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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if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 1000 , what is the least possible value of n ? | 1000 = 2 * 2 * 2 * 5 * 5 * 5 , so we need 3 factors of 2 and 3 factors of 5 . therefore , the smallest value of n is 15 , so the answer is e . | a ) 12 , b ) 11 , c ) 14 , d ) 13 , e ) 15 | e | divide(1000, const_2) | divide(n1,const_2)| | general |
in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 1 : 2 . in the subsequent n games , the ratio of the team ´ s wins to losses was 1 : 4 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ? | "m = 4 / 9 of total games n = 5 / 9 of total games wins = 1 / 3 * 4 / 9 + 1 / 5 * 5 / 9 = 4 / 27 + 3 / 27 = 7 / 27 losses = 1 - 7 / 27 = 20 / 27 the ratio of wins to losses is 7 : 20 . the answer is a ." | a ) 7 : 20 , b ) 9 : 23 , c ) 11 : 27 , d ) 23 : 54 , e ) 31 : 77 | a | divide(add(1, 1), add(const_3.0, 2)) | add(n0,n2)|add(n3,n1)|divide(#0,#1)| | general |
in an it company , there are a total of 120 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ? | "you could pick 70 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 75 . e" | a ) 10 , b ) 50 , c ) 55 , d ) 35 , e ) 75 | e | add(subtract(80, 120), subtract(50, 35)) | subtract(n2,n0)|subtract(n1,n3)|add(#0,#1)| | general |
a and b can do a piece of work in 6 days , b and c in 8 days , c and a in 12 days . how long will c take to do it ? | "2 c = 1 / 8 + 1 / 12 – 1 / 6 = 1 / 24 c = 1 / 48 = > 48 days answer : a" | a ) 48 days , b ) 55 days , c ) 24 days , d ) 33 days , e ) 40 days | a | divide(multiply(6, const_3), subtract(divide(add(divide(multiply(6, const_3), 12), add(divide(multiply(6, const_3), 6), divide(multiply(6, const_3), 8))), const_2), divide(multiply(6, const_3), 6))) | multiply(n0,const_3)|divide(#0,n0)|divide(#0,n1)|divide(#0,n2)|add(#1,#2)|add(#4,#3)|divide(#5,const_2)|subtract(#6,#1)|divide(#0,#7)| | physics |
john can row at 5 kmph and still water . he takes 5 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ? | let the distance between a and b be x km . total time = x / ( 5 + 1 ) + x / ( 5 - 1 ) = 5 = > x / 6 + x / 4 = 4 = > ( 2 x + 3 x ) / 12 = 5 = > x = 12 km . answer : b | a ) 28 km , b ) 12 km , c ) 16 km , d ) 30 km , e ) 20 km | b | divide(5, add(divide(1, add(5, 1)), divide(1, subtract(5, 1)))) | add(n0,n2)|subtract(n0,n2)|divide(n2,#0)|divide(n2,#1)|add(#2,#3)|divide(n0,#4) | physics |
a semicircle has a radius of 12 . what is the approximate perimeter of the semicircle ? | "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 12 + 2 * 12 which is about 62 . the answer is b ." | a ) 58 , b ) 62 , c ) 66 , d ) 70 , e ) 74 | b | add(divide(circumface(12), const_2), multiply(const_2, 12)) | circumface(n0)|multiply(n0,const_2)|divide(#0,const_2)|add(#2,#1)| | geometry |
a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 64 , find the sum of money ? | a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 64 41 - - - - ? = > rs . 328 answer : a | a ) 328 , b ) 262 , c ) 72 , d ) 205 , e ) 267 | a | multiply(divide(64, 40), add(add(const_100, 65), 40)) | add(n0,const_100)|divide(n2,n1)|add(n1,#0)|multiply(#2,#1) | general |
sonika bought a v . c . r . at the list price of 18,400 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r . | "sol . list price of v . c . r . = 18,400 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,400 = 8 ⁄ 100 × 18400 = 1472 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,400 + 1472 = 19,872 . answer a" | a ) 19,872 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these | a | floor(divide(divide(multiply(add(multiply(multiply(add(multiply(add(const_1, const_4), const_2), 8), const_100), multiply(add(const_1, const_4), const_2)), multiply(add(const_1, const_4), const_100)), add(const_100, 8)), const_100), multiply(multiply(add(const_1, const_4), const_100), const_2))) | add(const_1,const_4)|add(n1,const_100)|multiply(#0,const_2)|multiply(#0,const_100)|add(n1,#2)|multiply(#3,const_2)|multiply(#4,const_100)|multiply(#6,#2)|add(#7,#3)|multiply(#8,#1)|divide(#9,const_100)|divide(#10,#5)|floor(#11)| | gain |
if x is equal to the sum of the integers from 60 to 80 , inclusive , and y is the number of even integers from 60 to 80 , inclusive , what is the value of x + y ? | "x = 60 + 61 + . . . + 80 = 21 ( 70 ) = 1470 y = 11 x + y = 1481 the answer is b ." | a ) 1361 , b ) 1481 , c ) 1601 , d ) 1721 , e ) 1841 | b | add(multiply(divide(add(60, 80), const_2), add(subtract(80, 60), const_1)), add(divide(subtract(80, 60), const_2), const_1)) | add(n0,n1)|subtract(n1,n0)|add(#1,const_1)|divide(#1,const_2)|divide(#0,const_2)|add(#3,const_1)|multiply(#2,#4)|add(#5,#6)| | general |
a mixture contains alcohol and water in the ratio 2 : 5 . if 10 liters of water is added to the mixture , the ratio becomes 2 : 7 . find the quality of alcohol in the given mixture . | let the quantity of alcohol and water be 2 x and 5 x 2 x / ( 5 x + 10 ) = 2 / 7 20 x = 4 ( 3 x + 5 ) x = 5 quantity of alcohol = 2 * 5 = 10 liters . answer is b | a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25 | b | multiply(10, const_1) | multiply(n2,const_1) | general |
in the biology lab of ` ` jefferson ' ' high school there are 5.4 * 10 ^ 6 germs , equally divided among 10800 petri dishes . how many germs live happily in a single dish ? | 5.4 * 10 ^ 6 / 10800 = = > 54 * 10 ^ 3 / 108 = = > 54000 / 108 = 500 answer : c | a ) 100 , b ) 200 , c ) 500 , d ) 1000 , e ) 5000 | c | divide(multiply(power(10, 6), 5.4), 10800) | power(n1,n2)|multiply(n0,#0)|divide(#1,n3) | general |
if x is 11 percent greater than 80 , then x = | "11 % of 80 = ( 80 * 0.11 ) = 8.8 11 % greater than 80 = 80 + 8.8 = 88.8 answer is clearly a ." | a ) 88.8 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2 | a | add(80, multiply(divide(11, const_100), 80)) | divide(n0,const_100)|multiply(n1,#0)|add(n1,#1)| | general |
a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1628 ? | "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1628 74 x = 1628 = > x = 22 5 x = 110 rs . answer : c" | a ) s . 109 , b ) s . 108 , c ) s . 110 , d ) s . 103 , e ) s . 102 | c | multiply(5, divide(1628, add(add(multiply(6, 3), multiply(9, 4)), multiply(4, 5)))) | multiply(n0,n3)|multiply(n1,n2)|multiply(n2,n5)|add(#0,#1)|add(#3,#2)|divide(n6,#4)|multiply(n5,#5)| | physics |
8 people decided to split the restaurant bill evenly . if the bill was $ 314.12 dollars , how much money did they 1 cent is the smallest unit ? | "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 412 not divisible by a hence , we need to add 4 to this number for it to be divisible by 8 correct option : a" | a ) $ 314.16 , b ) $ 314.17 , c ) $ 314.18 , d ) $ 314.19 , e ) $ 314.20 | a | add(314.12, divide(const_3, const_100)) | divide(const_3,const_100)|add(n1,#0)| | general |
the average ( arithmetic mean ) monthly income of 4 workers is $ 1000 . after one worker ’ s income increases by 50 percent the new average income is $ 1200 . what was the original income of the worker whose monthly income increased ? | increase in total income was 200 * 4 = $ 800 , we know that this increase was 50 % ( 1 / 2 ) of the workers original income , thus his / her original income was 800 * 2 = $ 1,600 . answer : d | a ) $ 1,800 , b ) $ 1,500 , c ) $ 1,300 , d ) $ 1,600 , e ) $ 1,100 | d | subtract(subtract(subtract(multiply(1200, 4), multiply(subtract(4, const_1), 1000)), divide(subtract(multiply(1200, 4), multiply(subtract(4, const_1), 1000)), add(divide(50, const_100), const_1))), const_100) | divide(n2,const_100)|multiply(n0,n3)|subtract(n0,const_1)|add(#0,const_1)|multiply(n1,#2)|subtract(#1,#4)|divide(#5,#3)|subtract(#5,#6)|subtract(#7,const_100) | general |
if the numerator of a fraction be increased by 15 % and its denominator be diminished by 8 % , the value of the fraction is 15 / 16 . find the original fraction . | "let the original fraction be x / y . then ( 115 % of x ) / ( 92 % of y ) = 15 / 16 = > ( 115 x / 92 y ) = 15 / 16 = ( ( 15 / 16 ) * ( 92 / 115 ) ) = 3 / 4 answer is a ." | a ) 3 / 4 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 , e ) none of them | a | divide(multiply(subtract(const_100, 8), 15), multiply(add(const_100, 15), 16)) | add(n0,const_100)|subtract(const_100,n1)|multiply(n2,#1)|multiply(n3,#0)|divide(#2,#3)| | general |
in town x , 72 percent of the population are employed , and 36 percent of the population are employed males . what percent of the employed people in town x are females ? | "total employed people 72 % , out of which 36 are employed males , hence 36 % are employed females . ( employed females ) / ( total employed people ) = 36 / 72 = 1 / 2 = 50 % answer : e ." | a ) 16 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 50 % | e | multiply(divide(subtract(72, 36), 72), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | gain |
the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 100 resolutions . | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 100 resolutions . = 100 * 2 * 22 / 7 * 22.4 = 14100 cm = 141 m answer : b" | a ) 140 m , b ) 141 m , c ) 142 m , d ) 143 m , e ) 144 m | b | divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 100), const_100) | add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)| | physics |
speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is : | "sol . speed upstream = 3 kmph ; speed downstream = 9 kmph . ∴ total time taken = [ 210 / 3 + 210 / 9 ] hours = 84 hours . answer c" | a ) 92 hours , b ) 24 hours , c ) 84 hours , d ) 48 hours , e ) none | c | add(divide(210, add(9, 6)), divide(210, subtract(9, 6))) | add(n0,n1)|subtract(n0,n1)|divide(n2,#0)|divide(n2,#1)|add(#2,#3)| | physics |
a cistern 9 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is : | "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 9 x 1.25 ) + 9 x 4 ] m 2 = 68.5 m 2 . answer : option d" | a ) 49 m 2 , b ) 50 m 2 , c ) 53.5 m 2 , d ) 68.5 m 2 , e ) 57 m 2 | d | add(multiply(const_2, add(multiply(add(divide(25, const_100), 1), 4), multiply(add(divide(25, const_100), 1), 9))), multiply(4, 9)) | divide(n3,const_100)|multiply(n0,n1)|add(n2,#0)|multiply(n1,#2)|multiply(n0,#2)|add(#3,#4)|multiply(#5,const_2)|add(#6,#1)| | physics |
at a contest with 2,500 participants , 1 / 2 of the people are aged 10 to 12 . next year , the number of people aged 10 to 12 will increase by 1 / 5 . after this change , what percentage of the total 2,500 people will the 10 - to 12 - year - olds represent ? | "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 2,500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 5 , we are multiplying it by 1 + 1 / 5 = 6 / 5 , so the answer here must be ( 1 / 2 ) * ( 6 / 5 ) = 3 / 5 = 60 % . answe... | a ) 55 % , b ) 60 % , c ) 50 % , d ) 45 % , e ) 66 % | b | multiply(divide(multiply(divide(2,500, 2), add(1, divide(1, 5))), 2,500), const_100) | divide(n1,n8)|divide(n0,n2)|add(#0,n1)|multiply(#2,#1)|divide(#3,n0)|multiply(#4,const_100)| | general |
a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 140 km downstream | "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 140 km time taken = distance / speed = 140 / 28 = 5 hours answer : option c" | a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours | c | divide(140, add(24, 4)) | add(n0,n1)|divide(n2,#0)| | physics |
there are 10 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed . | first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 10 and for second = 9 so total methods = 10 * 9 = 90 answer : a | a ) 90 , b ) 85 , c ) 75 , d ) 95 , e ) 82 | a | add(choose(10, 2), choose(10, 2)) | choose(n0,n1)|add(#0,#0) | probability |
a large box contains 17 small boxes and each small box contains 26 chocolate bars . how many chocolate bars are in the large box ? | the only thing you have to do is a simple multiply we have : 17 * 26 = 442 correct answer is : a ) 442 | a ) a ) 442 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 690 | a | multiply(17, 26) | multiply(n0,n1) | general |
find out the ratio of milk to that of water , if a mixture is formed after mixing milk and water of 3 different vessels containning the mixture of milk to that of water in the proportion 3 : 2 , 7 : 3 , 9 : 2 respectively . | 3 + 2 = 57 + 3 = 109 + 2 = 11 now , 3 / 5 + 7 / 10 + 9 / 11 : 2 / 5 + 3 / 10 + 2 / 11 = > 233 / 110 : 97 / 110 = > 233 : 97 answer : a | a ) 233 : 97 , b ) 235 : 98 , c ) 236 : 97 , d ) 265 : 98 , e ) 234 : 97 | a | divide(add(divide(9, add(9, 2)), add(divide(3, add(3, 2)), divide(7, add(7, 3)))), add(divide(2, add(9, 2)), add(divide(2, add(3, 2)), divide(3, add(7, 3))))) | add(n0,n2)|add(n0,n3)|add(n2,n5)|divide(n0,#0)|divide(n3,#1)|divide(n5,#2)|divide(n2,#0)|divide(n0,#1)|divide(n2,#2)|add(#3,#4)|add(#6,#7)|add(#9,#5)|add(#10,#8)|divide(#11,#12) | other |
a student scored an average of 85 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ? | given m + p + c = 85 * 3 = 255 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 255 = 65 answer : d | a ) 86 , b ) 16 , c ) 76 , d ) 65 , e ) 26 | d | subtract(add(multiply(90, const_2), multiply(70, const_2)), multiply(85, 3)) | multiply(n2,const_2)|multiply(n3,const_2)|multiply(n0,n1)|add(#0,#1)|subtract(#3,#2) | general |
if you write down all the numbers from 1 to 100 , then how many times do you write 2 ? | "explanation : clearly , from 1 to 100 , there are ten numbers with 2 as the unit ' s digit - 2 , 12 , 22 , 32 , 42 , 52 , 62 , 72 , 82 , 92 ; and ten numbers with 2 as the ten ' s digit - 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 . so , required number = 10 + 10 = 20 . answer : c" | a ) a ) 11 , b ) b ) 18 , c ) c ) 20 , d ) d ) 21 , e ) e ) 22 | c | divide(subtract(100, 1), 2) | subtract(n1,n0)|divide(#0,n2)| | general |
abce is an isosceles trapezoid and acde is a rectangle . ab = 10 and ec = 20 . what is the length of ae . | as abce is an isosceles trapezoid and ec is twice times ab , we can consider the given trapezoid as half of a regular hexagon ( as length of diagonal in regular hexagon is always double the side ) . thus , sides ab = ae = bc . = > ae = 10 . answer : b | a ) 5 , b ) 10 , c ) 12 , d ) 15 , e ) 20 | b | sqrt(divide(add(subtract(power(20, const_2), power(subtract(20, divide(subtract(20, 10), const_2)), const_2)), power(divide(subtract(20, 10), const_2), const_2)), const_2)) | power(n1,const_2)|subtract(n1,n0)|divide(#1,const_2)|power(#2,const_2)|subtract(n1,#2)|power(#4,const_2)|subtract(#0,#5)|add(#3,#6)|divide(#7,const_2)|sqrt(#8) | geometry |
evaluate 24.39 + 562.093 + 35.96 | "24.39 + 562.093 + 35.96 = 622.443 option b" | a ) 631.344 , b ) 622.443 , c ) 623.434 , d ) 632.423 , e ) 632.443 | b | divide(24.39, divide(562.093, 24.39)) | divide(n1,n0)|divide(n0,#0)| | general |
rs 3400 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part . | "explanation : average rate = ( 144 / 3400 ) * 100 = 4.24 ratio = 7.65 : 12.35 so , first part = ( 7.65 / 20 ) * 3400 = rs 1300 . answer : e" | a ) s 4000 , b ) s 1800 , c ) s 800 , d ) s 500 , e ) s 1300 | e | divide(subtract(multiply(3400, divide(5, const_100)), 144), subtract(divide(5, const_100), divide(3, const_100))) | divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|subtract(#0,#1)|subtract(#2,n3)|divide(#4,#3)| | gain |
at a certain college , 40 percent of the total number of students are freshmen . if 50 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 50 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal ar... | "let ' s say there is a total of 100 students at this college . 40 percent of the total number of students are freshmen . # of freshmen = 40 % of 100 = 40 50 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 50 % of 40 = 20 . . . and , of these , 50 percent ar... | a ) 10 % , b ) 12 % , c ) 14 % , d ) 16 % , e ) 18 % | a | divide(multiply(divide(multiply(40, 50), const_100), 50), const_100) | multiply(n0,n1)|divide(#0,const_100)|multiply(n2,#1)|divide(#2,const_100)| | general |
90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 40 % of the total school population of x students , what is x ? | "90 = ( x / 100 ) * ( # boys ) # boys = . 4 x substitute and solve : 90 = ( x / 100 ) * ( . 4 x ) 9000 = . 4 ( x ^ 2 ) 25000 = x ^ 2 x = 150 answer : b" | a ) 125 , b ) 150 , c ) 225 , d ) 250 , e ) 500 | b | sqrt(divide(multiply(90, const_100), divide(40, const_100))) | divide(n1,const_100)|multiply(n0,const_100)|divide(#1,#0)|sqrt(#2)| | gain |
in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 100 ? | "c 25 x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 100 = ( 100 * 30 ) / 40 = 25 * 3 = 75 . in x game of 100 points , y gives ( 100 - 75 ) = 25 points to c ." | a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50 | c | subtract(multiply(subtract(60, 20), const_3), multiply(subtract(60, 30), const_3)) | subtract(n1,n0)|subtract(n1,n2)|multiply(#0,const_3)|multiply(#1,const_3)|subtract(#2,#3)| | general |
3500 – ( 1000 ÷ 20.50 ) is equal to : | explanation : given exp . = 3500 - ( ( 1000 ÷ 2050 ) * 100 ) = 3451.21 answer a | a ) 3451.21 , b ) 3029.0 , c ) 2993.03 , d ) 2984.36 , e ) none of these | a | subtract(3500, divide(1000, 20.5)) | divide(n1,n2)|subtract(n0,#0) | general |
a man swims downstream 60 km and upstream 40 km taking 4 hours each time ; what is the speed of the current ? | "explanation : 60 - - - 4 ds = 15 ? - - - - 1 40 - - - - 4 us = 10 ? - - - - 1 s = ? s = ( 15 - 10 ) / 2 = 2.5 answer : option b" | a ) 3 kmph , b ) 2.5 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph | b | divide(add(divide(40, 4), divide(60, 4)), const_2) | divide(n1,n2)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)| | physics |
two trains of equal length 120 metres move in the same direction . the faster train completely overtakes the slower one in 15 seconds . if the slower train were to move at half its speed , the over taking would take in 10 seconds . at what speeds are the 2 trains moving ( faster and slower respectively in m / s ) | the total distance covered for over taking = length of the two trains = 120 + 120 = 240 speed of faster train be x m / s and slower train be y m / s in the first case relative speed = x - y relative speed = distance / time taken = x - y = 240 / 15 = 16 m / s … … … ( 1 ) in the second case , the slower train moves at ha... | a ) 24 , 22 , b ) 32 , 16 , c ) 30 , 18 , d ) 28 , 14 , e ) none of these | b | subtract(multiply(divide(add(120, 120), 10), 2), divide(add(120, 120), 15)) | add(n0,n0)|divide(#0,n2)|divide(#0,n1)|multiply(n3,#1)|subtract(#3,#2) | physics |
present ages of abi and suji are in the ratio of 5 : 4 respectively . 3 years hence , the ratio of their ages will become 11 : 9 respectively . what is suji ' s present age in years ? | present ages = 5 x : 4 x three hence = 5 x + 3 : 4 x + 3 5 x + 3 : 4 x + 3 = 11 : 9 weget x = 6 suji age is = 4 x = 4 * 6 = 24 answer : e | a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24 | e | multiply(subtract(add(5, 4), 3), 4) | add(n0,n1)|subtract(#0,n2)|multiply(n1,#1) | other |
a can do a work in 15 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ? | a ' s 1 day ' s work = 1 ; 15 b ' s 1 day ' s work = 1 ; 20 ( a + b ) ' s 1 day ' s work = ( 1 + 1 ) = 7 . 15 20 60 ( a + b ) ' s 4 day ' s work = ( 7 x 4 ) = 7 . 60 15 therefore , remaining work = ( 1 - 7 ) = 8 . 15 15 option d | a ) 8 , b ) 8 / 11 , c ) 8 / 13 , d ) 8 / 15 , e ) none | d | subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 4)) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)|subtract(const_1,#3) | physics |
let f ( x ) = x ^ 2 + bx + c . if f ( 1 ) = 0 and f ( - 7 ) = 0 , then f ( x ) crosses the y - axis at what y - coordinate ? | "when x = 1 and when x = - 7 , the expression f ( x ) = x ² + bx + c equals 0 . then f ( x ) = ( x - 1 ) ( x + 7 ) f ( 0 ) = - 7 the answer is a ." | a ) - 7 , b ) - 1 , c ) 0 , d ) 1 , e ) 7 | a | negate(divide(subtract(power(7, 2), 1), add(7, 1))) | add(n3,n1)|power(n3,n0)|subtract(#1,n1)|divide(#2,#0)|negate(#3)| | general |
the ratio of flour to water to sugar in a recipe is 8 : 4 : 3 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ? | "the ratio of flour to water is 16 : 4 = 4 : 1 . the ratio of flour to sugar is 4 : 3 . the new ratio of flour to water to sugar is 4 : 1 : 3 if we need 2 cups of water , then we need 6 cups of sugar . the answer is a ." | a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2 | a | multiply(divide(2, 4), multiply(const_4, 3)) | divide(n3,n1)|multiply(n2,const_4)|multiply(#0,#1)| | other |
a train 165 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ? | "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 165 * 3 / 55 ] sec = 9 sec answer : c" | a ) 5 , b ) 6 , c ) 9 , d ) 8 , e ) 5 | c | multiply(const_3600, divide(divide(165, const_1000), add(60, 6))) | add(n1,n2)|divide(n0,const_1000)|divide(#1,#0)|multiply(#2,const_3600)| | physics |
joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 12100 , how many months will it take joan to pay back her mortgage ? | "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 12100 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 121 so we have 1 , 3 , 9 , 27 . . . . . 12100 in gp we know that a = 1 , and r... | a ) 6 , b ) 8 , c ) 10 , d ) 5 , e ) 13 | d | divide(log(add(divide(multiply(12100, const_2), 100), const_1)), log(const_3)) | log(const_3)|multiply(n1,const_2)|divide(#1,n0)|add(#2,const_1)|log(#3)|divide(#4,#0)| | general |
the diagonals of two squares are in the ratio of 2 : 5 . find the ratio of their areas . | explanation : let the diagonals of the squares be 2 x and 5 x . then ratio of their areas will be area of square = 1 / 2 ∗ diagonal 2 1 / 2 ∗ 2 x 2 : 1 / 2 ∗ 5 x 2 4 x 2 : 25 x 2 = 4 : 25 option a | ['a ) 4 : 25', 'b ) 4 : 15', 'c ) 3 : 25', 'd ) 3 : 15', 'e ) none of these'] | a | divide(const_4, power(5, const_2)) | power(n1,const_2)|divide(const_4,#0) | geometry |
s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits q are in s ( 99 ) ? | focus on the points where the number of digits q in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square ... | a ) q = 350 , b ) q = 353 , c ) q = 354 , d ) q = 356 , e ) 357 | b | add(add(add(add(const_60, const_4), 4), multiply(add(add(const_60, const_4), 4), 4)), add(multiply(3, 1), multiply(multiply(3, 2), 2))) | add(const_4,const_60)|multiply(n0,n4)|multiply(n2,n4)|add(n6,#0)|multiply(n2,#2)|add(#1,#4)|multiply(n6,#3)|add(#3,#6)|add(#7,#5) | general |
bhanu spends 30 % of his income on petrol on scooter 30 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ? | "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 30 % ( 700 ) = rs . 210 answer : d" | a ) 2287 , b ) 140 , c ) 128 , d ) 210 , e ) 123 | d | multiply(subtract(divide(300, divide(30, const_100)), 300), divide(30, const_100)) | divide(n1,const_100)|divide(n0,const_100)|divide(n2,#1)|subtract(#2,n2)|multiply(#0,#3)| | gain |
the slant height of a right circular cone is 10 m and its height is 8 m . find the area of its curved surface . | l = 10 m h = 8 m r = root ( i ^ 2 - h ^ 2 ) = root ( 10 ^ 2 - 8 ^ 2 ) = 6 m curved surface area = pi ri = 60 pi m ^ 2 answer c | ['a ) 30 pi m ^ 2', 'b ) 40 pi m ^ 2', 'c ) 60 pi m ^ 2', 'd ) 80 pi m ^ 2', 'e ) 100 pi m ^ 2'] | c | multiply(10, sqrt(subtract(power(10, const_2), power(8, const_2)))) | power(n0,const_2)|power(n1,const_2)|subtract(#0,#1)|sqrt(#2)|multiply(n0,#3) | geometry |
at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 150 male associates , how many female managers are there ? | "250 employees : 90 male , 160 female 40 managers , 210 associates 150 male associates implies 60 female associates which means the remaining 30 females must be managers d . 30" | a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35 | d | multiply(40, const_1) | multiply(n2,const_1)| | general |
the average height of 35 boys in a class was calculated as 183 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ? | "calculated average height of 35 boys = 183 cm . wrong total height of 35 boys = 183 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm - 106 cm ) / 35 = 183 cm - 60 / 35 cm = 183 cm - 1.71 cm = 181.29 cm . answer : b" | a ) 178.27 cm , b ) 181.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm | b | floor(divide(add(subtract(multiply(35, 183), 166), 106), 35)) | multiply(n0,n1)|subtract(#0,n2)|add(n3,#1)|divide(#2,n0)|floor(#3)| | general |
65 + 5 * 12 / ( 180 / 3 ) = ? | "65 + 5 * 12 / ( 180 / 3 ) = 65 + 5 * 12 / ( 60 ) = 65 + ( 5 * 12 ) / 60 = 65 + 1 = 66 . answer : d" | a ) 22 , b ) 77 , c ) 29 , d ) 66 , e ) 21 | d | add(65, divide(multiply(5, 12), divide(180, 3))) | divide(n3,n4)|multiply(n1,n2)|divide(#1,#0)|add(n0,#2)| | general |
what is the ratio between perimeters of two squares one having 1.5 times the diagonal then the other ? | "d = 1.5 d d = d a √ 2 = 1.5 d a √ 2 = d a = 1.5 d / √ 2 a = d / √ 2 = > 1.5 : 1 answer : b" | a ) 3 : 6 , b ) 1.5 : 1 , c ) 3 : 1.5 , d ) 2 : 1 , e ) 3 : 2 | b | divide(1.5, divide(1.5, 1.5)) | divide(n0,n0)|divide(n0,#0)| | geometry |
a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 6 of th area of the garden . what is the radius of the circular garden ? | "as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 6 ( pir ^ 2 ) pir ^ 2 = 12 pir r = 12 answer : e" | a ) 1 , b ) 2 , c ) 4 , d ) 8 , e ) 12 | e | multiply(const_2, sqrt(power(6, const_2))) | power(n1,const_2)|sqrt(#0)|multiply(#1,const_2)| | geometry |
what is the 28 th digit to the right of the decimal point in the decimal form of 4 / 11 ? | "4 / 11 = 0.363636 . . . the even numbered positions in the decimal expansion are all 6 . the answer is d ." | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | d | divide(4, 11) | divide(n1,n2)| | general |
the radius of the wheel of a bus is 140 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is | "radius of the wheel of bus = 140 cm . then , circumference of wheel = 2 ï € r = 280 ï € = 880 cm distance covered by bus in 1 minute = 66 â „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 880 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 880 = 125 answer a" | a ) 125 , b ) 250 , c ) 300 , d ) 330 , e ) none of these | a | divide(divide(multiply(const_100, multiply(const_1000, 66)), multiply(const_60, const_1)), multiply(multiply(const_2, 140), add(const_3, divide(add(const_2, multiply(const_3, const_4)), power(add(const_2, multiply(const_4, const_2)), const_2))))) | multiply(n1,const_1000)|multiply(const_1,const_60)|multiply(const_3,const_4)|multiply(const_2,const_4)|multiply(n0,const_2)|add(#2,const_2)|add(#3,const_2)|multiply(#0,const_100)|divide(#7,#1)|power(#6,const_2)|divide(#5,#9)|add(#10,const_3)|multiply(#11,#4)|divide(#8,#12)| | physics |
a can finish a work in 15 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ? | "b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 15 * 1 / 3 ) = 5 days . correct option : a" | a ) 5 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these | a | divide(multiply(multiply(divide(const_1, 15), 10), 15), const_2) | divide(const_1,n1)|multiply(n2,#0)|multiply(n0,#1)|divide(#2,const_2)| | physics |
in the county of veenapaniville , there are a total of 50 high schools , of 3 kinds : 25 public schools , 16 parochial schools , and 9 private independent schools . these 50 schools are divided between 3 districts : a , b , and c . district a has 18 high schools total . district b has 17 high schools total , and only t... | “ in the county of veenapaniville , there are a total of 50 high schools , of three kinds : 25 public schools , 16 parochial schools , and 9 private independent schools . ” “ district a has 18 high schools total . ” “ district b has 17 high schools total , and only two of those are private independent schools . ” “ dis... | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | a | subtract(9, add(divide(subtract(50, add(18, 17)), 3), const_2)) | add(n7,n8)|subtract(n0,#0)|divide(#1,n1)|add(#2,const_2)|subtract(n4,#3) | general |
a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 12 seconds . what is the length of the train in meters ? | "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 12 seconds distance = speed * time 36000 * 12 / 3600 = 120 meters . ... | a ) 400 meters , b ) 120 meters , c ) 1777 meters , d ) 60 meters , e ) none of these | b | multiply(multiply(subtract(100, 64), const_0_2778), 12) | subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(n2,#1)| | physics |
how many positive integers less than 22 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ? | "the number = 2 a + 3 b < 20 when a = 1 , b = 1 , 2 , 3 , 4 , 5 , 6 - > 2 a = 2 ; 3 b = 3 , 6 , 9 , 12 , 15 , 18 - > the number = 5 , 8 , 11 , 14 , 17 , 20 - - > 6 numbers when a = 2 , b = 1 , 2,3 , 4,5 , 6 - > . . . . - - > 6 numbers when a = 3 , b = 1,2 , 3,4 , 5 - - > . . . . - - > 5 numbers total number is already ... | a ) 17 , b ) 13 , c ) 12 , d ) 11 , e ) 10 | a | subtract(subtract(subtract(22, 2), const_4), const_1) | subtract(n0,n1)|subtract(#0,const_4)|subtract(#1,const_1)| | general |
the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.4 kg . the weight of the new student is ? | "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.4 - 19 x 15 ) kg = 3 kg . correct option : b" | a ) 10.6 kg , b ) 3 kg , c ) 11 kg , d ) 14.9 kg , e ) none | b | subtract(multiply(add(19, const_1), 14.4), multiply(19, 15)) | add(n0,const_1)|multiply(n0,n1)|multiply(n2,#0)|subtract(#2,#1)| | general |
a , b , c can complete a piece of work in 21 , 6,12 days . working together , they complete the same work in how many days ? | "a + b + c 1 day work = 1 / 21 + 1 / 6 + 1 / 12 = 25 / 84 a , b , c together will complete the job in 84 / 25 days answer is e" | a ) 2 , b ) 4 / 5 , c ) 7 / 9 , d ) 10 , e ) 84 / 25 | e | divide(const_1, add(add(divide(const_1, 21), divide(const_1, add(const_4, const_2))), divide(const_1, multiply(const_2, add(const_4, const_2))))) | add(const_2,const_4)|divide(const_1,n0)|divide(const_1,#0)|multiply(#0,const_2)|add(#1,#2)|divide(const_1,#3)|add(#4,#5)|divide(const_1,#6)| | physics |
ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age | "explanation : present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 answer : option b" | a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 23 | b | divide(multiply(subtract(26, 6), 3), 4) | subtract(n3,n2)|multiply(n1,#0)|divide(#1,n0)| | other |
a new model car was not selling as expected and the base retail price was lowered by 5 % to increase sales . a customer haggled on the price and negotiated a final agreed price of 90 % of the retail price . how much did the customer save off the retail price ? | quantity x rate = price 1 x 1 = 1 0.9 x 0.95 = 0.855 decrease in price = ( 0.145 / 1 ) ã — 100 = 14.5 % answer = option e | a ) 10.5 % , b ) 11.5 % , c ) 12.5 % , d ) 13.5 % , e ) 14.5 % | e | subtract(const_100, multiply(multiply(divide(90, const_100), divide(subtract(const_100, 5), const_100)), const_100)) | divide(n1,const_100)|subtract(const_100,n0)|divide(#1,const_100)|multiply(#0,#2)|multiply(#3,const_100)|subtract(const_100,#4) | general |
a machine , working at a constant rate , manufactures 40 pencils in 30 minutes . how many pencils does it make in 1 hr 30 min ? | "change 1 hr 30 min to 90 min . for this , we need to set up a simple proportion of pensils per time 40 / 30 = s / 90 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . instead , cancel before you multiply . for what we can and can ... | a ) 120 , b ) 125 , c ) 110 , d ) 115 , e ) 121 | a | multiply(divide(add(multiply(1, const_60), 30), 30), 40) | multiply(n2,const_60)|add(n3,#0)|divide(#1,n1)|multiply(n0,#2)| | physics |
sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1320 , what is the gain percent ? | "selling price / total cost = 1320 / 1200 = 1.1 the gain percent is 10 % . the answer is e ." | a ) 2 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) 10 % | e | multiply(divide(subtract(1320, add(300, 900)), add(300, 900)), const_100) | add(n0,n1)|subtract(n2,#0)|divide(#1,#0)|multiply(#2,const_100)| | gain |
the cross - section of a cannel is a trapezium in shape . if the cannel is 8 m wide at the top and 2 m wide at the bottom and the area of cross - section is 770 sq m , the depth of cannel is ? | "1 / 2 * d ( 8 + 2 ) = 770 d = 154 answer : c" | a ) 150 , b ) 152 , c ) 154 , d ) 156 , e ) 158 | c | divide(divide(divide(770, divide(add(8, 2), const_2)), 2), const_2) | add(n0,n1)|divide(#0,const_2)|divide(n2,#1)|divide(#2,n1)|divide(#3,const_2)| | physics |
a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 80 seconds . what is the length of the train in meters ? | "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 80 seconds distance = speed * time 36000 * 80 / 3600 = 800 meters . ... | a ) 400 meters , b ) 1111 meters , c ) 800 meters , d ) 1822 meters , e ) none of these | c | multiply(multiply(subtract(100, 64), const_0_2778), 80) | subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(n2,#1)| | physics |
if 8 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ? | "explanation : let the required no of hectares be x . then more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) men \ : 8 : 36 \ \ days \ : 24 : 30 \ end { matrix } \ right \ } : 80 : x \ inline \ fn _ jvn \ therefore \ inline \ fn _ jvn 8 \ times 24 \ times x = 36 \ times 30 \... | a ) 127 , b ) 237 , c ) 287 , d ) 450 , e ) 281 | d | divide(multiply(36, 30), divide(multiply(8, 24), 80)) | multiply(n3,n4)|multiply(n0,n2)|divide(#1,n1)|divide(#0,#2)| | physics |
1 / 4 of all married couples have more than one child . 1 / 5 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ? | "plug in simple numbers . take 100 couples for example . 1 / 4 of 100 couples have more than one child = 25 couples . 1 / 5 of 100 couples have more than 3 kids = 20 couples . this implies that 20 couples are a subset of 25 couples and the complement of 25 couples within those 100 couples , which equals 75 couples have... | a ) 1 / 5 , b ) b . 1 / 4 , c ) 1 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information . | c | subtract(divide(1, 4), divide(1, 4)) | divide(n0,n1)|divide(n2,n1)|subtract(#0,#1)| | general |
a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this order r ? ( 1 cubic meter = 1000 liters ) | i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . r = 12.5 * 6 = 75 . e | a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 75 | e | divide(multiply(power(power(1000, divide(const_1, const_3)), const_2), add(const_4, const_2)), multiply(const_4, const_2)) | add(const_2,const_4)|divide(const_1,const_3)|multiply(const_2,const_4)|power(n4,#1)|power(#3,const_2)|multiply(#0,#4)|divide(#5,#2) | general |
a man can row downstream at the rate of 26 kmph and upstream at 12 kmph . find the man ’ s rate in still water and rate of current ? | "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 26 + 12 ) = 19 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 26 - 12 ) = 1 / 2 ( 14 ) = 7 kmph answer is d ." | a ) 8.5 , b ) 8.0 , c ) 9.5 , d ) 7.0 , e ) 8.25 | d | divide(subtract(26, 12), const_2) | subtract(n0,n1)|divide(#0,const_2)| | gain |
the perimeter of a rectangle is equal to the perimeter of aright - angled triangle of height 12 cm . if the base of the triangle is equal to the breadth of the rectangle , what is the length of the rectangle ” | p = 2 ( l + b ) = l + b + h = l + b + 12 . data inadequate . answer d | ['a ) 18 cm', 'b ) 24 cm', 'c ) 22 cm', 'd ) data inadequate', 'e ) none of these'] | d | multiply(const_2, sqrt(add(const_1, power(12, const_2)))) | power(n0,const_2)|add(#0,const_1)|sqrt(#1)|multiply(#2,const_2) | geometry |
in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 1 people every two seconds . estimate the size of the population net increase that occurs in one day . | "every 2 seconds , 6 persons are added ( 7 - 1 ) . every second 3 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 3 = 259200 option e" | a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200 | e | multiply(multiply(subtract(7, 1), const_3600), const_12) | subtract(n0,n1)|multiply(#0,const_3600)|multiply(#1,const_12)| | general |
each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 45 hours if harry and ja... | "james worked for 41 hours hence he earned 40 * x + 5 * 2 x = 50 x dollars ; we know that harry also earned the same 50 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 20 x additional dollars . since for each additional hour he gets 1.5 x dollars then he worked for 20 x / 1.5 x = 13 additional... | a ) 35 , b ) 36 , c ) 37 , d ) 43 , e ) 39 | d | add(divide(subtract(add(40, 2), 30), 1.5), 30) | add(n2,n3)|subtract(#0,n0)|divide(#1,n1)|add(n0,#2)| | general |
a certain cube floating in a bucket of water has between 60 and 85 percent of its volume below the surface of the water . if between 9 and 26 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately | "if sides are 7 , vol = 7 ^ 3 = 343 60 % = 205.8 , 85 % = 291.55 so vol above water , between 137.2 and 51.45 - - > too big if side are 4 , vol = 64 60 % = 38.4 , 85 % = 54.4 vol above water between 25.6 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 60 % = 75 , . 85 % = 106.25 vol abov... | a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9 | a | cube_edge_by_volume(divide(multiply(26, const_100), subtract(const_100, 60))) | multiply(n3,const_100)|subtract(const_100,n0)|divide(#0,#1)|cube_edge_by_volume(#2)| | geometry |
how long does a train 150 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ? | "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 150 + 132 = 282 m . required time = 282 / 20 = 14.1 sec . answer : a" | a ) 14.1 sec , b ) 12.1 sec , c ) 16.1 sec , d ) 13.1 sec , e ) 12.15 sec | a | divide(add(150, 132), multiply(72, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | physics |
the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 800 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ? | "here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 800 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 part... | a ) 3.84 , b ) 1.75 , c ) 3.44 , d ) 2.72 , e ) none of these | c | divide(divide(multiply(4, add(multiply(3, 900), multiply(2, 800))), add(3, 2)), const_1000) | add(n2,n3)|multiply(n0,n2)|multiply(n1,n3)|add(#1,#2)|multiply(n4,#3)|divide(#4,#0)|divide(#5,const_1000)| | other |
what is the unit ’ s digit of 7 ^ 7 | "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 7 ^ 7 = 3 answer c" | a ) 9 , b ) 5 , c ) 3 , d ) 7 , e ) 1 | c | reminder(power(7, const_2), const_10) | power(n0,const_2)|reminder(#0,const_10)| | general |
the list price of an article is rs . 70 . a customer pays rs . 61.11 for it . he was given two successive discounts , one of them being 10 % . the other discount is ? | "explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 61.11 x = 3 % d" | a ) 8 % , b ) 7 % , c ) 10 % , d ) 3 % , e ) 4 % | d | multiply(divide(subtract(subtract(70, multiply(70, divide(10, const_100))), 61.11), subtract(70, multiply(70, divide(10, const_100)))), const_100) | divide(n2,const_100)|multiply(n0,#0)|subtract(n0,#1)|subtract(#2,n1)|divide(#3,#2)|multiply(#4,const_100)| | gain |
a train is 300 meter long is running at a speed of 35 km / hour . in what time will it pass a bridge of 115 meter length ? | "speed = 35 km / hr = 35 * ( 5 / 18 ) m / sec = 175 / 18 m / sec total distance = 300 + 115 = 415 meter time = distance / speed = 415 * ( 18 / 175 ) = 42.686 seconds . answer : e" | a ) 29 , b ) 23 , c ) 47.119 , d ) 44.586 , e ) 42.686 | e | divide(add(300, 115), divide(multiply(35, const_1000), const_3600)) | add(n0,n2)|multiply(n1,const_1000)|divide(#1,const_3600)|divide(#0,#2)| | physics |
the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 70 , then how long is the base of isosceles triangle ? | "the base of the isosceles triangle is 70 - 20 - 20 = 30 units the answer is d ." | a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35 | d | subtract(subtract(70, divide(60, const_3)), divide(60, const_3)) | divide(n0,const_3)|subtract(n1,#0)|subtract(#1,#0)| | geometry |
the ratio of male to female in a class is 2 : 7 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle sho... | here is my approach = > males = > 2 x and females = 7 x = > total = 9 x now 9 x = > 360 therefore 16 x / 3 = > 213 degree . p . s = > 16 x / 3 is nothing but total number of students with the given preference answer e | ['a ) a ) 160 degree', 'b ) b ) 168 degree', 'c ) c ) 191 degree', 'd ) d ) 192 degree', 'e ) e ) 213 degree'] | e | add(multiply(const_360, divide(divide(const_2, add(2, 7)), const_3)), multiply(const_360, multiply(divide(7, add(2, 7)), divide(const_2, const_3)))) | add(n0,n1)|divide(const_2,const_3)|divide(const_2,#0)|divide(n1,#0)|divide(#2,const_3)|multiply(#3,#1)|multiply(#4,const_360)|multiply(#5,const_360)|add(#6,#7) | geometry |
seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 28 % ryegrass , what percent of the weight of the mixture is from mixture x ? | "28 % is 3 % - points above 25 % and 12 % - points below 40 % . thus the ratio of mixture y to mixture x is 4 : 1 . the percent of mixture x is 1 / 5 = 20 % . the answer is b ." | a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 % | b | divide(subtract(28, add(25, const_1)), subtract(divide(40, const_100), divide(add(25, const_1), const_100))) | add(n2,const_1)|divide(n0,const_100)|divide(#0,const_100)|subtract(n4,#0)|subtract(#1,#2)|divide(#3,#4)| | gain |
which is the smallest number divides 2800 and gives a perfect square . | 7 is the smallest number which divides 2800 and gives a perfect square . as 2800 = 2 * 2 * 2 * 2 * 5 * 5 * 7 and 7 is not in a pair which gives 400 ( a perfect square of 20 ) on dividing 2800 . answer : c | ['a ) 5', 'b ) 6', 'c ) 7', 'd ) 8', 'e ) 9'] | c | divide(divide(divide(divide(divide(divide(2800, const_2), const_2), const_2), const_2), add(const_2, const_3)), add(const_2, const_3)) | add(const_2,const_3)|divide(n0,const_2)|divide(#1,const_2)|divide(#2,const_2)|divide(#3,const_2)|divide(#4,#0)|divide(#5,#0) | geometry |
if a light flashes every 6 seconds , how many times will it flash in 1 / 5 of an hour ? | "in 1 / 5 of an hour there are 12 * 60 = 720 seconds the number of 6 - second intervals = 720 / 6 = 120 after the first flash , there will be 120 more flashes for a total of 121 . the answer is c ." | a ) 81 , b ) 101 , c ) 121 , d ) 141 , e ) 161 | c | divide(multiply(divide(const_3600, const_4), const_3), 6) | divide(const_3600,const_4)|multiply(#0,const_3)|divide(#1,n0)| | physics |
in how many ways can the integer 800 be expressed as a product of two different positive integers ? | "800 = ( 2 ^ 5 ) * ( 5 ^ 2 ) since 800 is not a perfect square , no of ways = 7 answer b" | a ) 10 , b ) 7 , c ) 5 , d ) 4 , e ) 2 | b | subtract(divide(divide(800, const_1), const_3), const_3) | divide(n0,const_1)|divide(#0,const_3)|subtract(#1,const_3)| | general |
from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 15 percent . what percent of the stock â € ™ s 2007 starting price was the price of the stock at the end of 2009 ? | "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 20 % = 90 * 1.15 = 103.5 thus ratio = 103.5 / 100 = 1.03 ( in % terms = 103 % ) . thus b is th... | a ) 80 , b ) 103.5 , c ) 95 , d ) 100 , e ) 108 | b | multiply(multiply(multiply(const_100, divide(add(const_100, 20), const_100)), divide(subtract(const_100, 25), const_100)), divide(add(const_100, 15), const_100)) | add(n5,const_100)|add(n1,const_100)|subtract(const_100,n3)|divide(#0,const_100)|divide(#2,const_100)|divide(#1,const_100)|multiply(#5,const_100)|multiply(#4,#6)|multiply(#3,#7)| | gain |
d and e are two points respectively on sides ab and ac of triangle abc such that de is parallel to bc . if the ratio of area of triangle ade to that of the trapezium decb is 144 : 25 and de = 13 cm , then find the length of bc . | abc and ade are similar triangles . so ( side of abc / side of ade ) ^ 2 = 25 / 169 side of abc / side of ade = 5 / 13 so the length of bc = 5 answer - a | ['a ) 5', 'b ) 13', 'c ) 14', 'd ) 11', 'e ) 15'] | a | multiply(sqrt(divide(25, add(25, 144))), 13) | add(n0,n1)|divide(n1,#0)|sqrt(#1)|multiply(n2,#2) | geometry |
at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 15 males did not bring gifts to the party , how many females did bring gifts ? | the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 15 are males , so remaining 90 - 15 = 75 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 75 , 100 % = 75 * 100 / 60 = 125 . . ans 40 % of 125 = 50 c | a ) 18 , b ) 28 , c ) 50 , d ) 68 , e ) 70 | c | divide(multiply(divide(multiply(subtract(subtract(300, divide(multiply(70, 300), const_100)), 15), const_100), subtract(const_100, 40)), 40), const_100) | multiply(n0,n1)|subtract(const_100,n2)|divide(#0,const_100)|subtract(n0,#2)|subtract(#3,n3)|multiply(#4,const_100)|divide(#5,#1)|multiply(n2,#6)|divide(#7,const_100) | gain |
a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 34 inches and the width of the wall is 54 inches , what is the length of the wall , in inches ? | "since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 34 ^ 2 = 1156 . area of rectangle is double of that 2 * 1156 = 2312 . now a = lw and we need find w so a / l = w ; 2312 / 54 = 42.8 answer ! answer is c" | a ) 22.8 , b ) 33.8 , c ) 42.8 , d ) 63.8 , e ) 56.8 | c | divide(multiply(const_2, square_area(34)), 54) | square_area(n0)|multiply(#0,const_2)|divide(#1,n1)| | geometry |
how many positive integers less than 100 have a remainder of 11 when divided by 13 ? | "we have to include 11 also . as 13 * 0 + 11 = 11 if somebody says to divide 11 by 13 , we will be telling we have 0 quotient and remainder as 11 . answer is a" | a ) 11 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | a | divide(factorial(subtract(add(const_4, 11), const_1)), multiply(factorial(11), 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 |
last year elaine spent 20 % of her annual earnings on rent . this year she earned 25 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ? | "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 25 % more , or $ 125 . she would ' ve spent 30 % of this on rent , or $ 37.5 do $ 37.5 / $ 20 this will give you 187.5 % e is the correct... | a ) 182.5 , b ) 184.5 , c ) 167.5 , d ) 172.5 , e ) 187.5 | e | multiply(divide(multiply(add(divide(25, const_100), const_1), 30), 20), const_100) | divide(n1,const_100)|add(#0,const_1)|multiply(n2,#1)|divide(#2,n0)|multiply(#3,const_100)| | gain |
how much time does a train 150 metres long running at 90 km / hr take to pass a pole ? | "explanation : 90 km / hr = 90 * 5 / 18 = 25 m / s speed = distance / time ; v = d / t 25 = 150 / t t = 6 s answer : b" | a ) 7.9 s , b ) 6 s , c ) 7.5 s , d ) 7.6 s , e ) 7.4 s | b | multiply(divide(divide(150, const_1000), 90), const_3600) | divide(n0,const_1000)|divide(#0,n1)|multiply(#1,const_3600)| | general |
a dog takes 4 leaps for every 5 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is : | "explanation : dog : hare = ( 4 * 3 ) leaps of hare : 5 leaps of hare = 12 : 5 . answer : a ) 12 : 5" | a ) 12 : 5 , b ) 4 : 3 , c ) 9 : 5 , d ) 9 : 1 , e ) 9 : 2 | a | divide(multiply(4, 3), 5) | multiply(n0,n2)|divide(#0,n1)| | other |
if an article is sold at 19 % profit instead of 12 % profit , then the profit would be rs . 105 more . what is the cost price ? | "let the cost price of an article be rs . x . ( 19 % of x ) - ( 12 % of x ) = 105 19 x / 100 - 12 x / 100 = 105 = > 7 x = 105 * 100 = > x = 1500 cost price = rs . 1500 answer : c" | a ) 1890 , b ) 2790 , c ) 1990 , d ) 1500 , e ) 1701 | c | multiply(divide(105, 12), const_100) | divide(n2,n1)|multiply(#0,const_100)| | gain |
on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 130 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ? | "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 130 ) = 2 + 2 ( extra ) = > 2 x - 260 = x = > x = 260 . answer : a" | a ) 260 , b ) 620 , c ) 500 , d ) 520 , e ) 720 | a | multiply(130, const_2) | multiply(n0,const_2)| | general |
an intern wants to label folders with numbers using digit stickers only . if the intern uses 999 stickers , how many folders have been numbered ? ( the numbers of the folders are consecutive and the number of the first folder is 1 ) . | for the first 9 folders we need 9 stickers . for the next 90 we need 2 stickers each or 180 stickers . for the next 900 folders we need 3 stickers each . the first 99 folders correspond to 189 stickers . subtract 189 from the total number of stickers ( 999 ) . this leaves 810 stickers for folders that use 3 stickers ea... | a ) 287 , b ) 369 , c ) 370 , d ) 371 , e ) 430 | b | add(add(multiply(const_3, const_100), const_60), multiply(const_3, const_3)) | multiply(const_100,const_3)|multiply(const_3,const_3)|add(#0,const_60)|add(#2,#1) | physics |
each month a retailer sells 100 identical items . on each item he makes a profit of $ 50 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the... | "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 50 sell price = $ 500 + $ 50 thus , the sell price is $ 550 for each item . selling all 100 items gives the retailer . . .... | a ) 191 , b ) 213 , c ) 221 , d ) 223 , e ) 226 | d | divide(multiply(100, 50), subtract(50, divide(multiply(add(divide(multiply(100, 50), 10), 50), 5), 100))) | multiply(n0,n1)|divide(#0,n2)|add(n1,#1)|multiply(n3,#2)|divide(#3,n0)|subtract(n1,#4)|divide(#0,#5)| | gain |
the perimeter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) | "let the side of the square be a cm . perimeter of the rectangle = 2 ( 20 + 14 ) = 68 cm perimeter of the square = 68 cm i . e . 4 a = 68 a = 17 diameter of the semicircle = 17 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 17 ) = 1 / 2 ( 22 / 7 ) ( 17 ) = 26.71 cm to two decimal places answer : e" | a ) 23.57 , b ) 25.54 , c ) 26.5 , d ) 26.55 , e ) 26.71 | e | floor(divide(circumface(divide(divide(multiply(const_2, add(14, 20)), const_4), const_2)), const_2)) | add(n0,n1)|multiply(#0,const_2)|divide(#1,const_4)|divide(#2,const_2)|circumface(#3)|divide(#4,const_2)|floor(#5)| | geometry |
working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 16 , 12 , and 8 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at ... | the time it takes printer x is 16 hours . the combined rate of y and z is 1 / 12 + 1 / 8 = 5 / 24 the time it takes y and z is 24 / 5 the ratio of times is 16 / ( 24 / 5 ) = 5 * 16 / 24 = 10 / 3 the answer is d . | a ) 5 / 2 , b ) 7 / 4 , c ) 8 / 5 , d ) 10 / 3 , e ) 12 / 5 | d | divide(16, divide(const_1, add(divide(const_1, 12), divide(const_1, 8)))) | divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|divide(const_1,#2)|divide(n0,#3) | general |
a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs , then the weight of the pipe is | explanation : external radius = 4 cm , internal radius = 3 cm . volume of iron = = weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg answer : b ) 3.696 kg | a ) 3.496 kg , b ) 3.696 kg , c ) 3.690 kg , d ) 9.696 kg , e ) 3.296 kg | b | divide(multiply(8, multiply(multiply(divide(add(21, const_1), add(const_4, const_3)), subtract(power(const_4, const_2), power(const_3, const_2))), 21)), const_1000) | add(n0,const_1)|add(const_3,const_4)|power(const_4,const_2)|power(const_3,const_2)|divide(#0,#1)|subtract(#2,#3)|multiply(#4,#5)|multiply(n0,#6)|multiply(n1,#7)|divide(#8,const_1000) | physics |
in may , the grounds keeper at spring lake golf club built a circular green with an area of 49 π square feet . in august , he doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ? | "area of circle 49 pi sq feet = pi r ^ 2 therefore r = 7 now green radi doubled i . e r = 14 area = 196 pi c" | a ) 100 pi , b ) 144 pi , c ) 196 pi , d ) 80 , e ) 90 | c | circle_area(multiply(sqrt(49), const_2)) | sqrt(n0)|multiply(#0,const_2)|circle_area(#1)| | geometry |
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