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
values |
|---|---|---|---|---|---|---|
5 + 8 | b | a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2 | b | multiply(divide(5, 8), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
how many integers between 324,700 and 418,600 have tens digit 1 and units digit 3 ? | "the integers are : 324,713 324,813 etc . . . 418,513 the number of integers is 4186 - 3247 = 939 the answer is c ." | a ) 652 , b ) 827 , c ) 939 , d ) 1045 , e ) 1136 | c | subtract(418,600, add(add(multiply(const_2, const_100), multiply(add(const_3, const_4), const_10)), const_2)) | add(const_3,const_4)|multiply(const_100,const_2)|multiply(#0,const_10)|add(#1,#2)|add(#3,const_2)|subtract(n1,#4)| | general |
a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 250 . find the total worth of the stock ? | "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 250 = > x = 12500 answer : a" | a ) 12500 , b ) 20000 , c ) 20289 , d ) 20027 , e ) 20026 | a | divide(250, subtract(multiply(divide(5, const_100), divide(subtract(const_100, 20), const_100)), multiply(divide(10, const_100), divide(20, const_100)))) | divide(n2,const_100)|divide(n1,const_100)|divide(n0,const_100)|subtract(const_100,n0)|divide(#3,const_100)|multiply(#1,#2)|multiply(#0,#4)|subtract(#6,#5)|divide(n3,#7)| | gain |
two spherical balls lie on the ground touching . if one of the balls has a radius of 5 cm , and the point of contact is 7 cm above the ground , what is the radius of the other ball ? | "similar triangle properties . . 2 / r + 5 = 5 / r - 5 giving r = 35 / 3 . answer : c" | a ) 10 cm , b ) 25 / 2 cm , c ) 35 / 3 cm , d ) 15 cm , e ) none of the these | c | add(add(5, 7), 5) | add(n0,n1)|add(#0,n0)| | physics |
a couple spent $ 158.40 in total while dining out and paid this amount using a credit card . the $ 158.40 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ? | "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 158.40 x = 120 the correct answer is b ." | a ) $ 115 , b ) $ 120 , c ) $ 125 , d ) $ 130 , e ) $ 135 | b | divide(multiply(divide(multiply(158.40, const_100), add(const_100, 20)), const_100), add(const_100, 10)) | add(n2,const_100)|add(n3,const_100)|multiply(n0,const_100)|divide(#2,#0)|multiply(#3,const_100)|divide(#4,#1)| | general |
we have a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 120 inches and the width is 108 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ? | l = 120 / 12 = 10 ft w = 108 / 12 = 9 ft area of paper = 90 area of cube = 10 * side ^ 2 side of cube = 5 v of cube = 125 | ['a ) a 125', 'b ) b 120', 'c ) c 70', 'd ) d 40', 'e ) e 10'] | a | add(cube_edge_by_volume(120), 120) | cube_edge_by_volume(n0)|add(n0,#0) | geometry |
in the xy - coordinate system , if ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 3 , then k = | "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 3 and m + 2 = 2 * ( n + k ) + 3 . by 1 st equation we have m - 2 n = 3 and by 2 nd equation m - 2 n = 2 k + 1 - - - > 3 = 2 k + 1 - - - > k = 1 . the answer is , therefore , ( b ) ." | a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4 | b | divide(subtract(add(3, 2), 3), 2) | add(n0,n2)|subtract(#0,n2)|divide(#1,n1)| | general |
when positive integer x is divided by positive integer y , the remainder is 5 . if x / y = 96.2 , what is the value of y ? | "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.2 and remainder is 5 so . 2 x y = 5 hence y = 25 ans d" | a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12 | d | divide(5, subtract(96.2, floor(96.2))) | floor(n1)|subtract(n1,#0)|divide(n0,#1)| | general |
a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 3.5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ? | "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 3.5 = 5040 . answer : b" | a ) 5729 , b ) 5040 , c ) 2889 , d ) 2870 , e ) 2799 | b | divide(multiply(3.5, multiply(8, const_60)), subtract(divide(multiply(8, const_60), multiply(6, const_60)), const_1)) | multiply(n2,const_60)|multiply(n0,const_60)|divide(#0,#1)|multiply(n1,#0)|subtract(#2,const_1)|divide(#3,#4)| | physics |
what is the greater of the two numbers whose product is 2048 , given that the sum of the two numbers exceeds their difference by 64 ? | "let the greater and the smaller number be g and s respectively . gs = 2048 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2048 / s = 64 . answer : c" | a ) a ) 90 , b ) b ) 32 , c ) c ) 64 , d ) d ) 70 , e ) of these | c | divide(2048, multiply(power(const_2, const_4), const_2)) | power(const_2,const_4)|multiply(#0,const_2)|divide(n0,#1)| | general |
a can finish a work in 6 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ? | "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 6 b ' s 1 day work = 1 / 3 [ because b take half the time than a... | a ) 1 / 2 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 8 , e ) none of these | a | add(divide(const_1, 6), multiply(divide(const_1, 6), const_2)) | divide(const_1,n0)|multiply(#0,const_2)|add(#0,#1)| | physics |
a car averages 35 miles per hour for the first 4 hours of a trip and averages 53 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 50 miles per hour , how many hours long is the trip ? | "let t be the total time of the trip . 35 * 4 + 53 ( t - 4 ) = 50 t 3 t = 212 - 140 t = 24 the answer is e ." | a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24 | e | add(divide(subtract(multiply(50, 4), multiply(35, 4)), subtract(53, 50)), 4) | multiply(n1,n3)|multiply(n0,n1)|subtract(n2,n3)|subtract(#0,#1)|divide(#3,#2)|add(n1,#4)| | physics |
8 men , working 9 hours a day can complete a work in 24 days . how many hours a day must 12 men work to complete the same work in 16 days ? | "the number of hours required to complete the work is 8 * 9 * 24 = 1728 12 × 16 × ( x ) = 1728 x = 9 the answer is d ." | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | d | divide(multiply(multiply(8, 9), 24), multiply(12, 16)) | multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|divide(#2,#1)| | physics |
what percent of 13 is 13 percent of 1 ? | "13 % of 1 = ( 13 / 100 ) * 1 = 13 / 100 to determine what percentage of 13 this is : [ 13 ] [ / 100 * 13 ] * 100 = 1 % ans : c" | a ) 0.001 , b ) 0.01 , c ) 1 , d ) 10 , e ) 101 . | c | p_after_gain(13, 13) | p_after_gain(n1,n0)| | gain |
the volume of a cube is 1000 cc . find its surface . | "a 3 = 1000 = > a = 10 6 a 2 = 6 * 10 * 10 = 600 answer : d" | a ) 864 , b ) 556 , c ) 255 , d ) 600 , e ) 267 | d | surface_cube(cube_edge_by_volume(1000)) | cube_edge_by_volume(n0)|surface_cube(#0)| | geometry |
the speed of a boat in still water is 24 kmph . what is the speed of the stream if the boat can cover 64 km downstream or 32 km upstream in the same time ? | "x = the speed of the stream ( 24 + x ) / ( 24 - x ) = 2 / 1 24 + x = 48 - 2 x 3 x = 24 x = 8 km / hour if the speed of the stream is 8 km / hour , then the ' downstream ' speed of the boat is 24 + 8 = 32 km / hour and the ' upstream ' speed of the boat is 24 - 8 = 16 km / hour . in that way , if the boat traveled for ... | a ) 8 kmph , b ) 6 kmph , c ) 7 kmph , d ) 5 kmph , e ) 4 kmph | a | divide(24, add(const_1, const_2)) | add(const_1,const_2)|divide(n0,#0)| | physics |
a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number m is | "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb... | a ) 74 , b ) m = 75 , c ) m = 175 , d ) m = 680 , e ) 690 | b | add(multiply(34, const_2), divide(subtract(multiply(34, const_2), multiply(8, 5)), subtract(5, const_1))) | multiply(n2,const_2)|multiply(n0,n1)|subtract(n0,const_1)|subtract(#0,#1)|divide(#3,#2)|add(#4,#0)| | general |
a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 24 % home electronics ; 15 % food additives ; 19 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph i... | "14 % microphotonics ; 24 % home electronics ; 15 % food additives ; 19 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 15 + 19 + 8 ) = 20 % basic astrophysics . 10 % of 360 ° is 72 ° . answer : e ." | a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 72 ° | e | divide(multiply(subtract(const_100, add(add(add(add(14, 24), 15), 19), 8)), divide(const_3600, const_10)), const_100) | add(n0,n1)|divide(const_3600,const_10)|add(n2,#0)|add(n3,#2)|add(n4,#3)|subtract(const_100,#4)|multiply(#1,#5)|divide(#6,const_100)| | gain |
bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 36 white marbles . how many red marbles could be in bag a ? | "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 36 = 6 k + 4 p = > k = 4 , p = 3 total red ' s in bag a will be 2 k = 8 e" | a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8 | e | divide(36, add(multiply(3, 2), 4)) | multiply(n1,n2)|add(n5,#0)|divide(n6,#1)| | other |
when asked what the time is , a person answered that the amount of time left is 1 / 2 of the time already completed . what is the time . | "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 1 / 2 x ⇒ x = 16 time is 4 pm answer : d" | a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 4 pm , e ) 6 pm | d | subtract(multiply(1, const_12), divide(multiply(1, const_12), add(divide(1, 2), const_1))) | divide(n0,n1)|multiply(const_12,n0)|add(#0,const_1)|divide(#1,#2)|subtract(#1,#3)| | general |
ajay can ride 50 km in 1 hour . in how many hours he can ride 500 km ? | "1 hour he ride 50 km he ride 500 km in = 500 / 50 * 1 = 10 hours answer is a" | a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs | a | divide(500, 50) | divide(n2,n0)| | physics |
in a renowned city , the average birth rate is 10 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day . | "every 2 seconds , 8 persons are added ( 10 - 2 ) . every second 4 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 4 = 345600 option c" | a ) 32,300 , b ) 172,800 , c ) 345,600 , d ) 338,200 , e ) 259,200 | c | multiply(multiply(subtract(10, 2), const_3600), const_12) | subtract(n0,n1)|multiply(#0,const_3600)|multiply(#1,const_12)| | general |
two employees m and n are paid a total of $ 616 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ? | "1.2 n + n = 616 2.2 n = 616 n = 280 the answer is b ." | a ) $ 270 , b ) $ 280 , c ) $ 290 , d ) $ 300 , e ) $ 310 | b | divide(616, add(divide(120, const_100), const_1)) | divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)| | general |
in town x , 64 percent of the population are employed , and 38 percent of the population are employed males . what percent of the employed people in town x are females ? | "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 38 are employed males , hence 26 % are employed females . ( employed females ) / ( total employed people ) = 26 / 64 = 40 % answer : d ." | a ) 16 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 52 % | d | multiply(divide(subtract(64, 38), 64), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | gain |
there were two candidates in an election . winner candidate received 55 % of votes and won the election by 100 votes . find the number of votes casted to the winning candidate ? | "w = 55 % l = 45 % 55 % - 45 % = 10 % 10 % - - - - - - - - 100 55 % - - - - - - - - ? = > 550 answer : a" | a ) 550 , b ) 744 , c ) 255 , d ) 199 , e ) 231 | a | divide(multiply(divide(100, divide(subtract(55, subtract(const_100, 55)), const_100)), 55), const_100) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)| | gain |
5 friends adi , brian , close , derek and eli appeared in two aptitude tests . in the first aptitude test , derek score 50 % less than the average score of the 5 people . in the second aptitude test , derek score 50 % more than what he scored on the first aptitude test . if the score of his friend in the second aptitud... | average score in first test be x so derby score = 0.5 x ( first test ) derby score = 1.5 ( 0.5 x ) ( second test ) = . 75 x so less than x by . 25 answer a 25 % | a ) 25 % , b ) 28 % , c ) 33 % , d ) 40 % , e ) 50 % | a | divide(multiply(50, multiply(5, 5)), 50) | multiply(n0,n0)|multiply(n1,#0)|divide(#1,n1) | general |
an escalator moves towards the top level at the rate of 12 ft . sec and its length is 160 feet . if a person walks on the moving escalator at the rate of 8 feet per second towards the top level , how much time does he take to cover the entire length . | "explanation : time taken to cover the entire length = tot . dist / resultant speed = 160 / ( 12 + 8 ) = 8 sec answer : b" | a ) 10 sec , b ) 8 sec , c ) 9 sec , d ) 7 sec , e ) 12 sec | b | divide(160, add(12, 8)) | add(n0,n2)|divide(n1,#0)| | gain |
if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 41 then sum is | "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 41 4100 answer : e" | a ) s . 5000 , b ) s . 5100 , c ) s . 5800 , d ) s . 6000 , e ) s . 4100 | e | divide(41, multiply(divide(10, const_100), divide(10, const_100))) | divide(n0,const_100)|multiply(#0,#0)|divide(n2,#1)| | gain |
a leak in the bottom of a tank can empty the full tank in 4 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ? | solution work done by the inlet in 1 hour = ( 1 / 4 - 1 / 12 ) = 1 / 6 . work done by the inlet in 1 min . = ( 1 / 6 × 1 / 60 ) = 0.002778 volume of 0.002778 part = 6 litres . therefore , volume of whole = ( . 002778 × 6 ) ‹ = › 2160 litres . answer d | a ) 7580 , b ) 7960 , c ) 8290 , d ) 2160 , e ) none | d | divide(multiply(6, multiply(12, const_60)), subtract(divide(multiply(12, const_60), multiply(4, const_60)), const_1)) | multiply(n2,const_60)|multiply(n0,const_60)|divide(#0,#1)|multiply(n1,#0)|subtract(#2,const_1)|divide(#3,#4) | physics |
a can run 224 metre in 28 seconds and b in 32 seconds . by what distance a beat b ? | "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 224 / 32 = 28 / 4 = 7 m / sdistance covered by b in 4 seconds = speed × time = 7 × 4 = 28 metre i . e . , a beat b by 28 metre answer is b" | a ) 38 metre , b ) 28 metre , c ) 23 metre , d ) 15 metre , e ) 28 metre | b | subtract(224, multiply(divide(224, 32), 28)) | divide(n0,n2)|multiply(n1,#0)|subtract(n0,#1)| | physics |
in the manufacture of a certain product , 8 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ? | "percent of defective produced = 8 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 8 / 100 ) * 100 % = ( 32 / 10000 ) * 100 % = ( 32 / 100 ) % = . 32 % answer b" | a ) 0.125 % , b ) 0.32 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 % | b | multiply(8, divide(4, const_100)) | divide(n1,const_100)|multiply(n0,#0)| | gain |
$ 700 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is | a : ( b + c ) = 2 : 3 a ' s share = 700 * 2 / 5 = $ 280 answer is d | a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 280 , e ) $ 250 | d | multiply(divide(700, add(divide(const_2, const_3), const_1)), divide(const_2, const_3)) | divide(const_2,const_3)|add(#0,const_1)|divide(n0,#1)|multiply(#2,#0) | general |
the number of boxes in a warehouse can be divided evenly into 12 equal shipments by boat or 32 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ? | "answer is the lcm of 12 and 32 = 96 answer c" | a ) 27 , b ) 33 , c ) 96 , d ) 81 , e ) 162 | c | multiply(multiply(multiply(multiply(const_2, const_2), const_2), const_3), 12) | multiply(const_2,const_2)|multiply(#0,const_2)|multiply(#1,const_3)|multiply(n0,#2)| | general |
the salary of a worker is first increased by 20 % and afterwards reduced by 20 % . what is the net change in the worker ' s salary ? | "let x be the original salary . the final salary is 0.8 ( 1.2 x ) = 0.96 x the answer is a ." | a ) 4 % decrease , b ) 8 % decrease , c ) 4 % increase , d ) 8 % increase , e ) no change | a | subtract(const_100, subtract(add(20, const_100), divide(multiply(add(20, const_100), 20), const_100))) | add(n0,const_100)|multiply(n0,#0)|divide(#1,const_100)|subtract(#0,#2)|subtract(const_100,#3)| | gain |
one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 37 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 / 37 = > 4 / x = 1 / 37 x = 37 ∗ 4 = 148 mins option a" | a ) 148 mins , b ) 140 mins , c ) 136 mins , d ) 132 minw , e ) none of these | a | multiply(add(const_1, const_4), 37) | add(const_1,const_4)|multiply(n0,#0)| | physics |
the average age of applicants for a new job is 31 , with a standard deviation of 5 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ? | within one standard deviation of the average age means 31 + / - 7 26 - - 31 - - 36 number of dif . ages - 26 27 28 29 30 31 32 33 34 35 36 total = 11 a | a ) 11 , b ) 14 , c ) 15 , d ) 18 , e ) 30 | a | add(multiply(5, const_2), const_1) | multiply(n1,const_2)|add(#0,const_1) | general |
a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 78 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480 | "1 percent for 3 years = 78 1 percent for 1 year = 26 = > 100 percent = 2600 answer : b" | a ) 2000 , b ) 2600 , c ) 2200 , d ) 2300 , e ) 2400 | b | multiply(divide(78, 3), const_100) | divide(n2,n0)|multiply(#0,const_100)| | gain |
what is the dividend . divisor 16 , the quotient is 6 and the remainder is 2 | "c = d * q + r c = 16 * 6 + 2 c = 86 + 2 c = 88" | a ) 86 , b ) 87 , c ) 88 , d ) 89 , e ) 90 | c | add(multiply(16, 6), 2) | multiply(n0,n1)|add(n2,#0)| | general |
a can do a work in 15 days and b in 20 days . if they work on it together for 8 days , then the fraction of the work that is left is | "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 8 = 280 remaining work is 300 - 280 = 20 remaining fraction of work is = 20 / 300 = 1 / 15 answer e" | a ) 8 / 17 , b ) 7 / 15 , c ) 3 / 15 , d ) 8 / 15 , e ) 1 / 15 | e | subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 8)) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)|subtract(const_1,#3)| | physics |
in a college the ratio of the numbers of boys to the girls is 5 : 7 . if there are 140 girls , the total number of students in the college is ? | "let the number of boys and girls be 5 x and 7 x then , 7 x = 140 x = 20 total number of students = 12 x = 12 * 20 = 240 answer is b" | a ) 200 , b ) 240 , c ) 160 , d ) 250 , e ) 310 | b | add(multiply(divide(5, 7), 140), 140) | divide(n0,n1)|multiply(n2,#0)|add(n2,#1)| | other |
62467 × 9998 = ? | "d 624545066 62467 × 9998 = 62467 × ( 10000 - 2 ) = 62467 × 10000 - 62467 × 2 = 624670000 - 124934 = 624545066" | a ) 624545037 , b ) 627745452 , c ) 624545077 , d ) 624545066 , e ) 625454211 | d | multiply(divide(62467, 9998), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
a boat takes 38 hours for travelling downstream from point a to point b and coming back to point c midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ? | "explanation : velocity of the stream = 4 kmph speed of the boat in still water is 14 kmph speed downstream = ( 14 + 4 ) = 18 kmph speed upstream = ( 14 - 4 ) = 10 kmph let the distance between a and b be x km time taken to travel downstream from a to b + time taken to travel upstream from b to c ( mid of a and b ) = 3... | a ) 240 km , b ) 120 km , c ) 360 km , d ) 180 km , e ) none of these | c | divide(38, add(divide(const_1, add(14, 4)), divide(const_1, multiply(subtract(14, 4), const_2)))) | add(n1,n2)|subtract(n2,n1)|divide(const_1,#0)|multiply(#1,const_2)|divide(const_1,#3)|add(#2,#4)|divide(n0,#5)| | physics |
a boatman goes 3 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . how long will it take to go 5 km in stationary water ? | "speed ( upstream ) = 3 / 1 = 3 kmhr speed ( downstream ) = 1 / ( 10 / 60 ) = 6 kmhr speed in still water = 1 / 2 ( 3 + 6 ) = 4.5 kmhr time taken in stationary = 5 / 4.5 = 1 hrs 7 min answer : b" | a ) 40 minutes , b ) 1 hour 7 min , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 10 min | b | divide(5, divide(add(multiply(divide(1, 10), const_60), divide(3, 3)), const_2)) | divide(n0,n0)|divide(n2,n3)|multiply(#1,const_60)|add(#0,#2)|divide(#3,const_2)|divide(n4,#4)| | physics |
30 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ? | "capacity of the tank = 30 ã — 13.5 = 405 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 405 â „ 9 = 45 answer c" | a ) 30 , b ) 32 , c ) 45 , d ) data inadequate , e ) none of these | c | divide(multiply(13.5, 30), 9) | multiply(n0,n1)|divide(#0,n2)| | physics |
a man two flats for $ 675958 each . on one he gains 14 % while on the other he loses 14 % . how much does he gain or lose in the whole transaction ? | "in such a case there is always a loss loss % = ( 14 / 10 ) ^ 2 = 49 / 25 = 1.96 % answer is a" | a ) 1.96 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 % | a | multiply(divide(subtract(add(multiply(divide(const_100, add(const_100, 14)), 675958), multiply(divide(const_100, subtract(const_100, 14)), 675958)), add(675958, 675958)), add(multiply(divide(const_100, add(const_100, 14)), 675958), multiply(divide(const_100, subtract(const_100, 14)), 675958))), const_100) | add(n1,const_100)|add(n0,n0)|subtract(const_100,n1)|divide(const_100,#0)|divide(const_100,#2)|multiply(n0,#3)|multiply(n0,#4)|add(#5,#6)|subtract(#7,#1)|divide(#8,#7)|multiply(#9,const_100)| | gain |
two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 20 kmph respectively . in what time will they cross each other completely ? | "explanation : d = 250 m + 250 m = 500 m rs = 80 + 20 = 100 * 5 / 18 = 250 / 9 t = 500 * 9 / 250 = 18 sec answer : option b" | a ) 15 sec , b ) 18 sec , c ) 12 sec , d ) 10 sec , e ) 11 sec | b | divide(250, multiply(80, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics |
how many pairs ( r , r + 1 ) have one or more prime factors common , where r is an integer and 2 ≤ r ≤ 9 ? | r and r + 1 are consecutive integers . two consecutive integers are co - prime , which means that they do n ' t share any common factor but 1 . for example 20 and 21 are consecutive integers , thus only common factor they share is 1 . answer : a . | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | subtract(const_1, const_1) | subtract(const_1,const_1) | general |
walking at 4 / 5 of his usual speed a man is 10 mins too late . find his usual time . | "speed = s , time = t , 4 / 5 s * ( t + 10 ) = st t = 40 answer : d" | a ) 81 mins , b ) 64 mins , c ) 52 mins , d ) 40 mins , e ) none | d | divide(multiply(multiply(divide(multiply(10, 4), 5), 5), const_2), const_60) | multiply(n0,n2)|divide(#0,n1)|multiply(n1,#1)|multiply(#2,const_2)|divide(#3,const_60)| | physics |
tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 7 weeks have been $ 406 , $ 413 , $ 420 , $ 436 , $ 395 , $ 410 , $ 360 . what must his average ( arithmetic mean ) income over the next two weeks be to decrease his average... | official solution : ( b ) first , we need to add up the wages over the past 7 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 + $ 410 + $ 360 = $ 2840 . to average $ 400 over 9 weeks , the salesman would need to earn : $ 400 × 9 = $ 3600 . subtract $ 2840 from $ 3600 to determine how much he would need to earn , in total... | a ) $ 360 , b ) $ 380 , c ) $ 430 , d ) $ 290 , e ) $ 520 | b | divide(subtract(multiply(400, 9), add(add(add(add(add(add(406, 413), 420), 436), 395), 410), 360)), const_2) | add(n1,n2)|multiply(n8,n9)|add(n3,#0)|add(n4,#2)|add(n5,#3)|add(n6,#4)|add(n7,#5)|subtract(#1,#6)|divide(#7,const_2) | general |
a furniture manufacturer has two machines , but only one can be used at a time . machine q is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine q can do the job in 12 days working two shifts and machine b can do the job in 15 days working two sh... | machine q finish the job in 2 * 12 shifts = 24 shifts machine b finish the job in 2 * 15 shifts = 30 shifts lets assume total work require 120 shifts therefore , rate of q = 5 shifts / day rate of b = 4 shifts / day rate of ( q + b ) = 9 shifts / day according to current schedule work complete in a day = 5 + 4 + ( 9 / ... | a ) 14 , b ) 13 , c ) 11 , d ) 9 , e ) 7 | d | divide(const_1, add(add(divide(const_1, multiply(12, const_2)), divide(const_1, multiply(15, const_2))), add(divide(divide(const_1, multiply(12, const_2)), const_2), divide(divide(const_1, multiply(15, const_2)), const_2)))) | multiply(n0,const_2)|multiply(n1,const_2)|divide(const_1,#0)|divide(const_1,#1)|add(#2,#3)|divide(#2,const_2)|divide(#3,const_2)|add(#5,#6)|add(#4,#7)|divide(const_1,#8) | physics |
a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 4 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ? | "yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 4 hours . if the company used th... | a ) 3 , b ) 4 , c ) 9 / 5 , d ) 9 / 8 , e ) 12 | c | divide(const_1, multiply(const_2.0, add(divide(const_1, 36), divide(const_1, 4)))) | divide(const_1,n0)|divide(const_1,const_2.0)|add(#0,#1)|multiply(n1,#2)|divide(const_1,#3)| | gain |
mike earns $ 15 per hour and phil earns $ 10 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ? | "what % less of 15 is 10 let it be x % less , then = 15 ( 1 - x / 100 ) = 10 1 - x / 100 = 10 / 15 x = 100 / 3 x = 33.3 % ans a" | a ) 33.3 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 % | a | multiply(divide(10, 15), const_100) | divide(n1,n0)|multiply(#0,const_100)| | general |
a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 79 , how many questions did student a answer correctly ? | "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 79 ( subtracting twice of incorrect from correct ) 3 x = 279 x = 93 answer : c" | a ) 55 , b ) 60 , c ) 93 , d ) 82 , e ) 91 | c | subtract(100, divide(subtract(100, 79), const_3)) | subtract(n0,n1)|divide(#0,const_3)|subtract(n0,#1)| | general |
the edges of three metal cubes are 2 cm , 3 cm , and 4 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ? | "the total volume is 2 ^ 3 + 3 ^ 3 + 4 ^ 3 = 99 the edge of the new cube is the cube root of 99 which is about 4.6 cm . the answer is d ." | a ) 4.0 , b ) 4.2 , c ) 4.4 , d ) 4.6 , e ) 4.8 | d | power(add(power(4, 3), add(2, power(3, 3))), const_0_33) | power(n1,n1)|power(n2,n1)|add(n0,#0)|add(#2,#1)|power(#3,const_0_33)| | physics |
rahim bought 50 books for rs . 1000 from one shop and 40 books for rs . 800 from another . what is the average price he paid per book ? | "average price per book = ( 1000 + 800 ) / ( 50 + 40 ) = 1800 / 90 = rs . 20 answer : b" | a ) 28 , b ) 20 , c ) 27 , d ) 29 , e ) 21 | b | divide(add(1000, 800), add(50, 40)) | add(n1,n3)|add(n0,n2)|divide(#0,#1)| | general |
in a hostel there were 100 students . to accommodate 40 more students the average is decreased by rupees 10 . but total expenditure decreased by rs . 400 . find the total expenditure of the hostel now ? | "100 x - 400 = 140 ( x – 10 ) x = 25 100 * 25 - 400 = 2100 answer : e" | a ) 1400 , b ) 2500 , c ) 3000 , d ) 1500 , e ) 2100 | e | multiply(subtract(divide(add(multiply(add(100, 40), 10), 400), 40), 10), add(100, 40)) | add(n0,n1)|multiply(n2,#0)|add(n3,#1)|divide(#2,n1)|subtract(#3,n2)|multiply(#0,#4)| | general |
the radius of a cone is 8 m , height 6 m . find the slant height ? | "cone slant height ( l ) = √ r ( power 2 ) + h ( power 2 ) = √ 64 + 36 = 10 m . answer is b ." | a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25 | b | volume_cone(8, 6) | volume_cone(n0,n1)| | physics |
a store ’ s selling price of $ 2500 for a certain computer would yield a profit of 40 percent of the store ’ s cost for the computer . what selling price would yield a profit of 50 percent of the computer ’ s cost ? | 1.4 x = 2500 x = 2500 / 1.4 so , 1.5 x = 2500 * 1.5 / 1.4 = 2478 answer : - a | a ) $ 2678 , b ) $ 2464 , c ) $ 2650 , d ) $ 2732 , e ) $ 2800 | a | multiply(2500, divide(add(const_100, 50), add(const_100, 40))) | add(n2,const_100)|add(n1,const_100)|divide(#0,#1)|multiply(n0,#2) | gain |
what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 10 nor by 35 ? | "normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here s... | a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945 | d | subtract(1000, subtract(add(divide(1000, 10), divide(1000, 35)), divide(1000, multiply(10, 35)))) | divide(n1,n2)|divide(n1,n3)|multiply(n2,n3)|add(#0,#1)|divide(n1,#2)|subtract(#3,#4)|subtract(n1,#5)| | other |
the average age of applicants for a new job is 31 , with a standard deviation of 9 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ? | "within one standard deviation of the average age means 31 + / - 7 24 - - 31 - - 38 number of dif . ages - 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 total = 19 e" | a ) 8 , b ) 14 , c ) 15 , d ) 18 , e ) 19 | e | add(multiply(9, const_2), const_1) | multiply(n1,const_2)|add(#0,const_1)| | general |
a man walks at a rate of 10 mph . after every ten miles , he rests for 8 minutes . how much time does he take to walk 50 miles ? | "to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 8 = 32 minutes . total time = 300 + 32 = 332 minutes . answer : e ." | a ) 300 , b ) 318 , c ) 322 , d ) 324 , e ) 332 | e | add(multiply(8, const_4), multiply(divide(50, 10), const_60)) | divide(n2,n0)|multiply(n1,const_4)|multiply(#0,const_60)|add(#1,#2)| | physics |
what is the leastvalue of x . so that 45 x 09 is divisible by 3 ? | "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 4 + 5 + x + 0 + 9 = 18 + x least value of x may be 0 therefore 18 + 0 = 18 is divisible by 3 . a" | a ) 0 , b ) 5 , c ) 2 , d ) 6 , e ) 7 | a | subtract(3, reminder(add(add(add(floor(divide(45, const_10)), reminder(45, const_10)), floor(divide(09, const_10))), reminder(09, const_10)), 3)) | divide(n0,const_10)|divide(n1,const_10)|reminder(n0,const_10)|reminder(n1,const_10)|floor(#0)|floor(#1)|add(#4,#2)|add(#6,#5)|add(#7,#3)|reminder(#8,n2)|subtract(n2,#9)| | general |
roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 6 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ? | distance = relative speed * time = ( 6 + 3 ) * 4 = 36 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : e | a ) 22 km , b ) 20 km , c ) 65 km , d ) 18 km , e ) 36 km | e | multiply(add(6, 3), 4) | add(n0,n1)|multiply(n2,#0) | physics |
the price of a book is increased from $ 300 to $ 360 . what is the % of increase in its price ? | "explanation : change in the price = rs 360 – rs 300 = rs 60 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 60 300 ) * 100 = 20 % b" | a ) 10 % , b ) 20 % , c ) 35 % , d ) 40 % , e ) 50 % | b | multiply(divide(subtract(360, 300), 300), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
the simple interest on rs . 26 for 6 months at the rate of 7 paise per rupeeper month is | "sol . s . i . = rs . [ 26 * 7 / 100 * 6 ] = rs . 10.92 answer b" | a ) 1.2 , b ) 10.92 , c ) 12.98 , d ) 12.38 , e ) none | b | divide(multiply(multiply(26, 6), 7), const_100) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,const_100)| | gain |
ms . mary sold two properties , x and y , for $ 25000 each . she sold property x for 20 % more than she paid for it and sold property y for 20 % less than she paid for it . if expenses are disregarded , what was her total net gain or loss , if any , on the two properties ? | there is a property to solve such questions withcommon selling priceandcommon % gain and loss . such cases always result in a loss and . . . total % loss = ( common gain % or loss % / 10 ) ^ 2 hence here loss % = ( 20 / 10 ) ^ 2 = 4 % which means he recovered only 96 % of his investment which amount to a total revenue ... | a ) $ 2100 , b ) $ 2222 , c ) $ 2320 , d ) $ 2083.33 , e ) $ 2183.33 | d | add(divide(subtract(multiply(divide(20, const_100), 25000), const_1000), const_2), add(add(subtract(const_100, 20), const_3), const_0_33)) | divide(n1,const_100)|subtract(const_100,n1)|add(#1,const_3)|multiply(n0,#0)|add(#2,const_0_33)|subtract(#3,const_1000)|divide(#5,const_2)|add(#4,#6) | general |
harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 3 of her books to their new home . what fraction of millicent ' s old libra... | "because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h ' = 1 / 3 h = 10 books m ' = 1 / 3 m = 20 books total = 30 books m ' = 30 = 1 / 2 * 60 ratio : 1 / 2 ans : a" | a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6 | a | subtract(1, multiply(divide(1, 3), divide(1, 2))) | divide(n0,n3)|divide(n0,n1)|multiply(#0,#1)|subtract(n0,#2)| | general |
an engineer undertakes a project to build a road 10 km long in 150 days and employs 30 men for the purpose . after 50 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time . | "30 workers working already let x be the total men required to finish the task in next 100 days 2 km done hence remaining is 8 km also , work has to be completed in next 100 days ( 150 - 50 = 100 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion he... | a ) 22 , b ) 30 , c ) 15 , d ) 18 , e ) 20 | b | subtract(divide(multiply(multiply(30, subtract(10, 2)), 50), multiply(2, subtract(150, 50))), 30) | subtract(n0,n4)|subtract(n1,n3)|multiply(n2,#0)|multiply(n4,#1)|multiply(n3,#2)|divide(#4,#3)|subtract(#5,n2)| | physics |
a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 280 - mile journey ? assume that the train makes no intermediate stops . | "a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 280 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solv... | a ) 8 , b ) 7 , c ) 9 , d ) 7.5 , e ) 6 | b | divide(280, add(30, add(10, 20))) | add(n0,n1)|add(n2,#0)|divide(n3,#1)| | physics |
the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 28 years . the ratio of their ages after 8 years will be | "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 28 x = 4 mini ’ s age = 16 years and minakshi ’ s age = 12 years ratio of their ages after 8 years = ( 16 + 8 ) : ( 12 + 8 ) = 24 : 20 = 6 : 5 answer : d" | a ) 4 : 3 , b ) 12 : 11 , c ) 7 : 4 , d ) 6 : 5 , e ) 6 : 11 | d | divide(add(multiply(4, divide(28, add(4, 3))), 8), add(multiply(3, divide(28, add(4, 3))), 8)) | add(n0,n1)|divide(n2,#0)|multiply(n0,#1)|multiply(n1,#1)|add(n3,#2)|add(n3,#3)|divide(#4,#5)| | general |
a certain junior class has 1000 students and a certain senior class has 600 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ? | "let ' s see pick 60 / 1000 first then we can only pick 1 other pair from the 800 so total will be 60 / 600 * 1000 simplify and you get 1 / 10000 answer is b" | a ) 3 / 40000 , b ) 1 / 1000 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15 | b | divide(1, const_3) | divide(n3,const_3)| | probability |
what is the difference between the place values of two 1 ' s in the numeral 135.21 | required difference = 100 - 0.01 = 99.99 answer is d | a ) 99.999 , b ) 100.2 , c ) 134 , d ) 99.99 , e ) 99.9 | d | subtract(multiply(1, const_100), divide(1, const_100)) | divide(n0,const_100)|multiply(n0,const_100)|subtract(#1,#0) | general |
a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is four times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that ... | "water : soap = 3 : 2 soap : salt = 12 : 2 = > for 12 soap , salt = 2 = > for 2 soap , salt = ( 2 / 12 ) * 2 = 1 / 3 so , water : soap : salt = 3 : 2 : 1 / 3 = 36 : 24 : 4 after open container , water : soap : salt = 18 : 24 : 4 so , water : salt = 18 : 4 = 36 : 8 e" | a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 36 : 8 | e | divide(multiply(multiply(2, 3), 3), multiply(multiply(2, 2), 2)) | multiply(n0,n1)|multiply(n1,n1)|multiply(n0,#0)|multiply(n1,#1)|divide(#2,#3)| | other |
if x + ( 1 / x ) = 5 , what is the value of e = 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 ) e = 21 , b ) e = 22 , c ) e = 23 , d ) 24 , e ) 27 | c | subtract(power(5, 2), 2) | power(n1,n2)|subtract(#0,n2)| | general |
find the smallest number of five digits exactly divisible by 16 , 24,36 and 54 . | "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 16,24 , 36,54 i . e 432 , on dividing 10000 by 432 , we get 64 as remainder . therefore , required number = 10000 + ( 432 – 64 ) = 10368 . answer is a ." | a ) 10368 , b ) 10638 , c ) 10836 , d ) 10846 , e ) none of them | a | add(subtract(multiply(const_10, multiply(const_100, const_100)), const_100), 24,36) | multiply(const_100,const_100)|multiply(#0,const_10)|subtract(#1,const_100)|add(n1,#2)| | general |
8 is 4 % of a , and 4 is 8 % of b . c equals b / a . what is the value of c ? | "explanation : given , = > 4 a / 100 = 8 . = > a = 8 × ( 100 / 4 ) = 200 . - - - - - - - - - ( i ) and , = > ( 8 / 100 ) × b = 4 . = > b = 50 . - - - - - - - - - ( ii ) now , c = b / a ( from ( i ) and ( ii ) ) = > 50 / 200 . = > 1 / 4 . answer : b" | a ) 1 / 32 , b ) 1 / 4 , c ) 1 , d ) 4 , e ) 5 | b | divide(multiply(divide(4, 8), const_100), multiply(divide(8, 4), const_100)) | divide(n1,n0)|divide(n0,n1)|multiply(#0,const_100)|multiply(#1,const_100)|divide(#2,#3)| | general |
the volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ? | the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 10 = ( 1 ) 2 h 1 / ( 2 ) 2 h 2 = > h 1 / h 2 = 2 / 5 i . e . h 1 : h 2 = 2 : 5 answer : a | ['a ) 2 : 5', 'b ) 2 : 9', 'c ) 2 : 2', 'd ) 2 : 9', 'e ) 2 : 1'] | a | divide(divide(1, 10), power(divide(1, 2), const_2)) | divide(n0,n1)|divide(n0,n3)|power(#1,const_2)|divide(#0,#2) | geometry |
the average weight of a group of 30 friends increases by 10 kg when the weight of additional 30 friends was added . if average weight of the whole group after including the additional 30 members is 40 kg , what is the average weight of the additional friends ? | let a = avg . wt . of additional 30 friends original total weight = ( 30 friends ) ( 30 kg avge ) = 900 kg ( 900 + 30 a ) / ( 30 + 30 ) = 40 kg avge a = 50 kg answer - a | a ) 50 kg , b ) 60 kg , c ) 61 kg , d ) 62 kg , e ) 91 kg | a | divide(subtract(multiply(add(30, 30), 40), multiply(30, subtract(40, 10))), 30) | add(n0,n0)|subtract(n4,n1)|multiply(n4,#0)|multiply(n0,#1)|subtract(#2,#3)|divide(#4,n0) | general |
sum of two numbers is 50 . two times of the difference of first and seceond is 20 . then the numbers will be ? | explanation : x + y = 50 2 x ã ¢ â ‚ ¬ â € œ 2 y = 20 x = 30 y = 20 answer : d | a ) 10 , 40 , b ) 20 , 30 , c ) 35 , 15 , d ) 30 , 20 , e ) 15 , 35 | d | subtract(50, divide(subtract(50, divide(20, const_2)), const_2)) | divide(n1,const_2)|subtract(n0,#0)|divide(#1,const_2)|subtract(n0,#2) | general |
the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 25 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ? | "original price = 100 day 1 discount = 10 % , price = 100 - 10 = 90 day 2 discount = 10 % , price = 90 - 9 = 81 day 3 discount = 25 % , price = 81 - 20.25 = 60.75 which is 60.75 / 90 * 100 of the sale price on day 1 = ~ 67.5 % answer b" | a ) 28 % , b ) 67.5 % , c ) 64.8 % , d ) 70 % , e ) 72 % | b | add(multiply(divide(divide(25, const_100), subtract(1, divide(1, 10))), const_100), 2) | divide(n5,const_100)|divide(n1,n0)|subtract(n1,#1)|divide(#0,#2)|multiply(#3,const_100)|add(n2,#4)| | gain |
if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 160 , what is the value of a − c ? | "( a + b ) / 2 = 110 = = = > a + b = 220 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 220 - 320 = = = > a + b - b - c = - 100 = = = > a - c = - 100 answer : b" | a ) − 220 , b ) − 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given | b | subtract(multiply(const_60.0, const_2), multiply(110, const_2)) | multiply(const_60.0,const_2)|multiply(n0,const_2)|subtract(#0,#1)| | general |
if a and b are the roots of the equation x 2 - 7 x + 7 = 0 , then the value of a 2 + b 2 is : | sol . ( b ) the sum of roots = a + b = 7 product of roots = ab = 8 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 49 - 14 = 35 answer a | a ) 35 , b ) 24 , c ) 17 , d ) 6 , e ) 5 | a | add(power(divide(subtract(7, sqrt(subtract(power(7, const_2), multiply(const_4, 7)))), const_2), 2), power(divide(add(7, sqrt(subtract(power(7, const_2), multiply(const_4, 7)))), const_2), 2)) | multiply(n1,const_4)|power(n1,const_2)|subtract(#1,#0)|sqrt(#2)|add(n1,#3)|subtract(n1,#3)|divide(#5,const_2)|divide(#4,const_2)|power(#6,n0)|power(#7,n0)|add(#8,#9) | general |
each machine of type a has 4 steel parts and 2 chrome parts . each machine of type b has 2 steel parts and 1 chrome parts . if a certain group of type a and type b machines has a total of 30 steel parts and 33 chrome parts , how many machines are in the group | "look at the below representation of the problem : steel chrome total a 4 2 30 > > no . of type a machines = 30 / 6 = 5 b 2 1 33 > > no . of type b machines = 33 / 3 = 11 so the answer is 16 i . e d . hope its clear ." | a ) 12 , b ) 13 , c ) 14 , d ) 16 , e ) 19 | d | add(divide(33, add(1, 2)), divide(30, add(4, 2))) | add(n1,n3)|add(n0,n1)|divide(n5,#0)|divide(n4,#1)|add(#2,#3)| | general |
a circular well with a diameter of 2 meters , is dug to a depth of 14 meters . what is the volume of the earth dug out . | explanation : volume = π r 2 hvolume = ( 22 / 7 ∗ 1 ∗ 1 ∗ 14 ) m 3 = 44 m 3 option c | ['a ) 40 m 3', 'b ) 42 m 3', 'c ) 44 m 3', 'd ) 46 m 3', 'e ) none of these'] | c | volume_cylinder(divide(2, const_2), 14) | divide(n0,const_2)|volume_cylinder(#0,n1) | geometry |
there are 750 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ? | "female = x male = 750 - x x / 2 + 750 - x / 4 = 1 / 3 * ( 750 ) = 250 x = 250 x / 2 = 125 is supposed to be the answer answer : c" | a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 225 | c | divide(subtract(multiply(divide(750, const_3), const_4), 750), const_2) | divide(n0,const_3)|multiply(#0,const_4)|subtract(#1,n0)|divide(#2,const_2)| | general |
if m = 3 ^ n , what is the greatest value of n for which m is a factor of 16 ! | "solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 - - - - count 3 ' s = 6 so answer is 6" | a ) 8 , b ) 10 , c ) 6 , d ) 14 , e ) 16 | c | add(floor(divide(16, 3)), floor(divide(16, power(3, const_2)))) | divide(n1,n0)|power(n0,const_2)|divide(n1,#1)|floor(#0)|floor(#2)|add(#3,#4)| | other |
if 25 % of x is 5 less than 10 % of 500 , then x is ? | "25 % of x = x / 4 ; 10 % of 500 = 10 / 100 * 500 = 50 given that , x / 4 = 50 - 5 = > x / 4 = 45 = > x = 180 . answer : b" | a ) 188 , b ) 180 , c ) 156 , d ) 840 , e ) 121 | b | divide(subtract(multiply(500, divide(10, const_100)), 5), divide(25, const_100)) | divide(n2,const_100)|divide(n0,const_100)|multiply(n3,#0)|subtract(#2,n1)|divide(#3,#1)| | general |
two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 675 meters , after what time will they meet at the starting point ? | "they meet every 675 / 7 + 8 = 45 sec answer is c" | a ) 20 sec , b ) 15 sec , c ) 45 sec , d ) 50 sec , e ) 1 min | c | divide(675, add(8, 7)) | add(n0,n1)|divide(n2,#0)| | physics |
if x and y are integers such that ( x + 1 ) ^ 2 is less than or equal to 16 and ( y - 1 ) ^ 2 is less than 64 , what is the sum of the maximum possible value of xy and the minimum possible value of xy ? | "( x + 1 ) ^ 2 < = 16 x < = 3 x > = - 5 ( y - 1 ) ^ 2 < 64 y < 9 y > - 7 max possible value of xy is - 5 × - 6 = 30 minimum possible value of xy is - 5 × 8 = - 40 - 40 + 30 = - 10 answer : b" | a ) - 16 , b ) - 10 , c ) 0 , d ) 14 , e ) 16 | b | add(sqrt(16), sqrt(64)) | sqrt(n2)|sqrt(n5)|add(#0,#1)| | general |
what is the least possible value of expression e = ( x - 1 ) ( x - 3 ) ( x - 4 ) ( x - 6 ) + 10 for real values of x ? | explanation : e = ( x - 1 ) ( x - 6 ) ( x - 3 ) ( x - 4 ) + 10 e = ( x 2 - 7 x + 6 ) ( x 2 - 7 x + 12 ) + 10 let x 2 - 7 x + 6 = y e = y 2 + 6 y + 10 e = ( y + 3 ) 2 + 1 minimum value = 1 , when y = - 3 answer : a | a ) 1 , b ) 10 , c ) 9 , d ) 0 , e ) 8 | a | subtract(add(10, 1), add(6, 4)) | add(n0,n4)|add(n2,n3)|subtract(#0,#1) | general |
a and b can finish a work in 12 days while a alone can do the same work in 20 days . in how many days b alone will complete the work ? | "b = 1 / 12 – 1 / 20 = 2 / 60 = 1 / 30 = > 30 days answer : b" | a ) 76 days , b ) 30 days , c ) 98 days , d ) 31 days , e ) 22 days | b | inverse(subtract(inverse(12), inverse(20))) | inverse(n0)|inverse(n1)|subtract(#0,#1)|inverse(#2)| | physics |
a jogger running at 9 km / hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ? | speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 120 = 320 m . time taken = 320 / 10 = 32 sec . answer : e | a ) 76 sec , b ) 67 sec , c ) 98 sec , d ) 36 sec , e ) 32 sec | e | divide(add(200, 120), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2)))) | add(n1,n2)|divide(const_10,const_2)|subtract(n3,n0)|divide(#2,const_2)|divide(#1,#3)|multiply(#4,#2)|divide(#0,#5) | general |
a certain tax rate is $ 82 per $ 100.00 . what is the rate , expressed as a percent ? | "here in question it is asking $ . 82 is what percent of $ 100 . suppose $ . 82 is x % of 100 means 100 * ( x / 100 ) = 82 hence x = 82 % so answer is a" | a ) 82 % , b ) 8.2 % , c ) 0.82 % , d ) 0.082 % , e ) 0.0082 % | a | multiply(divide(82, 100.00), 100.00) | divide(n0,n1)|multiply(#0,n1)| | gain |
how many integers from 101 to 600 , inclusive , remains the value unchanged when the digits were reversed ? | "question is asking for palindrome first digit possibilities - 1 through 5 = 5 6 is not possible here because it would result in a number greater than 6 ( i . e 606 , 616 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 5 * 10... | a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90 | a | divide(const_100.0, const_10) | divide(const_100.0,const_10)| | general |
the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 16 , and k < m < r < s < t . if t is 30 , what is the greatest possible value of the median of the 5 integers ? | "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 16 which means that in effect , all numbers are equal to 16 . if the largest number is 30 , it is 14 more than 16 . we need r to be ma... | a ) 16 , b ) 18 , c ) 19 , d ) 20 , e ) 28 | e | subtract(divide(subtract(multiply(16, 5), 30), const_2), const_2) | multiply(n0,n1)|subtract(#0,n2)|divide(#1,const_2)|subtract(#2,const_2)| | general |
x , a , z , and b are single digit positive integers . x = 1 / 6 a . z = 1 / 6 b . ( 10 a + b ) – ( 10 x + z ) could not equal | "a = 6 x , b = 6 z therefore ( 6 x . 10 + 6 z ) - ( 10 x + z ) = ( 6 - 1 ) ( 10 x + z ) = 5 . ( 10 x + z ) number should be divisible by 5 c" | a ) 35 , b ) 30 , c ) 43 , d ) 60 , e ) 65 | c | add(add(subtract(add(multiply(6, 6), multiply(6, 10)), add(multiply(6, 10), 6)), 10), const_3) | multiply(n1,n1)|multiply(n1,n4)|add(#0,#1)|add(n1,#1)|subtract(#2,#3)|add(n4,#4)|add(#5,const_3)| | general |
rs . 200 amounts to rs . 800 in 8 years at simple interest . if the interest is increased by 5 % , it would amount to how much ? | "( 200 * 5 * 8 ) / 100 = 80 200 + 80 = 280 answer : d" | a ) 520 , b ) 440 , c ) 260 , d ) 280 , e ) 120 | d | multiply(power(add(const_1, divide(5, const_100)), 8), 200) | divide(n3,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)| | gain |
the product of three consecutive numbers is 336 . then the sum of the smallest two numbers is ? | "product of three numbers = 336 336 = 6 * 7 * 8 . so , the three numbers are 6 , 7 and 8 . and sum of smallest of these two = 6 + 7 = 13 . answer : option a" | a ) 13 , b ) 15 , c ) 20 , d ) 38 , e ) 56 | a | multiply(power(const_2, 336), factorial(336)) | factorial(n0)|power(const_2,n0)|multiply(#0,#1)| | general |
a , b , c are positive numbers such that they are in increasing geometric progression then how many such numbers are there in ( loga + logb + logc ) / 6 = log 6 | given that a , b , c are in gp so b / a = c / b = > b ^ 2 = ac ( loga + logb + logc ) / 6 = log 6 = > log ( abc ) = 6 * log 6 = > log ( ac * b ) = log ( 6 ^ 6 ) = > log ( b ^ 3 ) = log ( 6 ^ 6 ) = > b ^ 3 = 6 ^ 6 = > b ^ 3 = ( 6 ^ 2 ) ^ 3 = > b = 6 ^ 2 = 36 it means a = 2 , c = 18 or a = 3 c = 12 or a = 4 c = 9 or a = ... | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | d | subtract(add(log(6), const_2), divide(const_1, const_2)) | divide(const_1,const_2)|log(n0)|add(#1,const_2)|subtract(#2,#0) | general |
calculate the l . c . m of 2 / 5 , 4 / 7 , 3 / 7 , 6 / 13 is : | "required l . c . m = l . c . m . of 2 , 4 , 3 , 6 / h . c . f . of 5 , 7 , 7 , 13 = 12 / 1 = 12 answer is d" | a ) 15 , b ) 14 , c ) 13 , d ) 12 , e ) 11 | d | multiply(multiply(2, 4), multiply(3, 6)) | multiply(n0,n2)|multiply(n4,n6)|multiply(#0,#1)| | physics |
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