as a car takes in covering 40 meters . what will be the distance covered by amar during the time the car covers 1.9 km ? | distance covered by amar = 15 / 40 ( 1.9 km ) = 3 / 8 ( 1900 ) = 712 m answer : c | a ) 700 m , b ) 720 m , c ) 712 m , d ) 600 m , e ) 640 m | c | divide(multiply(15, multiply(1.9, const_1000)), 40) | multiply(n2,const_1000)|multiply(n0,#0)|divide(#1,n1) | physics |
at the end of the first quarter , the share price of a certain mutual fund was 25 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 55 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of... | "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 55 = 25 + b + 25 b / 100 b = 24 answer ( a )" | a ) 24 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 40 % | a | multiply(subtract(divide(add(const_100, 55), add(const_100, 25)), const_1), const_100) | add(n1,const_100)|add(n0,const_100)|divide(#0,#1)|subtract(#2,const_1)|multiply(#3,const_100)| | gain |
a marketing firm determined that , of 200 households surveyed , 80 used neither brand e nor brand b soap , 60 used only brand e soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ? | solution for soap e and soap b ( d ) 40 | a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45 | d | divide(subtract(200, 80), 3) | subtract(n0,n1)|divide(#0,n3) | other |
two employees x and y are paid a total of rs . 570 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ? | let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 570 but x = 120 % of y = 120 y / 100 = 12 y / 10 β΄ 12 y / 10 + y = 570 β y [ 12 / 10 + 1 ] = 570 β 22 y / 10 = 570 β 22 y = 5700 β y = 5700 / 22 = rs . 259 a ) | a ) s . 259 , b ) s . 289 , c ) s . 299 , d ) s . 300 , e ) s . 389 | a | divide(multiply(570, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2)) | add(const_1,const_4)|multiply(#0,const_2)|add(#1,const_1)|multiply(n0,#1)|multiply(#2,const_2)|divide(#3,#4) | general |
a train 390 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in : | "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 Γ 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 390 Γ 2 / 15 ) sec = 52 sec answer : e" | a ) 30 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 52 sec | e | multiply(const_3600, divide(divide(390, const_1000), add(25, 2))) | add(n1,n2)|divide(n0,const_1000)|divide(#1,#0)|multiply(#2,const_3600)| | physics |
if 90 % of a = 30 % of b and b = x % of a , then the value of x is ? | "0.9 a = 0.3 b so b = 3 a means 300 % of a answer : b" | a ) 800 , b ) 300 , c ) 700 , d ) 400 , e ) none of these | b | divide(30, 90) | divide(n1,n0)| | general |
data sufficiency question : if solution ( x ) with alcohol ( 14 % ) and solution ( y ) with alcohol ( 20 % ) mixed together to form 24 liters of mixture . | explanation : let a liters of first solution , and ' b ' liters of second solution has been taken . so using weighted average formula = n 1 Γ a 1 + n 2 Γ a 2 n 1 + n 2 n 1 Γ a 1 + n 2 Γ a 2 n 1 + n 2 = n 1 Γ 14 + n 2 Γ 20 n 1 + n 2 = 15 n 1 Γ 14 + n 2 Γ 20 n 1 + n 2 = 15 β n 1 = 5 n 2 β n 1 n 2 = 51 β n 1 = 5 n 2 β n 1... | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 3 | a | divide(add(multiply(multiply(const_0_25, 20), 14), 20), add(multiply(const_0_25, 20), const_1)) | multiply(n1,const_0_25)|add(#0,const_1)|multiply(n0,#0)|add(n1,#2)|divide(#3,#1) | gain |
the average of 6 number is 3.95 . the average of two of them is 3.8 , while the average of the other two is 3.85 . what is the average of the remaining two number ? | solution : sum of the remaining two numbers = ( 3.95 Γ 6 ) - [ ( 3.8 Γ 2 ) + ( 3.85 Γ 2 ) ] = 23.70 - ( 7.6 + 7.7 ) = 23.70 - 15.3 = 8.4 . β΄ required average = 8.4 / 2 = 4.2 answer b | a ) 4.5 , b ) 4.2 , c ) 4.7 , d ) 4.8 , e ) none of these | b | divide(subtract(multiply(3.95, 6), add(multiply(3.8, const_2), multiply(3.85, const_2))), const_2) | multiply(n0,n1)|multiply(n2,const_2)|multiply(n3,const_2)|add(#1,#2)|subtract(#0,#3)|divide(#4,const_2) | general |
a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points q that an individual player might have scored ? | general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum nu... | a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23 | e | add(subtract(100, multiply(12, 7)), 7) | multiply(n0,n2)|subtract(n1,#0)|add(n2,#1) | general |
jill has 7 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ? | let the number of each size of jar = w then 1 / 4 w + 1 / 2 w + w = 7 1 3 / 4 w = 7 w = 4 the total number of jars = 3 w = 12 answer : d | a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 14 | d | multiply(divide(7, add(const_1, add(const_0_25, divide(const_1, const_2)))), const_3) | divide(const_1,const_2)|add(#0,const_0_25)|add(#1,const_1)|divide(n0,#2)|multiply(#3,const_3) | general |
the sum of ages of 5 children born 2 years different each is 50 yrs . what is the age of the elder child ? | let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 50 5 x = 30 x = 6 x + 8 = 6 + 8 = 14 answer : b | a ) 8 , b ) 14 , c ) 16 , d ) 17 , e ) 18 | b | divide(add(add(add(add(2, const_4), add(2, const_4)), add(const_4, const_4)), 50), 5) | add(n1,const_4)|add(const_4,const_4)|add(#0,#0)|add(#2,#1)|add(n2,#3)|divide(#4,n0) | general |
vijay sells a cupboard at 14 % below cost price . had he got rs . 2086 more , he would have made a profit of 14 % . what is the cost price of the cupboard ? | "explanation : cost price = 2086 / ( 0.14 + 0.14 ) = 2086 / 0.28 = rs . 7450 answer : c" | a ) 7458 , b ) 7456 , c ) 7450 , d ) 7454 , e ) 7453 | c | divide(2086, divide(subtract(add(const_100, 14), subtract(const_100, 14)), const_100)) | add(n0,const_100)|subtract(const_100,n0)|subtract(#0,#1)|divide(#2,const_100)|divide(n1,#3)| | gain |
we bought a total of 80 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 390 . how many math books did we buy ? | "m + h = 80 h = 80 - m 4 m + 5 h = 390 4 m + 5 * ( 80 - m ) = 390 m = 10 the answer is a ." | a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50 | a | subtract(80, subtract(390, multiply(80, 4))) | multiply(n0,n1)|subtract(n3,#0)|subtract(n0,#1)| | general |
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 | "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 36 = > 4 / x = 1 / 36 x = 36 Γ’ Λ β 4 = 144 mins answer is a" | a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 132 mins , e ) 130 mins | a | multiply(add(const_1, const_4), 36) | add(const_1,const_4)|multiply(n0,#0)| | physics |
a hall 36 m long and 15 m broad is to be paved with stones , each measuring 6 dm by 5 dm . the number of stones required is : | "area of the hall = 3600 * 1500 area of each stone = ( 60 * 50 ) therefore , number of stones = ( 3600 * 1500 / 60 * 50 ) = 1800 answer : b" | a ) 180 , b ) 1800 , c ) 18 , d ) 18000 , e ) 1.8 | b | divide(multiply(36, 15), divide(multiply(6, 5), const_100)) | multiply(n0,n1)|multiply(n2,n3)|divide(#1,const_100)|divide(#0,#2)| | physics |
walking with 4 / 5 of my usual speed , i arrive at the bus stop 10 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ? | "let t = usual time = distance / usual speed t + 10 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 40 the answer is c ." | a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48 | c | divide(10, subtract(divide(5, 4), const_1)) | divide(n1,n0)|subtract(#0,const_1)|divide(n2,#1)| | physics |
eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 480 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy :... | "distance traveled by eddy = 480 km time taken by eddy = 3 hours average speed of eddy = 480 / 3 = 160 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 160 / 75 = 32 / 15 answer a" | a ) 32 / 15 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 5 / 3 | a | divide(divide(480, 3), divide(300, 4)) | divide(n2,n0)|divide(n3,n1)|divide(#0,#1)| | physics |
a pharmaceutical company received $ 2 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ? | "( 9 / 108 ) / ( 2 / 20 ) = 30 / 54 = 55,5 % it means that 9 / 108 represents only 83,3 % . therefore a decrease of 15 % . answer b" | a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 % | b | multiply(divide(2, 20), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
ram , who is half as efficient as krish , will take 24 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ? | "answer ram takes 24 days to complete the task , if he works alone . krish is twice as efficient as ram is . so , working alone , krish will take half the time to complete the task . i . e . , 12 days . ram will complete 1 / 24 th of the task in a day . krish will complete 1 / 12 th of the task in a day . when they wor... | a ) 16 days , b ) 12 days , c ) 8 days , d ) 6 days , e ) 18 days | c | inverse(add(divide(const_1, 24), divide(const_1, divide(24, const_2)))) | divide(const_1,n0)|divide(n0,const_2)|divide(const_1,#1)|add(#0,#2)|inverse(#3)| | physics |
i bought two books ; for rs . 540 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ? | "x * ( 85 / 100 ) = ( 540 - x ) 119 / 100 x = 315 answer : e" | a ) 197 , b ) 280 , c ) 189 , d ) 278 , e ) 315 | e | divide(multiply(540, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19))) | add(n2,const_100)|subtract(const_100,n1)|add(#0,#1)|multiply(n0,#0)|divide(#3,#2)| | gain |
a sum of money deposited at c . i . amounts to rs . 1980 in 3 years and to rs . 2492 in 4 years . find the rate percent ? | "1980 - - - 512 100 - - - ? = > 25 % answer : c" | a ) 30 % , b ) 10 % , c ) 25 % , d ) 19 % , e ) 50 % | c | multiply(divide(subtract(2492, 1980), 1980), const_100) | subtract(n2,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
what is the greatest possible length which can be used to measure exactly the lengths 10 m , 14 m 50 cm and 20 m 40 cm cm ? | "required length = hcf of 1000 cm , 1450 cm , 2040 cm = 10 cm answer is b" | a ) 20 cm , b ) 10 cm , c ) 25 cm , d ) 50 cm , e ) 28 cm | b | multiply(20, const_4) | multiply(n3,const_4)| | physics |
an alloy weighing 18 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ? | "in 24 ounces , gold is 18 * ( 70 / 100 ) = 12.6 ounces . now we add x ounces of pure gold to make it 90 % gold . so 12.6 + x = ( 24 + x ) * 90 / 100 = > x = 90 . answer is b ." | a ) 6 , b ) 90 , c ) 12 , d ) 24 , e ) 48 | b | divide(multiply(divide(90, const_100), 18), divide(70, const_100)) | divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|divide(#2,#1)| | gain |
john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 55 miles per hour , what is v in miles per hour ? | "hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 55 = > v = 50... | a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70 | c | multiply(subtract(const_100, 80), subtract(divide(const_100, 55), divide(80, 80))) | divide(const_100,n2)|divide(n0,n0)|subtract(const_100,n0)|subtract(#0,#1)|multiply(#2,#3)| | physics |
a train 400 m long can cross an electric pole in 40 sec and then find the speed of the train ? | "length = speed * time speed = l / t s = 400 / 40 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : a" | a ) 36 kmph , b ) 40 kmph , c ) 42 kmph , d ) 45 kmph , e ) 38 kmph | a | divide(divide(400, const_1000), divide(40, const_3600)) | divide(n0,const_1000)|divide(n1,const_3600)|divide(#0,#1)| | physics |
a train 220 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is : | "speed of the train relative to man = 220 / 20 = 11 m / sec . = 11 x 18 / 5 km / hr = 198 / 5 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 198 / 540.6 km / hr . answer : b" | a ) 41 , b ) 40.6 , c ) 40.8 , d ) 42 , e ) 42.6 | b | divide(divide(subtract(220, multiply(multiply(5, const_0_2778), 5)), 5), const_0_2778) | multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n1)|divide(#3,const_0_2778)| | physics |
the price of a certain painting increased by 10 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ? | "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 10 = 110 price at the end of year 2 = 110 - 110 * 0.15 = 110 * 0.85 = 93.5 hence required answer = ( 93.5 / 100 ) * 100 % = 93.5 % answer is d ." | a ) 102 % , b ) 105 % , c ) 95 % , d ) 93.5 % , e ) 90 % | d | add(subtract(subtract(10, 15), divide(multiply(15, 10), const_100)), const_100) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,const_100)|subtract(#1,#2)|add(#3,const_100)| | general |
two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 16 seconds . the length of the faster train is | "solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 16 ) m = 360 m . answer e" | a ) 80 m , b ) 100 m , c ) 120 m , d ) 180 m , e ) none | e | multiply(multiply(add(36, 45), const_0_2778), 16) | add(n0,n1)|multiply(#0,const_0_2778)|multiply(n2,#1)| | physics |
a and b began business with rs . 7000 and rs . 15000 after 6 months , a advances rs . 3000 and b withdraws rs . 5000 . at the end of the year , their profits amounted to rs . 2940 find the share of a and b respectively . | "7 * 6 + 10 * 6 ) : ( 15 * 6 + 10 * 6 ) = 102 : 150 = 51 : 75 = 17 : 25 17 : 25 a ' s share = 17 / 42 * 2940 = 1190 . b ' s share = 25 / 42 * 2940 = 1750 . a and b shares respectively 1190 and 1750 . answer : d" | a ) 1100 , 1750 , b ) 1140 , 1800 , c ) 940 , 2000 , d ) 1190 , 1750 , e ) 1000 : 1690 | d | multiply(divide(2940, add(add(multiply(7000, 6), multiply(subtract(7000, 3000), subtract(const_12, 6))), add(multiply(15000, 6), multiply(add(15000, 3000), subtract(const_12, 6))))), add(multiply(7000, 6), multiply(subtract(7000, 3000), subtract(const_12, 6)))) | add(n1,n3)|multiply(n0,n2)|multiply(n1,n2)|subtract(n0,n3)|subtract(const_12,n2)|multiply(#3,#4)|multiply(#0,#4)|add(#1,#5)|add(#2,#6)|add(#7,#8)|divide(n5,#9)|multiply(#7,#10)| | gain |
in country z , 10 % of the people do not have a university diploma but have the job of their choice , and 15 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ? | "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 10 % job of choice total = 40 % not job of choice with diploma = . 15 x not job of choice w / o diploma = . 85 x total not job of choice = x total with diploma total without diploma total cit... | a ) 39 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 % | a | add(divide(multiply(15, subtract(const_100, 40)), const_100), subtract(40, 10)) | subtract(const_100,n2)|subtract(n2,n0)|multiply(n1,#0)|divide(#2,const_100)|add(#3,#1)| | gain |
the present worth of rs . 676 due in 2 years at 4 % per annum compound interest is | solution present worth = rs . [ 676 / ( 1 + 4 / 100 ) Β² ] = rs . ( 676 x 25 / 26 x 25 / 26 ) = rs . 625 answer d | a ) rs . 150.50 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 625 , e ) none | d | divide(676, power(add(divide(4, const_100), const_1), 2)) | divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|divide(n0,#2) | gain |
a shopkeeper sold an article for rs 2591.36 . approximately what was his profit percent if the cost price of the article was rs 2400 | "explanation : gain % = ( 191.36 * 100 / 2400 ) = 7.97 % = 8 % approx option d" | a ) 4 % , b ) 5 % , c ) 6 % , d ) 8 % , e ) 10 % | d | floor(multiply(const_100, divide(subtract(2591.36, 2400), 2400))) | subtract(n0,n1)|divide(#0,n1)|multiply(#1,const_100)|floor(#2)| | gain |
dacid obtained 86 , 89 , 82 , 87 and 81 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ? | "average = ( 86 + 89 + 82 + 87 + 81 ) / 5 = 425 / 5 = 85 . answer : d" | a ) 79 , b ) 99 , c ) 88 , d ) 85 , e ) 75 | d | divide(add(add(add(add(86, 89), 82), 87), 81), divide(const_10, const_2)) | add(n0,n1)|divide(const_10,const_2)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)| | general |
the product of two positive integers is 783 and their difference is 2 . what is the bigger number ? | "let ' s use trial and error to find the two numbers . 30 * 28 = 840 ( too high ) 29 * 27 = 783 the answer is d ." | a ) 23 , b ) 25 , c ) 27 , d ) 29 , e ) 31 | d | subtract(add(multiply(divide(783, divide(783, 2)), const_4), const_10), const_1) | divide(n0,n1)|divide(n0,#0)|multiply(#1,const_4)|add(#2,const_10)|subtract(#3,const_1)| | general |
matt gets a $ 1,000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 700 , how many sales has matt made ? | "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 700 = 150 + x i . e . ... | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | a | divide(subtract(1,000, const_100), subtract(700, subtract(700, 150))) | subtract(n0,const_100)|subtract(n2,n1)|subtract(n2,#1)|divide(#0,#2)| | general |
water is poured into a cylindrical well at the rate of 22 cubic meters per hour , the level of water in the tank rises at a rate of 0.7 meters per hour . which of the following best approximates the diameter of the tank in meters ? | here ' s my re - worked solution : volume = 22 = pi ( r ^ 2 ) ( 0.7 ) 22 = 22 / 7 ( 7 / 10 ) ( r ^ 2 ) 10 = r ^ 2 r = sqrt ( 10 ) diameter = 2 * sqrt ( 10 ) ans : c | ['a ) β 10 / 2', 'b ) β 10', 'c ) 2 β 10', 'd ) 5', 'e ) 10'] | c | multiply(sqrt(divide(divide(22, const_pi), 0.7)), const_2) | divide(n0,const_pi)|divide(#0,n1)|sqrt(#1)|multiply(#2,const_2) | physics |
how many different 3 - digit multiples of 5 can be composed of digits 1 , 2 , 3 , 4 , and 5 if none of the digits is repeated ? | can you explain your method . i solved it differently xyz , where z must be 5 . therefore 1 variation of digit in z . y can be any of the 4 possible choices . x can be any of the 3 possible choices . 4 + 3 + 1 = 8 c | a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 18 | c | subtract(multiply(4, 3), 4) | multiply(n0,n5)|subtract(#0,n5) | general |
a student finds the sum 1 + 2 + 3 + . . . as his patience runs out . he found the sum as 575 . when the teacher declared the result wrong , the student realized that he missed a number . what was the number the student missed ? | explanation : sum of 1 st 10 natural numbers ( 1 β 10 ) = 1 + 2 + β¦ 10 = 55 . sum of next 10 natural numbers ( 11 β 20 ) = 10 + 11 + 12 + β¦ 20 = 100 + 55 = 155 . sum of next 10 natural numbers ( 31 β 40 ) = 255 . sum of numbers from 31 β 40 = 355 and so on and on . so , we have here 55 + 155 + 255 = 465 . if we add 355... | a ) 16 , b ) 18 , c ) 14 , d ) 20 , e ) 22 | d | subtract(divide(multiply(add(floor(divide(subtract(sqrt(add(multiply(multiply(575, 2), const_4), 1)), 1), const_2)), 1), add(add(floor(divide(subtract(sqrt(add(multiply(multiply(575, 2), const_4), 1)), 1), const_2)), 1), 1)), 2), 575) | multiply(n1,n3)|multiply(#0,const_4)|add(n0,#1)|sqrt(#2)|subtract(#3,n0)|divide(#4,const_2)|floor(#5)|add(n0,#6)|add(n0,#7)|multiply(#7,#8)|divide(#9,n1)|subtract(#10,n3) | general |
dhoni spends $ 300 buying his favorite dolls . if he buys only small monkey dolls , which are $ 2 cheaper than the large monkey dolls , he could buy 25 more dolls than if he were to buy only large monkey dolls . how much does a large monkey doll cost ? | a is not an integer . so we start with b . if large doll costs $ 6 , then he can buy 300 / 6 = 50 large dolls and 300 / 4 = 75 small dolls . difference is 25 , which is we wanted . answer b . | a ) $ 6.5 , b ) $ 6 , c ) $ 7 , d ) $ 8 , e ) $ 9 | b | divide(divide(300, 25), 2) | divide(n0,n2)|divide(#0,n1) | general |
set x consists of 5 integers and has median of 20 and a range of 20 . what is the value of the greatest possible integer that can be present in the set ? | "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between an... | a ) 20 , b ) 37 , c ) c . 40 , d ) 43 , e ) 50 | a | add(20, 20) | add(n1,n2)| | general |
find the principle on a certain sum of money at 8 % per annum for 2 2 / 5 years if the amount being rs . 1120 ? | "1120 = p [ 1 + ( 8 * 12 / 5 ) / 100 ] p = 939.60 answer : a" | a ) 939.6 , b ) 928.8 , c ) 927.78 , d ) 926.82 , e ) 902.1 | a | divide(1120, add(divide(multiply(divide(add(multiply(2, 5), 2), 5), 8), 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 |
a shopkeeper sold an article offering a discount of 5 % and earned a profit of 21.6 % . what would have been the percentage of profit earned if no discount was offered ? | "let c . p . be rs . 100 . then , s . p . = rs . 121.60 let marked price be rs . x . then , 95 / 100 x = 121.60 x = 12160 / 95 = rs . 128 now , s . p . = rs . 128 , c . p . = rs . 100 profit % = 28 % . answer : b" | a ) 60 % , b ) 28 % , c ) 30 % , d ) 56 % , e ) 73 % | b | subtract(divide(multiply(add(const_100, 21.6), const_100), subtract(const_100, 5)), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,const_100)|divide(#2,#1)|subtract(#3,const_100)| | gain |
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 10 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is : | "explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 10 ) + 6000 ( v - 10 ) < = > 2000 v = 60000 < = > v = 30 answer : d ) 30" | a ) 22 , b ) 21 , c ) 88 , d ) 30 , e ) 29 | d | add(10, divide(multiply(10, subtract(12000, 8000)), subtract(8000, 6000))) | subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)| | general |
in a kilometer race , a beats b by 100 meters or 10 seconds . what time does a take to complete the race ? | "time taken by b run 1000 meters = ( 1000 * 10 ) / 100 = 100 sec . time taken by a = 100 - 10 = 90 sec . answer : a" | a ) 90 sec , b ) 190 sec , c ) 290 sec , d ) 490 sec , e ) 390 sec | a | subtract(divide(multiply(const_1, const_1000), divide(100, 10)), 10) | divide(n0,n1)|multiply(const_1,const_1000)|divide(#1,#0)|subtract(#2,n1)| | physics |
a space shuttle orbits the earth at about 4 kilometers per second . this speed is equal to how many kilometers per hour ? | "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 4 * 3600 = 14,400 answer : b" | a ) 480 , b ) 14,400 , c ) 24,200 , d ) 28,800 , e ) 48,000 | b | multiply(4, const_3600) | multiply(n0,const_3600)| | physics |
what is the remainder when 14452 Γ 15652 Γ 16781 is divided by 5 ? | only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 2 * 2 * 1 = will give units digit as 4 so , whatever be the number , if it ends in 4 , the remainder after dividing with 5 will be 4 . optione | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | e | reminder(multiply(multiply(14452, 15652), 16781), 5) | multiply(n0,n1)|multiply(n2,#0)|reminder(#1,n3) | general |
a jar contains only red , yellow , and orange marbles . if there are 3 red , 3 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? | "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so... | a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22 | c | divide(multiply(choose(3, 2), choose(3, 1)), choose(add(add(3, 4), 3), 3)) | add(n1,n2)|choose(n1,n4)|choose(n0,n5)|add(n0,#0)|multiply(#1,#2)|choose(#3,n0)|divide(#4,#5)| | probability |
there are 2 friends peter and paul . peter age is twice as old as paul when peter was as old as paul is now . sum of the present ages of peter and paul is 35 . what is the present age of peter ? | let pauls age be ' a ' and peters be ' e ' e + a = 35 ( given ) e = 35 - a - - - - - - eq 1 when peter was as old as paul that is when peter ' s age was ' a ' pauls age was a - ( e - a ) = 2 a - e now peters age is e = 2 ( 2 a - e ) e = 4 a - 2 e 3 e = 4 a 3 ( 35 - a ) = 4 a 105 - 3 a = 4 a a = 15 hence e = 20 answer :... | a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30 | c | multiply(divide(35, add(const_4, const_3)), const_4) | add(const_3,const_4)|divide(n1,#0)|multiply(#1,const_4) | general |
the area of a parallelogram is 162 sq m and its altitude is twice the corresponding base . then the length of the base is ? | "2 x * x = 162 = > x = 9 answer : b" | a ) 8 , b ) 9 , c ) 7 , d ) 62 , e ) 2 | b | sqrt(divide(162, const_2)) | divide(n0,const_2)|sqrt(#0)| | geometry |
34 . the side surface of a cylinder is rolled with a rectangular plate . if the height of a cylinder tank is 10 feet and the perimeter of the circular base is 4 feet , what is the area of the rectangular plate ? | think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both you can multiply them together to find the area , 40 . ( correct answer d ) | a ) 24 , b ) 34 , c ) 28 , d ) 40 , e ) 14 | d | sqrt(subtract(power(4, const_2), power(10, const_2))) | power(n2,const_2)|power(n1,const_2)|subtract(#0,#1)|sqrt(#2)| | geometry |
8 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ? | "x * ( 92 / 100 ) * ( 85 / 100 ) = 3553 x = 4543 answer : b" | a ) 2988 , b ) 4543 , c ) 4400 , d ) 2871 , e ) 881 | b | floor(divide(3553, multiply(divide(subtract(const_100, 8), const_100), divide(subtract(const_100, 15), const_100)))) | subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|divide(n2,#4)|floor(#5)| | general |
57 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 ? | "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 57 x 12 x 5 = 30 x 6 x x x = 19 hence , the number of days = 19 . answer : e" | a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 19 | e | divide(multiply(multiply(57, 12), 5), multiply(30, 6)) | multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|divide(#2,#1)| | physics |
how many plants will be there in a circular bed whose outer edge measure 30 cms , allowing 4 cm 2 for each plant ? | "circumference of circular bed = 30 cm area of circular bed = ( 30 ) 2 β 4 Ο space for each plant = 4 cm 2 β΄ required number of plants = ( 30 ) 2 β 4 Ο Γ· 4 = 17.89 = 18 ( approx ) answer a" | a ) 18 , b ) 750 , c ) 24 , d ) 120 , e ) none of these | a | divide(circle_area(divide(30, multiply(2, const_pi))), 4) | multiply(n2,const_pi)|divide(n0,#0)|circle_area(#1)|divide(#2,n1)| | physics |
the product z of two prime numbers is between 20 and 60 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 18 but less than 36 then what is z ? | "the smallest possible product is 57 which is 3 * 19 . all other products are too big . the answer is e ." | a ) 21 , b ) 35 , c ) 39 , d ) 51 , e ) 57 | e | multiply(subtract(20, const_4), const_3) | subtract(n0,const_4)|multiply(#0,const_3)| | general |
a boat goes 100 km downstream in 10 hours , and 60 m upstream in 15 hours . the speed of the stream is ? | "100 - - - 10 ds = 10 ? - - - - 1 60 - - - - 15 us = 4 ? - - - - - 1 s = ( 10 - 4 ) / 2 = 3 kmp answer : a" | a ) 3 , b ) 22 1 / 4 , c ) 22 1 / 2 , d ) 22 1 / 1 , e ) 22 1 / 3 | a | divide(subtract(divide(100, 10), divide(60, 15)), const_2) | divide(n0,n1)|divide(n2,n3)|subtract(#0,#1)|divide(#2,const_2)| | physics |
in how many ways can 16 different gifts be divided among 4 children such that each child receives exactly two gifts ? | total 16 different gifts , and 4 children . thus any one child gets 16 c 2 gifts , then the other child gets 14 c 2 gifts ( 16 total - 2 already given ) , then the third one gets 12 c 2 gifts , and the last child gets 10 c 2 gifts . since order in which each child gets the gift is not imp , thus , ans : 16 c 2 * 14 c 2... | a ) 16 ^ 4 , b ) ( 4 ! ) ^ 4 , c ) 16 ! / ( 2 ! ) ^ 4 , d ) 16 ! / 2 ! , e ) 4 ^ 16 | c | divide(divide(factorial(16), power(const_2, 4)), divide(factorial(16), power(const_2, 4))) | factorial(n0)|power(const_2,n1)|divide(#0,#1)|divide(#2,#2) | general |
how many different values of positive integer x , for which | x + 4 | < x , are there ? | answer d i opted to put the random value option . i used 0 , 4 , - 4 and the the extreme of 60 and - 60 . . i was able to solve it in 1 : 09 d | a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16 | d | add(4, const_4) | add(n0,const_4) | general |
at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 15 employees are trained to work in the family buffet , 18 are trained to work in the dinin... | "39 = 15 + 18 + 12 - 4 - 2 x 2 x = 15 + 18 + 12 - 4 - 39 = 41 - 39 = 2 x = 1 e" | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 1 | e | divide(subtract(subtract(add(add(15, 18), 12), 4), 39), 2) | add(n4,n5)|add(n6,#0)|subtract(#1,n7)|subtract(#2,n0)|divide(#3,n8)| | physics |
the edges of a cuboid are 2 cm , 5 cm and 3 cm . find the volume of the cuboid ? | 2 * 5 * 3 = 30 answer : d | ['a ) 20', 'b ) 60', 'c ) 80', 'd ) 30', 'e ) 45'] | d | volume_rectangular_prism(2, 5, 3) | volume_rectangular_prism(n0,n1,n2) | physics |
a computer manufacturer produces a certain electronic component at a cost of $ 60 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces... | "this question can be solved easily using a equation model . 150 * p = 16500 ( fixed cost ) + 150 * 60 + 150 * 2 . = 16500 + 9000 + 300 = p = $ 172 . c" | a ) $ 28 , b ) $ 82 , c ) $ 172 , d ) $ 138 , e ) $ 192 | c | divide(add(add(multiply(multiply(const_4, const_4), const_1000), multiply(2, const_100)), multiply(add(60, 2), 150)), 150) | add(n0,n1)|multiply(const_4,const_4)|multiply(n1,const_100)|multiply(#1,const_1000)|multiply(n3,#0)|add(#3,#2)|add(#5,#4)|divide(#6,n3)| | general |
a beaker contains 180 liters of alcohol . on 1 st day , 60 l of alcohol is taken out and replaced by water . 2 nd day , 60 l of mixture iss taken out and replaced by water and the process continues day after day . what will be the quantity of alcohol in beaker after 3 days | use the formula , final alcohol = initial alcohol Γ ( 1 β replacementquantityfinalvolume ) n Γ ( 1 β replacementquantityfinalvolume ) n final alcohol = 180 ( 1 β 60180 ) 3180 ( 1 β 60180 ) 3 = 180 Γ ( 23 ) 3 = 53.3 ans : a | a ) 53.3 , b ) 53.8 , c ) 53.7 , d ) 53.5 , e ) 353.3 | a | multiply(180, power(subtract(1, divide(60, 180)), 3)) | divide(n2,n0)|subtract(n1,#0)|power(#1,n5)|multiply(n0,#2) | physics |
how many two - digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6 ? | the possible number n can be written as follow : n = multiple of lcm ( 6,10 ) + 1 st such number n = 30 x + 1 possible values = 1 , 31 , 61 , 91 answer : 3 such 2 digit number . answer : d | a ) none , b ) one , c ) two , d ) three , e ) four | d | add(add(const_1, const_1), 1) | add(const_1,const_1)|add(n0,#0) | general |
how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 150 m in length ? | "d = 110 + 150 = 260 m s = 60 * 5 / 18 = 50 / 3 t = 260 * 3 / 50 = 15.6 sec answer : d" | a ) sec , b ) sec , c ) sec , d ) sec , e ) sec | d | divide(add(110, 150), multiply(60, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | physics |
a car travels uphill at 30 km / hr and downhill at 70 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ? | avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 7 ; avg speed = 150 / ( 10 / 3 + 5 / 7 ) = 37 kmph answer : e | a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 37 kmph | e | divide(add(100, 50), add(divide(100, 30), divide(50, 70))) | add(n2,n3)|divide(n2,n0)|divide(n3,n1)|add(#1,#2)|divide(#0,#3) | general |
in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 75 % of the total ? | "answer is d : 687 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 75 % of total is 515 , so 100 % is approx . 687 ." | a ) 515 . , b ) 545 . , c ) 618 . , d ) 687 . , e ) 666 . | d | add(226, 423) | add(n0,n1)| | general |
in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 77 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ? | "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 77 , s... | a ) 550 , b ) 245 , c ) 150 , d ) 35 , e ) 350 | a | divide(77, multiply(divide(subtract(const_100, 30), const_100), divide(20, const_100))) | divide(n0,const_100)|subtract(const_100,n1)|divide(#1,const_100)|multiply(#2,#0)|divide(n2,#3)| | gain |
if x = 1 + β 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 1 ? | "answer x = 1 + β 2 β΄ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 1 = x 2 ( x - 2 ) 2 + 1 = ( 1 + β 2 ) 2 ( 1 + β 2 - 2 ) 2 + 1 = ( β 2 + 1 ) 2 ( β 2 - 1 ) 2 + 1 = [ ( β 2 ) 2 - ( 1 ) 2 ] 2 + 1 = ( 2 - 1 ) 2 = 1 + 1 = 2 correct option : d" | a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3 | d | add(multiply(power(add(1, sqrt(2)), 2), power(subtract(add(1, sqrt(2)), 2), 2)), 4) | sqrt(n1)|add(n0,#0)|power(#1,n1)|subtract(#1,n1)|power(#3,n1)|multiply(#2,#4)|add(n2,#5)| | general |
vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ? | vlaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement . 2 candles from 4 candles : 4 c 2 : 6 8 flowers from 9 flowers : 9 c 8 : 9 so total grouping 9 * 6 = 54 . answer is a . | a ) 54 , b ) 72 , c ) 96 , d ) 144 , e ) 432 | a | multiply(divide(factorial(9), factorial(8)), divide(factorial(4), multiply(const_2, const_2))) | factorial(n2)|factorial(n1)|factorial(n0)|multiply(const_2,const_2)|divide(#0,#1)|divide(#2,#3)|multiply(#4,#5) | general |
how many odd integers from 1 to 100 ( both inclusive ) have odd number of factors ? | integers having odd number of factors will be perfect squares . odd numbers will have odd perfect squares . thus , the possible values for the perfect squares are : 1 , 9,25 , 49,81 and the corresponding integers are 1 , 3,5 , 7,9 ( more than 4 ) . thus c is the correct answer . | a ) 13 , b ) 14 , c ) 5 , d ) 6 , e ) 7 | c | subtract(subtract(divide(divide(100, const_2), const_2), const_10), const_10) | divide(n1,const_2)|divide(#0,const_2)|subtract(#1,const_10)|subtract(#2,const_10) | other |
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