Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
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a special municipal payroll tax charges not tax on a payroll less than $ 300,000 and only 1 % on a company β s payroll above $ 300,000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ? | "answer : c , ( with different approach ) : the 300 paid is 1 % of the additional amount above 200,000 . let it be x now 1 % of x = 300 therefore x = 30,000 total = 200,000 + x = 230,000" | a ) $ 180,000 , b ) $ 202,000 , c ) $ 230,000 , d ) $ 400,000 , e ) $ 2 , 200,000 | c | multiply(multiply(200, const_100), const_10) | multiply(n3,const_100)|multiply(#0,const_10)| | general |
the compound interest earned by sunil on a certain amount at the end of two years at the rate of 8 % p . a . was rs . 2828.80 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned . | "let the sum be rs . p p { [ 1 + 8 / 100 ] 2 - 1 } = 2828.80 p ( 8 / 100 ) ( 2 + 8 / 100 ) = 2828.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 2828.80 / ( 0.08 ) ( 2.08 ) = 1360 / 0.08 = 17000 principal + interest = rs . 19828.80 answer : b" | a ) rs . 18 , 828.80 , b ) rs . 19 , 828.80 , c ) rs . 18 , 028.80 , d ) rs . 17 , 828.80 , e ) none of these | b | add(divide(2828.80, subtract(power(add(const_1, divide(8, const_100)), const_2), const_1)), 2828.80) | divide(n0,const_100)|add(#0,const_1)|power(#1,const_2)|subtract(#2,const_1)|divide(n1,#3)|add(n1,#4)| | gain |
in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability r this college gr... | "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that i... | a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43 | d | divide(divide(divide(1, 8), divide(2, 3)), add(divide(divide(1, 8), divide(2, 3)), 1)) | divide(n0,n1)|divide(n2,n3)|divide(#0,#1)|add(#2,n0)|divide(#2,#3)| | other |
if a / b = 5 / 4 , then ( 4 a + 3 b ) / ( 4 a - 3 b ) = ? | "answer dividing numerator as well as denominator by b , we get given exp . = ( 4 a + 3 b ) / ( 4 a - 3 b ) = ( 4 a / b + 3 ) / ( 4 a / b - 3 ) since a / b = 5 / 4 this implies that = [ ( 4 * 5 ) / 4 + 3 ] / [ ( 4 * 5 ) / 4 - 3 ) ] = ( 5 + 3 ) / ( 5 - 3 ) = 4 option : e" | a ) 7 , b ) 6 , c ) 3 , d ) 5 , e ) 4 | e | divide(add(multiply(4, 5), multiply(3, 4)), subtract(multiply(4, 5), multiply(3, 4))) | multiply(n0,n1)|multiply(n1,n3)|add(#0,#1)|subtract(#0,#1)|divide(#2,#3)| | general |
total 63 matches are conducted in knockout match type . how many players will be participated in that tournament ? | "64 players answer : e" | a ) 60 , b ) 61 , c ) 62 , d ) 63 , e ) 64 | e | add(63, const_1) | add(n0,const_1)| | general |
if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2012 ) = ? | "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 β β f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 β β f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 β β f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2012 ) = 2013 ans : a" | a ) 2013 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781 | a | add(1, 2012) | add(n3,n4)| | general |
what is ( 21 ^ 7 + 21 ) / 21 ? | ( 21 ^ 7 + 21 ) / 21 = 21 * ( 21 ^ 6 + 1 ) / 21 = 21 ^ 6 + 1 clearly this is a number which ends with a 2 in the units place . the answer is d . | a ) 82216043 , b ) 83786095 , c ) 84316108 , d ) 85766122 , e ) 86426237 | d | divide(add(power(21, 7), 21), 21) | power(n0,n1)|add(n0,#0)|divide(#1,n0) | general |
if 102 x = 25 , then 10 - x equals : | "102 x = 25 ( 10 x ) 2 = 52 10 x = 5 1 / 10 x = 1 / 5 10 - x = 1 / 5 answer : e" | a ) a ) 3 , b ) b ) 2 , c ) c ) 6 , d ) d ) 9 , e ) e ) 1 / 5 | e | divide(subtract(divide(multiply(102, const_100), const_2), const_2), add(divide(multiply(102, const_100), const_2), const_2)) | multiply(n0,const_100)|divide(#0,const_2)|add(#1,const_2)|subtract(#1,const_2)|divide(#3,#2)| | general |
in an examination 35 % of the students passed and 520 failed . how many students appeared for the examination ? | "let the number of students appeared be x then , 65 % of x = 520 65 x / 100 = 520 x = 520 * 100 / 65 = 800 answer is c" | a ) a ) 540 , b ) b ) 400 , c ) c ) 800 , d ) d ) 650 , e ) e ) 840 | c | divide(multiply(520, const_100), subtract(const_100, 35)) | multiply(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)| | gain |
a cube has a volume of 343 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ? | "volume = 343 = side ^ 3 i . e . side of cube = 7 new cube has dimensions 14 , 14 , and 14 as all sides are twice of teh side of first cube volume = 14 * 14 * 14 = 2744 square feet answer : option d" | a ) 24 , b ) 48 , c ) 64 , d ) 2744 , e ) 100 | d | volume_cube(multiply(const_2, cube_edge_by_volume(343))) | cube_edge_by_volume(n0)|multiply(#0,const_2)|volume_cube(#1)| | geometry |
a train crosses a platform of 170 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ? | "length of the train be β x β x + 170 / 15 = x + 250 / 20 20 x + 3400 = 15 x + 3750 5 x = 350 x = 70 m answer : a" | a ) 70 , b ) 88 , c ) 167 , d ) 197 , e ) 161 | a | subtract(multiply(250, divide(15, divide(15, const_3))), multiply(170, divide(20, divide(15, const_3)))) | divide(n1,const_3)|divide(n1,#0)|divide(n3,#0)|multiply(n2,#1)|multiply(n0,#2)|subtract(#3,#4)| | physics |
a 6 litre sol is 25 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ? | "25 % of 6 = 1.5 50 % of 6 = 3 shortage is 1.5 so we need to have 1.5 / 50 % to get 50 % alcohol content . = 3 d" | a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 3 , e ) e . 5.4 | d | subtract(6, multiply(const_2, multiply(divide(25, const_100), 6))) | divide(n1,const_100)|multiply(n0,#0)|multiply(#1,const_2)|subtract(n0,#2)| | gain |
sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 40 ps per meter is ? | "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.40 = rs . 100 answer : c" | a ) 287 , b ) 369 , c ) 100 , d ) 279 , e ) 361 | c | divide(multiply(40, rectangle_perimeter(sqrt(divide(multiply(3750, 2), 3)), divide(3750, sqrt(divide(multiply(3750, 2), 3))))), const_100) | multiply(n1,n2)|divide(#0,n0)|sqrt(#1)|divide(n2,#2)|rectangle_perimeter(#3,#2)|multiply(n3,#4)|divide(#5,const_100)| | physics |
the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 2000 , then what is the income of p 1 ? | "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x β 3 y = 2000 β¦ ( i ) and 4 x β 2 y = 2000 β¦ β¦ . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 2000 - > x = 1000 p 1 β s income = rs 5 * 1000 =... | a ) s . 5000 , b ) s . 2400 , c ) s . 4000 , d ) s . 3200 , e ) s . 4200 | a | multiply(subtract(multiply(divide(2000, 2), 3), 2000), 5) | divide(n6,n1)|multiply(n4,#0)|subtract(#1,n6)|multiply(n2,#2)| | other |
cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 26 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ? | "use the options . the options which after getting added to 26 shows a cube of a number could be right . here 64 + 26 = 90 72 + 26 = 98 86 + 26 = 112 98 + 26 + 124 99 + 26 = 125 - - - ( 5 * 5 * 5 ) so we have 99 as the answer ! e" | a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 99 | e | subtract(power(add(const_1, add(const_1, const_3)), const_3), 26) | add(const_1,const_3)|add(#0,const_1)|power(#1,const_3)|subtract(#2,n0)| | geometry |
in a certain quiz that consists of 10 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 320 points , how many points is the third question worth ? | "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 x + 32 x + 36 10 x + 180 = 320 10 x = 140 x = 14 3 rd question = x + 8 = 14 + 8 = 22 answer c" | a ) 39 , b ) 24 , c ) 22 , d ) 20 , e ) 18 | c | add(divide(320, 10), subtract(subtract(10, 4), const_1)) | divide(n3,n2)|subtract(n0,n1)|subtract(#1,const_1)|add(#0,#2)| | general |
it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill 1 / 32 of the dish ? | "the bacteria doubles each day , so after 29 days , the dish was half full . after 28 days , the dish was one quarter full . after 27 days , the dish was one eighth full . after 26 days , the dish was one sixteenth full . after 25 days , the dish was 1 / 32 full . the answer is a ." | a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29 | a | subtract(30, log(32)) | log(n2)|subtract(n0,#0)| | general |
rahim bought 32 books for rs . 1500 from one shop and 60 books for rs . 340 from another . what is the average price he paid per book ? | "average price per book = ( 1500 + 340 ) / ( 32 + 60 ) = 1840 / 92 = rs . 20 answer : e" | a ) s . 17 , b ) s . 18 , c ) s . 12 , d ) s . 11 , e ) s . 20 | e | divide(add(1500, 340), add(32, 60)) | add(n1,n3)|add(n0,n2)|divide(#0,#1)| | general |
the average of numbers 0.64204 , 0.64203 , 0.64202 and 0.64201 is ? | "answer average = ( 0.64204 + 0.64203 + 0.64202 + 0.64201 ) / 4 = 2.5681 / 4 = 0.642025 correct option : d" | a ) 0.64202 , b ) 0.64204 , c ) 0.642022 , d ) 0.642025 , e ) none | d | divide(add(multiply(0.64204, 0.64203), multiply(0.64204, 0.64202)), 0.64204) | multiply(n0,n1)|multiply(n0,n2)|add(#0,#1)|divide(#2,n0)| | general |
there are 16 teams in a tournament . if during the first round , each team plays every other team exactly once , how many games will be played in the first round ? | number of ways to pick 2 teams from a total of 16 = 16 c 2 = 16 ! / 14 ! * 2 ! = 120 . hence c . | a ) 15 , b ) 30 , c ) 120 , d ) 240 , e ) 256 | c | divide(factorial(16), multiply(factorial(subtract(16, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4) | general |
there are 193 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 25 are members of both sets a and b . how many of the members of set u are members of set a ? | you had the answer almost right . the x = 85 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 85 + set ab = 85 + 25 = 110 c | a ) 72 , b ) 85 , c ) 110 , d ) 98 , e ) 108 | c | subtract(add(subtract(193, 59), 25), 49) | subtract(n0,n2)|add(n3,#0)|subtract(#1,n1) | other |
18 balls are numbered 1 to 18 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ? | "p ( 1 st ball is even ) = 9 / 18 p ( 2 nd ball is also even ) = 8 / 17 p ( both balls are even ) = 9 / 18 * 8 / 17 = 4 / 17 the answer is b ." | a ) 2 / 9 , b ) 4 / 17 , c ) 6 / 29 , d ) 8 / 35 , e ) 10 / 43 | b | multiply(divide(add(const_4, const_4), 18), divide(subtract(add(const_4, const_4), 1), subtract(18, 1))) | add(const_4,const_4)|subtract(n0,n1)|divide(#0,n0)|subtract(#0,n1)|divide(#3,#1)|multiply(#2,#4)| | other |
what is the probability that the sum of two dice will yield a 8 , and then when both are thrown again , their sum will again yield a 8 ? assume that each die has 7 sides with faces numbered 1 to 7 . | "solution - rolling dices is an independent event . the combinations to get 8 are ( 1,7 ) , ( 7,1 ) , ( 2,6 ) , ( 6,2 ) , ( 3,5 ) , ( 5,3 ) , ( 4 , , 4 ) and total combinations of both dices is 49 . the probability of getting 8 in first attempt is 7 / 49 = 1 / 7 . probability of getting 8 again in second attempt = ( 1 ... | a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 49 | e | multiply(divide(7, power(7, const_2)), divide(7, power(7, const_2))) | power(n2,const_2)|divide(n2,#0)|multiply(#1,#1)| | probability |
two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 15 seconds . find the length of the faster train ? | "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 15 sec = 15 * 10 = 150 m . the length of the faster train = 150 m . answer : e" | a ) 270 , b ) 277 , c ) 187 , d ) 257 , e ) 150 | e | multiply(divide(subtract(72, 36), const_3_6), 15) | subtract(n0,n1)|divide(#0,const_3_6)|multiply(n2,#1)| | physics |
a man swims downstream 72 km and upstream 45 km taking 12 hours each time ; what is the speed of the current ? | "72 - - - 12 ds = 6 ? - - - - 1 45 - - - - 12 us = 3.75 ? - - - - 1 s = ? s = ( 6 - 3.75 ) / 2 = 1.125 answer : a" | a ) 1.125 , b ) 1.128 , c ) 1.126 , d ) 1.123 , e ) 1.121 | a | divide(add(divide(45, 12), divide(72, 12)), const_2) | divide(n1,n2)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)| | physics |
find the simple interest on rs . 850 for 10 months at 7 paisa per month ? | "explanation : i = ( 850 * 10 * 7 ) / 100 = 595 answer : option c" | a ) s . 768 , b ) s . 329 , c ) s . 595 , d ) s . 600 , e ) s . 725 | c | multiply(850, divide(10, const_100)) | divide(n1,const_100)|multiply(n0,#0)| | gain |
sandy bought 65 books for $ 1480 from one shop and 55 books for $ 920 from another shop . what is the average price that sandy paid per book ? | "average price per book = ( 1480 + 920 ) / ( 65 + 55 ) = 2400 / 120 = $ 20 the answer is e ." | a ) $ 38 , b ) $ 18 , c ) $ 99 , d ) $ 27 , e ) $ 20 | e | divide(add(1480, 920), add(65, 55)) | add(n1,n3)|add(n0,n2)|divide(#0,#1)| | general |
how many of the positive divisors d of 120 are also multiples of 4 not including 120 ? | "4 , 8,12 , 20,24 , 40,60 . ( 7 ) is the answer other way : factors of 120 = 2 ^ 3 * 3 * 5 separate 2 ^ 2 ( which means 4 ) now , calculate the number of other factors . d = 2 * 3 * 5 = total positive factors are 2 * 2 * 2 = 8 this 8 factors include 120 so subtract 1 from 8 ans is 7 = d" | a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 . | d | divide(divide(divide(120, 4), const_2), const_3) | divide(n0,n1)|divide(#0,const_2)|divide(#1,const_3)| | general |
calculate 1307 x 1307 = ? | "answer 1307 x 1307 = ( 1307 ) 2 = ( 1300 + 7 ) 2 = ( 1300 ) 2 + ( 7 ) 2 + 2 x 1300 x 7 = 1690000 + 49 + 18200 = 1708249 option : d" | a ) 1601249 , b ) 1607249 , c ) 1701249 , d ) 1708249 , e ) none | d | multiply(1307, 1307) | multiply(n0,n1)| | general |
the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 80 , then 1 / m + 1 / n is equal to | "answer we have , m x n = 6 x 210 = 1260 Γ’ Λ Β΄ 1 / m + 1 / n = ( m + n ) / mn = 80 / 1260 = 4 / 63 correct option : d" | a ) 1 / 35 , b ) 3 / 35 , c ) 5 / 37 , d ) 4 / 63 , e ) none | d | divide(80, multiply(6, 210)) | multiply(n0,n1)|divide(n2,#0)| | general |
bottle r contains 100 capsules and costs $ 6.30 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ? | "cost per capsule in r is 6.30 / 100 = 0.063 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.004 the answer is a" | a ) $ 0.04 , b ) $ 0.12 , c ) $ 0.05 , d ) $ 0.03 , e ) $ 0.002 | a | subtract(divide(2.99, 130), divide(6.30, 100)) | divide(n3,n2)|divide(n1,n0)|subtract(#0,#1)| | general |
in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 250 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? | "the probability of survival for each of the first 3 months of life is 1 - 1 / 10 = 9 / 10 , so of 250 newborn 250 * 9 / 10 * 9 / 10 * 9 / 10 = ~ 183 is expected to survive . answer : e ." | a ) 140 , b ) 146 , c ) 152 , d ) 162 , e ) 183 | e | multiply(multiply(multiply(250, subtract(1, divide(1, 10))), subtract(1, divide(1, 10))), subtract(1, divide(1, 10))) | divide(n1,n2)|subtract(n1,#0)|multiply(n3,#1)|multiply(#2,#1)|multiply(#3,#1)| | probability |
if 3 a = 4 b and ab β 0 , what is the ratio of a / 4 to b / 3 ? | "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 3 a = 4 b here ' s one pair : a = 4 and b = 3 what is the ratio of a / 9 to b / 8 ? in other words , what is the value of ( a / 4 ) / ( b / 3 ) ? plug in values to get : ( a / 4 ) / ( b / 3 ) = ( 4 / 4 ) / ( 3 / 3 ) = 1 / 1 = 1 ... | a ) 64 / 27 , b ) 9 / 16 , c ) 1 , d ) 6 / 8 , e ) 8 / 6 | c | divide(multiply(3, 4), multiply(4, 3)) | multiply(n0,n1)|divide(#0,#0)| | general |
what is the smallest integer x such that 2 x + 2 is divisible by 33 , 44 , 55 , and 666 ? | 33 = 3 * 11 44 = 2 * 2 * 11 55 = 5 * 11 666 = 2 * 3 * 3 * 37 so 2 x + 2 = 2 * 2 * 3 * 3 * 5 * 11 * 37 = 73260 , and x = ( 73260 - 2 ) / 2 = 36629 , which is option d . | a ) x = 53186760 , b ) x = 26593379 , c ) x = 73260 , d ) x = 36629 , e ) x = 6666 | d | divide(subtract(lcm(lcm(lcm(33, 44), 55), 666), 2), 2) | lcm(n2,n3)|lcm(n4,#0)|lcm(n5,#1)|subtract(#2,n0)|divide(#3,n0) | general |
if 12 men do a work in 80 days , in how many days will 20 men do it ? | "12 * 80 = 20 * x x = 48 days answer : d" | a ) 18 days , b ) 38 days , c ) 42 days , d ) 48 days , e ) 44 days | d | divide(multiply(12, 80), 20) | multiply(n0,n1)|divide(#0,n2)| | physics |
5358 x 81 = ? | "d 273258 5358 x 81 = 5358 x ( 80 + 1 ) = 5358 x 80 + 5358 x 1 = 428640 + 5358 = 433998" | a ) 423762 , b ) 433758 , c ) 433298 , d ) 433998 , e ) 437382 | d | multiply(divide(5358, 81), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 126 , what is the common ratio of the g . p ? | "126 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 126 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 126 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 1... | a ) 3 , b ) 1 / 3 , c ) 2 , d ) 5 , e ) 1 / 5 | d | power(subtract(126, const_1), divide(const_1, 3)) | divide(const_1,n1)|subtract(n2,const_1)|power(#1,#0)| | other |
there are 6 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 15 other amateurs , what is the total number of chess games possible to be played in the tournament ? | "each person is one participant of 6 games . so there are in all 6 * 15 = 90 instances of one participant games . but each game has 2 participants so total number of games = 90 / 2 = 45 c" | a ) 10 , b ) 20 , c ) 45 , d ) 60 , e ) 120 | c | divide(multiply(6, 15), const_2) | multiply(n0,n1)|divide(#0,const_2)| | general |
tough and tricky questions : probability . medical analysts predict that a quarter of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote . what fraction of a group of 1000 people could be expected to be killed... | at the end of each day we will have 3 / 4 alive . so after 3 days we will have ( 3 / 4 ) ^ 3 people alive . therefore , fraction of dead people will be 1 - ( 3 / 4 ) ^ 3 = 37 / 64 . the correct answer is a . | a ) 37 / 64 , b ) 8 / 27 , c ) 2 / 3 , d ) 19 / 27 , e ) 65 / 81 | a | add(add(divide(const_1, add(3, const_1)), multiply(subtract(const_1, divide(const_1, add(3, const_1))), divide(const_1, add(3, const_1)))), multiply(subtract(const_1, add(multiply(subtract(const_1, divide(const_1, add(3, const_1))), divide(const_1, add(3, const_1))), divide(const_1, add(3, const_1)))), divide(const_1, ... | add(n1,const_1)|divide(const_1,#0)|subtract(const_1,#1)|multiply(#1,#2)|add(#1,#3)|subtract(const_1,#4)|multiply(#1,#5)|add(#4,#6) | general |
if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 10800 ? | "required difference = [ 3 Β½ % of rs . 10800 ] β [ 3 1 / 3 % of rs . 10800 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 10800 = 1 / 6 % of rs . 10800 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 10800 ] = rs . 18 . answer is d ." | a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10 | d | divide(multiply(subtract(add(divide(1, 2), 3), add(divide(1, 3), 3)), 10800), const_100) | divide(n1,n2)|divide(n1,n0)|add(n0,#0)|add(n0,#1)|subtract(#2,#3)|multiply(n6,#4)|divide(#5,const_100)| | general |
in 1985 a company sold a brand of shoes to retailers for a fixed price per pair . in 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent , while the price per pair increased by 20 percent . if the company β s revenue from the sale of the shoes in 1986 was $ 3.0 million , wha... | let the number of pairs of shoes sold in 1985 = n let price per pair of shoe sold in 1985 = p in 1986 , number of pairs of shoes sold decreased by 20 % = . 8 n price per pair increased by 20 % = 1.2 p company ' s revenue from sale of shoes in 1986 = 3 million $ = > . 8 n * 1.2 p = 3 = > . 96 np = 3 = > np = 3 / . 96 = ... | a ) $ 2.4 million , b ) $ 2.9 million , c ) $ 3.0 million , d ) $ 3.1 million , e ) $ 3.6 million | d | divide(subtract(subtract(const_100, 20), 20), 20) | subtract(const_100,n2)|subtract(#0,n2)|divide(#1,n2) | general |
the ratio of the volumes of two cubes is 3375 : 1331 . what is the ratio of their total surface areas ? | "explanation : ratio of the sides = Β³ β 3375 : Β³ β 1331 = 15 : 11 ratio of surface areas = 15 ^ 2 : 11 ^ 2 = 225 : 121 answer : option a" | a ) 225 : 121 , b ) 221 : 127 , c ) 225 : 191 , d ) 181 : 161 , e ) 81 : 182 | a | power(divide(3375, 1331), divide(const_1, const_3)) | divide(n0,n1)|divide(const_1,const_3)|power(#0,#1)| | geometry |
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 2 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 2 hours . if the company used the... | a ) 3 / 4 , b ) 4 , c ) 18 / 19 , d ) 9 , e ) 12 | c | divide(const_1, multiply(2, add(divide(const_1, 36), divide(const_1, 2)))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n1,#2)|divide(const_1,#3) | gain |
the difference between compound and simple interest on a particular sum of money for 3 years at 6 and 2 / 3 % p . a is rs . 184 . what is the sum ? | "p = ( 184 * 10 ^ 6 ) / ( 6 2 / 3 * 6 2 / 3 * ( 300 * 6 2 / 3 ) ) = = > 13500 answer b" | a ) 13000 , b ) 13500 , c ) 14000 , d ) 14500 , e ) 15000 | b | subtract(divide(multiply(multiply(multiply(multiply(184, 3), 3), 3), 6), 2), const_1000) | multiply(n0,n4)|multiply(n0,#0)|multiply(n0,#1)|multiply(n1,#2)|divide(#3,n2)|subtract(#4,const_1000)| | general |
triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 36 , what is the measure of side xy ? | "ans c . . 12 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 36 or yz = 3 * \ sqrt { 2 } . . therefore hyp = xy = 12" | a ) 4 , b ) 4 β 2 , c ) 12 , d ) 8 β 2 , e ) can not be determined from the information provided | c | sqrt(add(power(multiply(sqrt(36), sqrt(const_2)), const_2), power(multiply(sqrt(36), sqrt(const_2)), const_2))) | sqrt(n0)|sqrt(const_2)|multiply(#0,#1)|power(#2,const_2)|add(#3,#3)|sqrt(#4)| | geometry |
at 6 β² o a clock ticks 6 times . the time between first and last ticks is 40 seconds . how long does it tick at 12 β² o clock | "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 40 / 5 = 8 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 Γ 8 = 88 secs . answer : b" | a ) 47 , b ) 88 , c ) 28 , d ) 66 , e ) 11 | b | multiply(divide(40, subtract(6, const_1)), subtract(12, const_1)) | subtract(n0,const_1)|subtract(n3,const_1)|divide(n2,#0)|multiply(#2,#1)| | physics |
the sum of two numbers is 12 and the product of the numbers is 35 . find sum of the squares of that numbers . | let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 12 ab = 35 so , 12 ^ 2 = a ^ 2 + b ^ 2 + 2 * 35 144 = a ^ 2 + b ^ 2 + 70 a ^ 2 + b ^ 2 = 74 ans e | a ) 84 , b ) 87 , c ) 96 , d ) 79 , e ) 74 | e | divide(subtract(35, power(12, const_2)), const_2) | power(n0,const_2)|subtract(n1,#0)|divide(#1,const_2)| | general |
the balance of a trader weighs 20 % less than it should . still the trader marks up his goods to get an overall profit of 30 % . what is the mark up on the cost price ? | the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 80 gms because it weighs 20 % less . say , the cost price is $ 80 ( $ 1 / gm ) . since he gets a profit of 30 % , the selling price must be 80 + ( 30 / 100 ) * 80 = $ 104 since the c... | a ) 4 % , b ) 8 % , c ) 25 % , d ) 16.66 % , e ) 9 % | a | subtract(add(multiply(multiply(const_4, 20), divide(30, const_100)), multiply(const_4, 20)), const_100) | divide(n1,const_100)|multiply(n0,const_4)|multiply(#0,#1)|add(#2,#1)|subtract(#3,const_100) | gain |
it takes 2 workers a total of 12 hours to build a giant machine with each worker working at the same rate . if 3 workers start to build the machine at 11 : 00 am , and one extra worker per hour is added beginning at 2 : 00 pm , at what time will the machine be complete ? | 2 workers build 1 / 12 of a machine in one hour . 1 worker builds 1 / 24 of a machine in one hour . in the first 3 hours , 3 workers build 3 * ( 1 / 24 ) * 3 = 9 / 24 of a machine from 2 : 00 to 3 : 00 , 4 workers build another 4 / 24 . the total is 13 / 24 . from 3 : 00 to 4 : 00 , 5 workers build another 5 / 24 . the... | a ) 4 : 30 , b ) 4 : 45 , c ) 5 : 00 , d ) 5 : 15 , e ) 5 : 30 | c | subtract(divide(multiply(2, 12), 12), const_0_33) | multiply(n0,n1)|divide(#0,n1)|subtract(#1,const_0_33) | general |
find the number , difference between number and its 3 / 5 is 50 . | "explanation : let the number = x , then , x - ( 3 / 5 ) x = 50 , = > ( 2 / 5 ) x = 50 = > 2 x = 50 * 5 , = > x = 125 option d" | a ) 120 , b ) 123 , c ) 124 , d ) 125 , e ) 359 | d | multiply(divide(50, const_2), 5) | divide(n2,const_2)|multiply(n1,#0)| | general |
in a coconut grove , ( x + 3 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x β 3 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x . | "( x + 3 ) Γ 60 + x Γ 120 + ( x β 3 ) Γ 180 / ( x + 3 ) + x + ( x β 3 ) = 100 β 360 x β 360 / 3 x = 100 β 60 x = 360 β x = 6 answer d" | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) none of the above | d | divide(subtract(multiply(180, 3), multiply(60, 3)), subtract(add(add(60, 120), 180), multiply(100, const_3))) | add(n1,n2)|multiply(n0,n4)|multiply(n0,n1)|multiply(n5,const_3)|add(n4,#0)|subtract(#1,#2)|subtract(#4,#3)|divide(#5,#6)| | general |
jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much w does she have in her account after two years ? | "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer" | a ) $ 10079.44 , b ) w = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11 | b | multiply(10000, power(add(const_1, divide(divide(3.96, const_100), const_2)), const_4)) | divide(n1,const_100)|divide(#0,const_2)|add(#1,const_1)|power(#2,const_4)|multiply(n0,#3)| | gain |
a 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ? | "relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 290 ) / 9 = 500 / 9 x + 290 = 500 x = 210 . b" | a ) 230 m , b ) 210 m , c ) 260 m , d ) 320 m , e ) 330 m | b | subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 290) | add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)| | physics |
find the average of all prime numbers between 4 and 15 . | sol . there are four prime numbers between 4 and 15 . they are 5 , 7 , 11 , 13 Γ’ Λ Β΄ required average = [ 5 + 7 + 11 + 13 / 4 ] = 36 / 4 = 9 answer c | a ) 30 , b ) 4 , c ) 9 , d ) 8 , e ) none | c | divide(add(add(add(4, const_1), add(add(4, const_1), const_2)), add(subtract(15, 4), subtract(15, const_2))), const_4) | add(n0,const_1)|subtract(n1,n0)|subtract(n1,const_2)|add(#0,const_2)|add(#1,#2)|add(#0,#3)|add(#5,#4)|divide(#6,const_4) | general |
100 people are attending a newspaper conference . 40 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ? | "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 40 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 40 + { editors } - x + 2 x - - > x = 60 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } i... | a ) 21 , b ) 24 , c ) 28 , d ) 30 , e ) 32 | a | subtract(100, add(add(38, const_1), 40)) | add(n2,const_1)|add(n1,#0)|subtract(n0,#1)| | other |
a milkman purchases the milk at rs . x per litre and sells it at rs . 2 x per litre still he mixes 2 litres water with every 6 litres of pure milk . what is the profit percentage ? | let the cost price of 1 litre pure milk be re . 1 , then \ inline \ begin { bmatrix } 6 & litres ( milk ) & \ rightarrow & cp = rs . 6 \ \ 2 & litres ( water ) & \ rightarrow & cp = rs . 0 \ end { bmatrix } \ rightarrow cp = rs . 6 only and 8 litre mixture \ rightarrow sp \ rightarrow 8 x 2 = rs . 16 profit % = % answe... | a ) 166.69 % , b ) 166.66 % , c ) 166.76 % , d ) 136.66 % , e ) 566.66 % | b | multiply(subtract(divide(multiply(add(6, 2), 2), 6), const_1), const_100) | add(n0,n2)|multiply(n0,#0)|divide(#1,n2)|subtract(#2,const_1)|multiply(#3,const_100) | gain |
a and b can do a work in 12 days , b and c in 15 days , c and a in 20 days . if a , b and c work together , they will complete the work in : | "( a + b ) ' s 1 day ' s work = 1 / 12 , ( b + c ) ' s 1 day ' s work = 1 / 15 ; ( a + c ) ' s 1 day ' s work = 1 / 20 adding , we get : 2 ( a + b + c ) ' s 1 day ' s work = ( 1 / 12 + 1 / 15 + 1 / 20 ) = 12 / 60 = 1 / 5 ( a + b + c ) ' s 1 day ' s work = 1 / 10 so , a , b and c together can complete the work in 10 day... | a ) 5 days , b ) 7 5 / 6 days , c ) 10 days , d ) 15 2 / 3 days , e ) none of these | c | divide(const_1, divide(add(add(inverse(12), inverse(15)), inverse(20)), const_2)) | inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|divide(#4,const_2)|divide(const_1,#5)| | physics |
a person distributed 15 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 10 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ? | 3 children got = 3 * 15 % = 45 % wife got = 30 % orphan house = 10 % total = 45 + 30 + 10 = 85 % remaining = 100 - 85 = 15 % 15 % = 40000 100 % = 40000 * 100 / 15 = $ 266666.7 answer is a | a ) a ) 266666.7 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 500000 , e ) e ) 652000 | a | multiply(divide(40000, subtract(const_100, add(add(multiply(15, 3), 30), 10))), const_100) | multiply(n0,n1)|add(n2,#0)|add(n3,#1)|subtract(const_100,#2)|divide(n4,#3)|multiply(#4,const_100) | gain |
how many positive integers less than 250 are there such that they are multiples of 15 or multiples of 14 ? | "250 / 15 = 16 ( plus remainder ) so there are 16 multiples of 15 250 / 14 = 17 ( plus remainder ) so there are 17 multiples of 14 we need to subtract 1 because 15 * 14 is a multiple of both so it was counted twice . the total is 16 + 17 - 1 = 32 the answer is c ." | a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34 | c | divide(factorial(subtract(add(const_4, 15), const_1)), multiply(factorial(15), factorial(subtract(const_4, const_1)))) | add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)| | general |
a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 240 m long ? | speed = 45 km / hr = 45 Γ£ β ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 240 = 600 meter time taken to cross the platform = 600 / ( 25 / 2 ) = 600 Γ£ β 2 / 25 = 48 seconds answer : d | a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 48 sec , e ) none of these | d | multiply(divide(add(divide(240, const_1000), divide(360, const_1000)), 45), const_3600) | divide(n2,const_1000)|divide(n0,const_1000)|add(#0,#1)|divide(#2,n1)|multiply(#3,const_3600) | physics |
a train 300 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ? | "s = ( 300 + 300 ) / 45 = 600 / 45 * 18 / 5 = 48 answer : b" | a ) 32 , b ) 48 , c ) 29 , d ) 27 , e ) 21 | b | divide(divide(add(300, 300), const_1000), divide(45, const_3600)) | add(n0,n1)|divide(n2,const_3600)|divide(#0,const_1000)|divide(#2,#1)| | physics |
how long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length ? | "t = ( 660 + 165 ) / 72 * 18 / 5 t = 41.25 answer : b" | a ) 28 , b ) 41.25 , c ) 55 , d ) 18 , e ) 12 | b | divide(add(165, 660), multiply(72, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | physics |
how many integers from 101 to 700 , inclusive , remains the value unchanged when the digits were reversed ? | "question is asking for palindrome first digit possibilities - 1 through 6 = 6 7 is not possible here because it would result in a number greater than 7 ( i . e 707 , 717 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 6 * 10... | a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90 | b | divide(700, const_10) | divide(n1,const_10)| | general |
what sum of money put at c . i amounts in 2 years to rs . 8800 and in 3 years to rs . 9261 ? | "8800 - - - - 461 100 - - - - ? = > 5.238 % x * 105.238 / 100 * 105.238 / 100 = 8800 x * 1.1075 = 8800 x = 8800 / 1.1075 = > 7945.70 answer : a" | a ) 7945 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011 | a | divide(8800, power(add(subtract(divide(9261, 8800), const_1), const_1), 2)) | divide(n3,n1)|subtract(#0,const_1)|add(#1,const_1)|power(#2,n0)|divide(n1,#3)| | general |
find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 63 = x ? | c ) 3 | a ) 1 , b ) 5 , c ) 3 , d ) 6 , e ) 7 | c | floor(add(reminder(add(subtract(multiply(divide(47, const_100), 1442), multiply(divide(36, const_100), 1412)), 63), const_10), const_1)) | divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|multiply(n3,#1)|subtract(#2,#3)|add(n4,#4)|reminder(#5,const_10)|add(#6,const_1)|floor(#7)| | general |
if in a certain code ` ` range ' ' is coded as 12345 and ` ` random ' ' is coded as 123678 . then the code for the word ` ` gone ' ' would be | g - 4 o - 7 n - 3 e - 5 so for mango the code is 4735 answer : d | a ) 3569 , b ) 1552 , c ) 4573 , d ) 4735 , e ) 5235 | d | add(divide(const_1000, const_2), divide(12345, const_3)) | divide(const_1000,const_2)|divide(n0,const_3)|add(#0,#1) | general |
if henry were to add 4 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ? | "7 / 8 x - 3 / 4 x = 4 galls 1 / 8 * x = 4 gallons x = 32 gallons answer a" | a ) 32 , b ) 40 , c ) 64 , d ) 80 , e ) 96 | a | multiply(4, divide(const_1, subtract(divide(7, 8), divide(3, 4)))) | divide(n3,n4)|divide(n1,n2)|subtract(#0,#1)|divide(const_1,#2)|multiply(n0,#3)| | general |
a train 120 m long crosses a platform with a speed of 60 kmph in 15 sec ; find the length of the platform ? | d = 120 + x t = 15 s = 120 + x / 15 * 18 / 5 = 60 kmph . = > ( 120 + x ) * 18 = 4500 = > 120 + x = 250 = > x = 130 m answer : b | a ) 110 , b ) 130 , c ) 120 , d ) 125 , e ) 135 | b | subtract(multiply(15, multiply(60, const_0_2778)), 120) | multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0) | physics |
a sum fetched a total simple interest of rs . 4016.25 at the rate of 5 % p . a . in 5 years . what is the sum ? | "principal = ( 100 * 4016.25 ) / ( 5 * 5 ) = rs . 16065 . answer : c" | a ) 12021 , b ) 14520 , c ) 16065 , d ) 18925 , e ) 12887 | c | divide(divide(multiply(4016.25, const_100), 5), 5) | multiply(n0,const_100)|divide(#0,n1)|divide(#1,n2)| | gain |
a man rows his boat 84 km downstream and 48 km upstream , taking 2 hours each time . find the speed of the stream ? | "speed downstream = d / t = 84 / ( 2 ) = 42 kmph speed upstream = d / t = 48 / ( 2 ) = 24 kmph the speed of the stream = ( 42 - 24 ) / 2 = 9 kmph answer : c" | a ) 6 kmph , b ) 5 kmph , c ) 9 kmph , d ) 8 kmph , e ) 1 kmph | c | divide(subtract(divide(84, 2), divide(48, 2)), const_2) | divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2)| | physics |
ratio between length and breath of a rectangle is 25 : 16 . the area of the rectangle is same with a square whose side is 200 . find the breadth and length of the rectangle ? | let length l = 25 x and breadth b = 16 x area of the square = 200 ^ 2 = 40000 16 x * 25 x = 40000 400 x ^ 2 = 40000 x ^ 2 = 100 x = 10 length = 25 * 10 = 250 breadth = 16 * 10 = 160 answer : d | ['a ) 150,200', 'b ) 140,300', 'c ) 100,300', 'd ) 160,250', 'e ) 100,200'] | d | add(multiply(const_1000, multiply(sqrt(divide(square_area(200), multiply(25, 16))), 16)), multiply(sqrt(divide(square_area(200), multiply(25, 16))), 25)) | multiply(n0,n1)|square_area(n2)|divide(#1,#0)|sqrt(#2)|multiply(n1,#3)|multiply(n0,#3)|multiply(#4,const_1000)|add(#6,#5) | geometry |
what number has a 20 : 1 ratio to the number 10 ? | "20 : 1 = x : 10 x = 10 * 20 x = 150 answer : c" | a ) 130 , b ) 100 , c ) 200 , d ) 150 , e ) 120 | c | multiply(10, 20) | multiply(n0,n2)| | other |
the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 146 , what is the difference between the ages of patrick and monica ? | "ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 146 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b" | a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 18 | b | subtract(multiply(multiply(5, 5), divide(146, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5)))), multiply(multiply(3, 3), divide(146, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5))))) | multiply(n0,n0)|multiply(n1,n0)|multiply(n1,n3)|add(#0,#1)|add(#3,#2)|divide(n4,#4)|multiply(#5,#2)|multiply(#5,#0)|subtract(#6,#7)| | general |
mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.25 . each pot cost 0.3 more than the next one below it in size . what was the cost , in dollars , of the largest pot ? | "this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 30 cents more than the nex... | a ) $ 1.75 , b ) $ 1.85 , c ) $ 2.00 , d ) $ 2.12 , e ) $ 2.30 | d | add(divide(subtract(8.25, multiply(divide(multiply(subtract(6, const_1), 6), const_2), 0.3)), 6), multiply(subtract(6, const_1), 0.3)) | subtract(n0,const_1)|multiply(n0,#0)|multiply(n2,#0)|divide(#1,const_2)|multiply(n2,#3)|subtract(n1,#4)|divide(#5,n0)|add(#6,#2)| | general |
what quantity of water should taken out to concentrate 15 liters of 40 % acidic liquid to 60 % acidic liquid ? | required answer is = 15 ( 60 - 40 ) / 60 = 5 liters answer is a | a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters | a | subtract(15, divide(multiply(15, 40), 60)) | multiply(n0,n1)|divide(#0,n2)|subtract(n0,#1) | gain |
what is the remainder when 9 ^ 19 is divided by 5 ? | "9 ^ 0 = 1 9 ^ 1 = 9 9 ^ 2 = 81 9 ^ 3 = 729 9 ^ 4 = . . . 1 9 ^ 5 = . . . . . 9 and so on in a distinct last - digit pattern of 9,1 , 9,1 . . . after ignoring the first last - digit of 1 19 / 2 = 9 ( with a remainder of 1 ) so the last number is a 9 . alternatively , 19 is an odd number and hence the last digit is a 9 ... | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | e | subtract(divide(5, const_2), multiply(9, 9)) | divide(n2,const_2)|multiply(n0,n0)|subtract(#0,#1)| | general |
eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 5 hours ? | "8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 5 hours ) = 1125 cans . the answer is c ." | a ) 675 , b ) 750 , c ) 1,125 , d ) 5,900 , e ) 7,500 | c | subtract(multiply(5, 360), multiply(5, divide(multiply(5, 360), add(const_4, const_4)))) | add(const_4,const_4)|multiply(n0,n2)|multiply(n0,n1)|divide(#2,#0)|multiply(n2,#3)|subtract(#1,#4)| | physics |
a trained covered x km at 65 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km . | "total time taken = x / 65 + 2 x / 20 hours = 3 x / 26 hours average speed = 3 x / ( 3 x / 26 ) = 26 kmph answer : c" | a ) 22 , b ) 99 , c ) 26 , d ) 66 , e ) 887 | c | divide(multiply(65, 3), add(divide(65, 65), divide(multiply(2, 65), 20))) | divide(n0,n0)|multiply(n0,n3)|multiply(n0,n1)|divide(#2,n2)|add(#0,#3)|divide(#1,#4)| | general |
what is the remainder when 2676 * 1487 * 4459 is divided by 12 | "2679 / 12 = = > remainder = 3 1487 / 12 = = > remainder = 11 4459 / 12 = = > remainder = 7 = 3 * 11 * 7 = 231 / 12 = = > remainder = 3 answer : a" | a ) 3 , b ) 8 , c ) 12 , d ) 9 , e ) 27 | a | reminder(multiply(1487, 2676), 4459) | multiply(n0,n1)|reminder(#0,n2)| | general |
ms . lopez deposits $ 140 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ? | using formula - a = p ( 1 + r / n ) ^ nt given p = 140 n = 2 t = 1 r = 0.2 substituting value in formula a = 140 ( 1 + 0.2 / 2 ) ^ 2 a = 169.40 $ = c | a ) $ 118.00 , b ) $ 120.00 , c ) $ 169.40 , d ) $ 122.00 , e ) $ 140.00 | c | multiply(140, power(add(const_1, divide(divide(20, const_100), const_2)), const_2)) | divide(n1,const_100)|divide(#0,const_2)|add(#1,const_1)|power(#2,const_2)|multiply(n0,#3) | gain |
a train running at the speed of 72 km / hr crosses a pole in 9 seconds . what is the length of the train ? | "speed = ( 72 * 5 / 18 ) m / sec = ( 20 ) m / sec length of the train = ( speed x time ) = ( 20 * 9 ) m = 180 m . answer : d" | a ) 286 , b ) 278 , c ) 255 , d ) 180 , e ) 287 | d | multiply(divide(multiply(72, const_1000), const_3600), 9) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
the speed at which a man can row a boat in still water is 20 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 60 metres ? | "speed of the boat downstream = 20 + 3 = 23 kmph = 23 * 5 / 18 = 115 / 18 m / s hence time taken to cover 60 m = 60 * 18 / 115 = 9.4 seconds . answer : d" | a ) 16 seconds , b ) 76 seconds , c ) 26 seconds , d ) 9.4 seconds , e ) 18 seconds | d | divide(60, multiply(add(20, 3), const_0_2778)) | add(n0,n1)|multiply(#0,const_0_2778)|divide(n2,#1)| | physics |
a 16 % stock yielding 14 % is quoted at : | "income of rs 14 on investment of rs 100 income of rs 16 on investment of ? = ( 16 * 100 ) / 14 = 114 answer : c" | a ) s . 83.33 , b ) s . 110 , c ) s . 114 , d ) s . 120 , e ) s . 140 | c | multiply(divide(const_100, 14), 16) | divide(const_100,n1)|multiply(n0,#0)| | gain |
in filling a lot with sand , that is 40 m * 20 m * 2 m the volumes of the sand filled will be ? | 40 * 20 * 2 = 1600 answer : d | ['a ) 1200 cu . m', 'b ) 2200 cu . m', 'c ) 4800 cu . m', 'd ) 1600 cu . m', 'e ) 4000 cu . m'] | d | volume_rectangular_prism(40, 20, 2) | volume_rectangular_prism(n0,n1,n2) | physics |
the value of ( ( x β y ) Β³ + ( y - z ) Β³ + ( z β x ) Β³ ) / ( 15 ( x β y ) ( y β z ) ( z β x ) ) is equal to : | since ( x β y ) + ( y β z ) + ( z β x ) = 0 , so ( x β y ) Β³ + ( y β z ) Β³ + ( z β x ) Β³ = 3 ( x β y ) ( y β z ) ( z β x ) . ( 3 ( x β y ) ( y β z ) ( z β x ) ) / ( 15 ( x β y ) ( y β z ) ( z β x ) ) = 1 / 5 . answer : d | a ) 0 , b ) 1 / 12 , c ) 1 , d ) 1 / 5 , e ) 1 / 3 | d | divide(const_3, 15) | divide(const_3,n0) | general |
a is the product of each integer from 1 to 50 , inclusive and b = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of a ? | the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k β€ n x = 1 * 2 * 3 . . . . * 50 = 50 ! no . of trailing zeros in 50 ! = 50 / 5 + 50 / 5 ^ 2 = 10... | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | a | divide(add(divide(50, divide(const_10, const_2)), const_2), const_2) | divide(const_10,const_2)|divide(n1,#0)|add(#1,const_2)|divide(#2,const_2) | general |
reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 432 as interest at the end of the loan period , what was the rate of interest ? | "let rate = r % and time = r years . then , 1200 x r x r / 100 = 432 12 r 2 = 432 r 2 = 36 r = 6 . answer : b" | a ) 3.6 , b ) 6 , c ) 18 , d ) can not be determined , e ) none of these | b | sqrt(divide(multiply(432, const_100), 1200)) | multiply(n1,const_100)|divide(#0,n0)|sqrt(#1)| | gain |
if n is the greatest positive integer for which 4 ^ n is a factor of 10 ! , then n = ? | 10 ! = 3628800 e . 4 ^ 10 = 1048576 ( 3628800 / 1048576 ) - this is not a factor of 10 ! d . 4 ^ 8 = 65536 ( 3628800 / 65536 ) - this is not a factor of 10 ! c . 4 ^ 6 = 4096 ( 3628800 / 4096 ) - this is not a factor of 10 ! b . 4 ^ 4 = 256 ( 3628800 / 256 ) - this is a factor of 10 ! b is answer | a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10 | b | subtract(divide(10, const_2), const_1) | divide(n1,const_2)|subtract(#0,const_1) | other |
an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 1400 sculptures are not on display , how many pieces of art does the gallery have ? | "too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 ... | a ) 360 , b ) 3150 , c ) 540 , d ) 640 , e ) 720 | b | divide(divide(1400, subtract(1, divide(1, 3))), subtract(1, divide(1, 3))) | divide(n0,n1)|subtract(n0,#0)|divide(n6,#1)|divide(#2,#1)| | general |
the grade point average of one third of the classroom is 60 ; the grade point average of the rest is 66 . what is the grade point average of the whole class ? | "let n = total students in class total points for 1 / 3 class = 60 n / 3 = 20 n total points for 2 / 3 class = 66 * 2 n / 3 = 44 n total points for whole class = 20 n + 44 n = 64 n 64 n total class points / n total students = 64 grade point average for total class answer : c" | a ) 55 , b ) 56 , c ) 64 , d ) 65 , e ) 66 | c | add(multiply(divide(66, const_3), const_2), divide(60, const_3)) | divide(n0,const_3)|divide(n1,const_3)|multiply(#1,const_2)|add(#0,#2)| | general |
if the digits 33 in the decimal 0.00033 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00033 ) ? | 99 * 0.33 = 32.67 approx . 33 answer : b | a ) 0.33 , b ) 33 , c ) 0.033 , d ) 0.0033 , e ) 3.3 e - 05 | b | multiply(divide(multiply(multiply(multiply(10, 10), subtract(multiply(10, 10), const_1)), divide(33, subtract(multiply(10, 10), const_1))), const_1000), 10) | multiply(n2,n2)|subtract(#0,const_1)|divide(n0,#1)|multiply(#0,#1)|multiply(#2,#3)|divide(#4,const_1000)|multiply(n2,#5) | general |
sum of two numbers is 10 . two times of the first exceeds by 5 from the 3 times of the other . then the numbers will be ? | explanation : x + y = 10 2 x β 3 y = 5 x = 7 y = 3 a ) | a ) a ) 7 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15 | a | divide(add(multiply(10, 3), 5), add(const_2, 3)) | add(n2,const_2)|multiply(n0,n2)|add(n1,#1)|divide(#2,#0) | general |
two whole numbers whose sum is 72 can not be in the ratio | "sol . the sum of the ratio terms must divide 72 . so , the ratio can not be 3 : 4 . answer a" | a ) 3 : 4 , b ) 3 : 5 , c ) 4 : 5 , d ) 5 : 7 , e ) none | a | divide(divide(subtract(divide(72, const_2), const_10), const_2), add(divide(72, const_2), const_10)) | divide(n0,const_2)|add(#0,const_10)|subtract(#0,const_10)|divide(#2,const_2)|divide(#3,#1)| | other |
a group of men decided to do a work in 20 days , but 2 of them became absent . if the rest of the group did the work in 22 days , find the original number of men ? | "original number of men = 2 * 22 / ( 22 - 20 ) = 22 answer is b" | a ) 15 , b ) 22 , c ) 27 , d ) 29 , e ) 18 | b | divide(multiply(2, 22), subtract(22, 20)) | multiply(n1,n2)|subtract(n2,n0)|divide(#0,#1)| | physics |
a train 280 m long is running at 70 kmph . in how much time will it pass a platform 210 m long ? | distance travelled = 280 + 210 m = 490 m speed = 70 * 5 / 8 = 205 / 4 m time = 490 * 4 / 205 = 9.56 seconds answer : b . | a ) 1.5 seconds , b ) 9.56 seconds , c ) 28.56 seconds , d ) 30.56 seconds , e ) 3.5 seconds | b | divide(add(280, 210), multiply(const_60.0, const_0_2778)) | add(n0,n2)|multiply(const_60.0,const_0_2778)|divide(#0,#1)| | physics |
a reduction of 20 % in the price of salt enables a lady to obtain 25 kgs more for rs . 100 , find the original price per kg ? | "100 * ( 20 / 100 ) = 20 - - - 25 ? - - - 1 = > rs . 0.8 100 - - - 80 ? - - - 0.8 = > rs . 1 answer : b" | a ) 6 , b ) 1 , c ) 5 , d ) 4 , e ) 7 | b | multiply(divide(divide(multiply(divide(20, const_100), 100), 25), multiply(divide(20, const_100), 100)), const_100) | divide(n0,const_100)|multiply(n2,#0)|divide(#1,n1)|divide(#2,#1)|multiply(#3,const_100)| | gain |
in how many no . between 10 and 30 exactly two of the digits is 3 ? | it ' s simple can be solved by elimination of answer choices . option b and c are too large , not possible . even de are large to have correct choice . ans : a | a ) 1 , b ) 20 , c ) 30 , d ) 40 , e ) 50 | a | divide(divide(30, 10), 3) | divide(n1,n0)|divide(#0,n2) | general |
( 208 % of 1265 ) Γ· 6 = ? | "explanation : ? = ( 208 x 1265 / 100 ) Γ· 6 = 263120 / 600 = 439 answer : option b" | a ) a ) 125 , b ) b ) 439 , c ) c ) 225 , d ) d ) 375 , e ) e ) 524 | b | divide(multiply(divide(208, const_100), 1265), 6) | divide(n0,const_100)|multiply(n1,#0)|divide(#1,n2)| | general |
by selling an article at rs . 120 , a profit of 25 % is made . find its cost price ? | "sp = 120 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 120 * [ 100 / ( 100 + 25 ) ] = 120 * [ 100 / 125 ] = rs . 96 answer : a" | a ) s . 96 , b ) s . 45 , c ) s . 120 , d ) s . 180 , e ) s . 189 | a | divide(multiply(120, const_100), add(const_100, 25)) | add(n1,const_100)|multiply(n0,const_100)|divide(#1,#0)| | gain |
the average score of a cricketer in 2 matches is 40 and in other 3 matches is 10 . then find the average score in all the 5 matches ? | "average in 5 matches = ( 2 * 40 + 3 * 10 ) / 2 + 3 = 80 + 30 / 5 = 110 / 5 = 22 answer is b" | a ) 25 , b ) 22 , c ) 30 , d ) 35 , e ) 42 | b | divide(add(multiply(2, 40), multiply(3, 10)), 5) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|divide(#2,n4)| | general |
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