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 the digits 35 in the decimal 0.00035 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00035 ) ? | "99 * 0.35 = 34.65 approx . 35 answer : b" | a ) 37 , b ) 41 , c ) 3.5 e - 05 , d ) 35 , e ) 3.5 e - 07 | b | multiply(divide(multiply(multiply(multiply(10, 10), subtract(multiply(10, 10), const_1)), divide(35, 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 |
product of two co - prime numbers is 117 . their l . c . m should be | h . c . f of co - prime numbers is 1 . so , l . c . m = \ inline \ fn _ jvn \ frac { 117 } { 1 } = 117 answer : b | a ) 222 , b ) 117 , c ) 278 , d ) 767 , e ) 298 | b | multiply(117, const_1) | multiply(n0,const_1) | general |
if to a certain number , 720 be added , and the sum be divided by 125 ; the quotient will be equal to 7392 divided by 462 . what is that number ? | solution let x = the number required . a = 720 d = 7392 b = 125 h = 462 then by the conditions of the problem ( x + a ) / b = d / h therefore x = ( bd - ah ) / h restoring the numbers , x = [ ( 125.7392 ) - ( 720.462 ) ] / 462 = 1280 . answer a | a ) 1280 , b ) 1270 , c ) 1260 , d ) 1250 , e ) none | a | divide(subtract(multiply(125, 7392), multiply(462, 720)), 462) | multiply(n1,n2)|multiply(n0,n3)|subtract(#0,#1)|divide(#2,n3) | general |
10 women can complete a work in 9 days and 10 children take 12 days to complete the work . how many days will 6 women and 7 children take to complete the work ? | "1 women ' s 1 day work = 1 / 90 1 child ' s 1 day work = 1 / 120 ( 6 women + 7 children ) ' s 1 day work = ( 6 / 90 + 7 / 120 ) = 1 / 8 6 women and 7 children will complete the work in 8 days . d" | a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 2 | d | inverse(add(divide(6, multiply(10, 9)), divide(10, multiply(10, 12)))) | multiply(n0,n1)|multiply(n0,n3)|divide(n4,#0)|divide(n0,#1)|add(#2,#3)|inverse(#4)| | physics |
a cricket player whose bowling average was 22.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ? | average = total runs / total wickets total runs after last match = 22.5 w + 52 total wickets after last match = w + 5 ( 22.5 w + 52 ) / ( w + 5 ) = 22.5 - 0.5 = 22 w = 116 so total wickets aftr last match = w + 5 = 121 answer : c | a ) 64 , b ) 72 , c ) 121 , d ) 984 , e ) 108 | c | divide(subtract(multiply(subtract(22.5, 0.5), 5), 52), 0.5) | subtract(n0,n3)|multiply(n1,#0)|subtract(#1,n2)|divide(#2,n3) | general |
the radius of the wheel of a bus is 35 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 = 35 cm . then , circumference of wheel = 2 ï € r = 70 ï € = 220 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 = 220 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 220 = 500 answer d | a ) 200 , b ) 250 , c ) 300 , d ) 500 , e ) none of these | d | divide(divide(multiply(const_100, multiply(const_1000, 66)), multiply(const_60, const_1)), multiply(multiply(const_2, 35), 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 furniture manufacturer has two machines , but only one can be used at a time . machine e is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine e can do the job in 12 days working two shifts and machine b can do the job in 15 days working two sh... | machine e finish the job in 2 * 12 shifts = 24 shifts machine b finish the job in 2 * 15 shifts = 30 shifts lets assume total work require 120 shifts therefore , rate of e = 5 shifts / day rate of b = 4 shifts / day rate of ( e + b ) = 9 shifts / day according to current schedule work complete in a day = 5 + 4 + ( 9 / ... | a ) 14 , b ) 13 , c ) 11 , d ) 9 , e ) 7 | d | inverse(add(add(add(divide(const_1, multiply(12, const_2)), divide(divide(const_1, multiply(12, const_2)), const_2)), divide(const_1, multiply(15, const_2))), divide(divide(const_1, multiply(15, const_2)), const_2))) | multiply(n0,const_2)|multiply(n1,const_2)|divide(const_1,#0)|divide(const_1,#1)|divide(#2,const_2)|divide(#3,const_2)|add(#2,#4)|add(#6,#3)|add(#7,#5)|inverse(#8) | physics |
a train 110 m long is running with a speed of 84 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ? | "speed of train relative to man = 84 + 6 = 90 km / hr . = 90 * 5 / 18 = 25 m / sec . time taken to pass the men = 110 / 25 = 4.4 sec . answer : d" | a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4.4 sec , e ) 2 sec | d | divide(110, multiply(add(84, 6), const_0_2778)) | add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 25 payments is to be $ 500 ; each of the remaining payments is to be $ 100 more than each of the first 25 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the ye... | "total = 500 ( 25 ) + 600 ( 27 ) number of installments = 52 average = total / number of installments = 552 approximately answer : c" | a ) 500 , b ) 450 , c ) 552 , d ) 600 , e ) 400 | c | divide(add(multiply(25, 500), multiply(add(500, 100), subtract(52, 25))), 52) | add(n4,n5)|multiply(n3,n4)|subtract(n0,n3)|multiply(#0,#2)|add(#1,#3)|divide(#4,n0)| | general |
there are 6 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ? | "number of ways of selecting 2 fiction books = 6 c 2 number of ways of selecting 2 non fiction books = 6 c 2 6 c 2 * 6 c 2 = 15 * 15 = 225 answer : c" | a ) 90 , b ) 120 , c ) 225 , d ) 180 , e ) 200 | c | divide(multiply(multiply(6, const_4), multiply(6, 6)), power(factorial(2), 2)) | factorial(n2)|multiply(n0,const_4)|multiply(n0,n1)|multiply(#1,#2)|power(#0,n2)|divide(#3,#4)| | general |
a certain school implemented a reading program for its students , with the goal of getting each student to read 4 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ? | "ans : c solution : simple multiplication s students , c classes , 4 books / month = 48 books a year total number of books = 48 cs" | a ) 20 cs , b ) cs / 2 , c ) 48 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s | c | multiply(4, const_12) | multiply(n0,const_12)| | general |
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 340 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 = 340 10 x = 160 x = 16 3 rd question = x + 8 = 16 + 8 = 24 answer b" | a ) 39 , b ) 24 , c ) 28 , d ) 26 , e ) 30 | b | add(divide(340, 10), subtract(subtract(10, 4), const_1)) | divide(n3,n2)|subtract(n0,n1)|subtract(#1,const_1)|add(#0,#2)| | general |
how many natural numbers are there between 43 and 200 which are exactly divisible by 6 ? | "43 / 6 = 7 , remainder = 1 . hence 5 more should be added to 43 to get the minimum number divisible by 6 between 43 and 200 . = > minimum number divisible by 6 between 43 and 200 = 43 + 5 = 48 200 / 6 = 33 , remainder = 2 . hence 2 should be decreased from 200 to get the maximum number divisible by 6 between 43 and 20... | a ) 26 , b ) 25 , c ) 24 , d ) 22 , e ) 23 | a | add(divide(subtract(subtract(200, const_4), add(43, const_1)), 6), const_1) | add(n0,const_1)|subtract(n1,const_4)|subtract(#1,#0)|divide(#2,n2)|add(#3,const_1)| | general |
right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x - and y - coordinates of p , q , and r are to be integers that satisfy the inequalities - 4 < = x < = 5 and 6 < = y < = 16 . how many different triangles with these properties could be co... | "p can take a total of 10 * 11 co - ordinates . for a given p , r can take a total of 9 co - ordinates and q can take a total of 10 co - ordinates . hence , total = 110 * 9 * 10 = 9900 ans : c" | a ) 110 , b ) 1,100 , c ) 9,900 , d ) 10,000 , e ) 12,100 | c | multiply(multiply(subtract(const_10, const_1), multiply(add(6, 4), subtract(16, 5))), const_10) | add(n0,n2)|subtract(n3,n1)|subtract(const_10,const_1)|multiply(#0,#1)|multiply(#3,#2)|multiply(#4,const_10)| | general |
in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 160 marks , the no of questions he attempts correctly is : | "explanation : let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 160 = > 5 x = 220 = > x = 44 answer : e" | a ) 35 , b ) 38 , c ) 40 , d ) 42 , e ) 44 | e | divide(add(160, 60), add(4, 1)) | add(n2,n3)|add(n0,n1)|divide(#0,#1)| | physics |
in the coordinate plane , points ( x , 1 ) and ( 18 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y = | "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 1 ) = ( 2 , 1 ) and ( 18 , y ) = ( 18,9 ) - - > x + y = 2 + 9 = 11 . answer : d ." | a ) 4.5 , b ) 7 , c ) 8 , d ) 11 , e ) 12 | d | multiply(multiply(18, 2), divide(1, 2)) | divide(n0,n3)|multiply(n1,n3)|multiply(#0,#1)| | general |
find the simple interest on $ 1200 for 5 years at 20 % per annum ? | "si = ptr / 100 = 1200 * 5 * 20 / 100 = $ 1200 answer is a" | a ) $ 1200 , b ) $ 1000 , c ) $ 500 , d ) $ 1100 , e ) $ 1500 | a | multiply(1200, divide(5, const_100)) | divide(n1,const_100)|multiply(n0,#0)| | gain |
a batsman makes a score of 50 runs in the 17 th inning and thus increases his averages by 2 . what is his average after 17 th inning ? | "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 50 then average run after 17 th inning = ( 16 x + 50 ) / 17 ( 16 x + 50 ) / 17 = x + 2 = > 16 x + 50 = 17 x + 34 = > x = 16 x = 16 ; average after 17 th inning = 16 + 2 = 18 answer : b" | a ) 39 , b ) 18 , c ) 42 , d ) 40.5 , e ) 41.5 | b | add(subtract(50, multiply(17, 2)), 2) | multiply(n1,n2)|subtract(n0,#0)|add(n2,#1)| | general |
to produce an annual income of rs . 800 from a 8 % stock at 90 , what is the amount of stock needed ? | "since face value is not given , take it as rs . 100 . as it is an 8 % stock , income ( dividend ) per stock = rs . 8 ie , for an income of rs . 8 , amount of stock needed = rs . 100 for an income of rs . 800 , amount of stock needed = 100 × 800 / 8 = 10000 answer is a ." | a ) 10000 , b ) 11000 , c ) 12000 , d ) 13000 , e ) 14000 | a | subtract(const_100, 90) | subtract(const_100,n2)| | gain |
in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 7.5 ) , ( 8 , 0 ) , ( 0 , - 7.5 ) , ( - 8 , 0 ) ? | "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 7.5 + 7.5 = 15 area = 1 / 2 * 16 * 15 = 120 e is the answer" | a ) 56 , b ) 88 , c ) 112 , d ) 116 , e ) 120 | e | rhombus_area(multiply(8, const_2), multiply(7.5, const_2)) | multiply(n2,const_2)|multiply(n1,const_2)|rhombus_area(#0,#1)| | geometry |
ramu bought an old car for rs . 40000 . he spent rs . 13000 on repairs and sold it for rs . 64900 . what is his profit percent ? | "total cp = rs . 40000 + rs . 13000 = rs . 53000 and sp = rs . 64900 profit ( % ) = ( 64900 - 53000 ) / 55000 * 100 = 21.6 % answer : d" | a ) a ) 14 % , b ) b ) 16 % , c ) c ) 18 % , d ) d ) 21.6 % , e ) of these | d | multiply(divide(subtract(64900, add(40000, 13000)), add(40000, 13000)), const_100) | add(n0,n1)|subtract(n2,#0)|divide(#1,#0)|multiply(#2,const_100)| | gain |
on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 44 centimeters assuming that 1 - inch is 2.54 centimeters ? | "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 44 cm . : 44 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 44 / ( 3.81 ) = 277 answer will be b ." | a ) 174.2 , b ) 277 , c ) 288.1 , d ) 296 , e ) 282.4 | b | multiply(divide(44, 2.54), divide(24, 1.5)) | divide(n2,n4)|divide(n1,n0)|multiply(#0,#1)| | physics |
if 0.12 ÷ x 2 = 12 , than x = ? | explanation : 0.12 ÷ x 2 = 12 = > 0.12 / x 2 = 12 = > x 2 = 0.12 / 12 = 0.01 = > x = 0.1 answer : option c | a ) 0.001 , b ) 0.01 , c ) 0.1 , d ) 1 , e ) 0 | c | sqrt(divide(0.12, 12)) | divide(n0,n2)|sqrt(#0) | general |
a woman complete a journey in 30 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km . | "0.5 x / 21 + 0.5 x / 24 = 30 - - > x / 21 + x / 24 = 60 - - > x = 672 km . e" | a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 672 km . | e | multiply(multiply(divide(multiply(30, 24), add(24, 21)), 21), const_2) | add(n1,n2)|multiply(n0,n2)|divide(#1,#0)|multiply(n1,#2)|multiply(#3,const_2)| | physics |
in a class of 35 students 26 play football and play 20 long tennis , if 17 play above , many play neither ? | "26 + 20 - 17 = 29 35 - 29 = 6 play neither answer is a" | a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14 | a | subtract(35, subtract(add(26, 20), 17)) | add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)| | other |
a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 4 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ? | 1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 4 = 480 answer : a | a ) 480 , b ) 488 , c ) 882 , d ) 269 , e ) 298 | a | multiply(24, 20) | multiply(n0,n2) | physics |
the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21 , is ? | let x be subtracted . then , 6 - x 7 - x < 16 21 21 ( 6 - x ) < 16 ( 7 - x ) 5 x > 14 x > 2.8 least such whole number is 3 . answer : a | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | a | add(divide(subtract(multiply(21, 6), multiply(7, 16)), subtract(21, 16)), divide(const_2, const_10)) | divide(const_2,const_10)|multiply(n0,n3)|multiply(n1,n2)|subtract(n3,n2)|subtract(#1,#2)|divide(#4,#3)|add(#5,#0) | other |
a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent should the number of hours worked be increased ? | "assume hours worked : 10 hours hourly wage : 10 $ weekly wage : 100 $ after decrease of 20 % in hourly wage would become 8 $ hours worked would have to be 12.5 hours in order to maintain weekly wage of 100 $ % increase in number of hours worked = ( 12.5 - 10 ) / 10 = 0.25 * 100 = 25 % answer is c" | a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 % | c | multiply(divide(subtract(divide(multiply(const_10, const_4), multiply(divide(subtract(const_100, 20), const_100), const_10)), const_4), const_4), const_100) | multiply(const_10,const_4)|subtract(const_100,n0)|divide(#1,const_100)|multiply(#2,const_10)|divide(#0,#3)|subtract(#4,const_4)|divide(#5,const_4)|multiply(#6,const_100)| | general |
a and b can do a piece of work in 8 days . with the help of c they finish the work in 4 days . c alone can do that piece of work in ? | "c 8 days c = 1 / 4 – 1 / 8 = 1 / 8 = > 8 days" | a ) 40 days , b ) 20 days , c ) 8 days , d ) 60 days , e ) 40 days | c | inverse(subtract(4, divide(4, 8))) | divide(n1,n0)|subtract(n1,#0)|inverse(#1)| | physics |
patrick purchased 60 pencils and sold them at a loss equal to the selling price of 20 pencils . the cost of 60 pencils is how many times the selling price of 60 pencils ? | "say the cost price of 60 pencils was $ 60 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 60 - 60 p = 20 p - - > p = 3 / 4 . ( cost price ) / ( selling price ) = 1 / ( 3 / 4 ) = 4 / 3 = 1.33 . answer : d ." | a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.33 , e ) 1.75 | d | inverse(divide(60, add(60, 20))) | add(n0,n1)|divide(n0,#0)|inverse(#1)| | general |
the distance between two cities a and b is 600 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ? | "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 600 . therefore , 60 x + 75 ( x - 1 ) = 600 . = > x = 5 . so , they meet at ( 8 + 5 ) i . e , 1 p . m . answer : c )" | a ) 09 am , b ) 07 am , c ) 01 pm , d ) 05 pm , e ) 03 pm | c | add(divide(add(600, 75), add(60, 75)), 8) | add(n0,n4)|add(n2,n4)|divide(#0,#1)|add(n1,#2)| | physics |
in a group of 800 people , 1 / 5 play at least one instrument , 128 play two or more . what is the probability that one student play exactly one instrument ? | "p ( playing 2 or more instruments ) = 128 / 800 = 4 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 4 / 25 = 1 / 25 . answer e ." | a ) 2 / 125 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 25 | e | divide(subtract(divide(multiply(800, 1), 5), 128), 800) | multiply(n0,n1)|divide(#0,n2)|subtract(#1,n3)|divide(#2,n0)| | general |
the present worth of a sum due sometime hence is rs . 576 and the banker ’ s gain is rs . 16 . the true discount is : | "sol . t . d . = √ p . w . * b . g . = √ 576 * 16 = 96 . answer d" | a ) 36 , b ) 52 , c ) 66 , d ) 96 , e ) none | d | sqrt(multiply(576, 16)) | multiply(n0,n1)|sqrt(#0)| | gain |
car a runs at the speed of 52 km / hr & reaches its destination in 10 hr . car b runs at the speed of 46 km / h & reaches its destination in 8 h . what is the respective ratio of distances covered by car a & car b ? | "sol . distance travelled by car a = 52 × 10 = 520 km distance travelled by car b = 46 × 8 = 368 km ratio = 520 / 368 = 65 : 41 d" | a ) 62 : 25 , b ) 66 : 52 , c ) 68 : 15 , d ) 65 : 41 , e ) 23 : 59 | d | divide(multiply(52, 10), multiply(46, 8)) | multiply(n0,n1)|multiply(n2,n3)|divide(#0,#1)| | physics |
the distance from city a to city b is 60 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ? | "the time it takes bob to drive to city b is 60 / 40 = 1.5 hours . alice needs to take less than 1 hour for the trip . alice needs to exceed a constant speed of 60 / 1 = 60 miles per hour . the answer is e ." | a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 60 | e | divide(60, subtract(divide(60, 40), divide(30, const_60))) | divide(n0,n1)|divide(n2,const_60)|subtract(#0,#1)|divide(n0,#2)| | physics |
if 18 persons can build a wall 140 m long in 42 days , the number of days that 30 persons will take to complete a similar wall 100 m long , is ? | "explanation : ( length 140 : 100 ) : ( persons 30 : 18 ) : : 42 : x 140 x 30 x x = 100 x 18 x 42 or x = 18 answer : b" | a ) 28 , b ) 18 , c ) 24 , d ) 21 , e ) 16 | b | divide(multiply(multiply(18, 100), 42), multiply(140, 30)) | multiply(n0,n4)|multiply(n1,n3)|multiply(n2,#0)|divide(#2,#1)| | physics |
a pharmaceutical company received $ 7 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in ... | "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sa... | a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 76 % | e | multiply(divide(subtract(multiply(divide(7, 20), const_100), multiply(divide(9, 108), const_100)), multiply(divide(7, 20), const_100)), const_100) | divide(n0,n1)|divide(n2,n3)|multiply(#0,const_100)|multiply(#1,const_100)|subtract(#2,#3)|divide(#4,#2)|multiply(#5,const_100)| | general |
the sum of three consecutive even numbers is 93 . find the middle number of the three ? | "middle value = 93 / 3 = 31 ans d" | a ) 14 , b ) 35 , c ) 39 , d ) 31 , e ) 12 | d | add(add(power(add(add(divide(subtract(subtract(93, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(93, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(93, const_10), const_2), const_4), const_2), power(add... | subtract(n0,const_10)|subtract(#0,const_2)|divide(#1,const_4)|add(#2,const_2)|power(#2,const_2)|add(#3,const_2)|power(#3,const_2)|add(#5,const_2)|add(#4,#6)|power(#5,const_2)|power(#7,const_2)|add(#9,#10)|add(#11,#8)| | physics |
an error 6 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is : | "explanation : 100 cm is read as 106 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 106 × 106 ) cm 2 = 11236 ( a 2 - a 1 ) = 11236 - 10000 = 1236 = > 1236 / 10000 * 100 = 12.36 answer : a" | a ) 12.36 , b ) 8.36 , c ) 9.36 , d ) 10.36 , e ) 11.36 | a | divide(multiply(subtract(square_area(add(const_100, 6)), square_area(const_100)), const_100), square_area(const_100)) | add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)| | gain |
12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height . find the diameter of each sphere . | "explanation : in this type of question , just equate the two volumes to get the answer as , volume of cylinder = π r 2 h volume of sphere = 43 π r 3 = > 12 ∗ 4 / 3 π r 3 = π r 2 h = > 12 ∗ 4 / 3 π r 3 = π ∗ 8 ∗ 8 ∗ 2 = > r 3 = 8 ∗ 8 ∗ 2 ∗ 3 / 12 ∗ 4 = > r 3 = 8 = > r = 2 cm = > diameter = 2 ∗ 2 = 4 cm option a" | a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm | a | multiply(divide(divide(divide(divide(multiply(divide(volume_cylinder(divide(16, const_2), 2), const_pi), const_3), const_4), 12), const_4), const_4), const_2) | divide(n1,const_2)|volume_cylinder(#0,n2)|divide(#1,const_pi)|multiply(#2,const_3)|divide(#3,const_4)|divide(#4,n0)|divide(#5,const_4)|divide(#6,const_4)|multiply(#7,const_2)| | physics |
what is the decimal equivalent of ( 1 / 9 ) ^ 2 ? | "( 1 / 9 ) ² = ( 1 / 9 ) ( 1 / 9 ) = 1 / 81 approach # 1 : use long division to divide 81 into 1 to get 1 / 81 = 0.0123 a" | a ) 0.0123 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5 | a | power(divide(1, 9), 2) | divide(n0,n1)|power(#0,n2)| | general |
7589 - ? = 3434 | "let 7589 - x = 3434 then x = 7589 - 3434 = 4155 answer is b" | a ) 4242 , b ) 4155 , c ) 1123 , d ) 11023 , e ) none of them | b | multiply(divide(7589, 3434), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 30 overs to reach the target of 282 runs ? | "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 30 run rate needed = 250 / 30 = 8.3 answer : option d" | a ) 6.25 , b ) 5.5 , c ) 7.4 , d ) 8.3 , e ) 6.2 | d | divide(subtract(282, multiply(10, 3.2)), 30) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | gain |
with a slope of 4 , with a straight line in the xy - plane which has a point with x - coordinate of the point 14 and y - coordinate 19 , find the y - intercept . | eq of line = y = mx + c m = 4 x = 14 y = 19 c = y - mx substitute given : c = 19 - ( 4 ) ( 14 ) c = - 37 correct option is c | a ) - 19 , b ) 18 , c ) - 37 , d ) 50 , e ) 37 | c | subtract(19, multiply(14, 4)) | multiply(n0,n1)|subtract(n2,#0) | general |
elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ? | "number of cups flour needed for 3 ounces of butter = 4 number of cups flour needed for 1 ounce of butter = 4 / 3 number of cups flour needed for 12 ounces of butter = 4 / 3 * 12 = 16 answer e" | a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 16 | e | multiply(4, 4) | multiply(n1,n2)| | general |
excluding stoppages , the speed of a bus is 52 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ? | "due to stoppages , it covers 7 km less . time taken to cover 7 km = ( 7 / 52 ) x 60 = 8 min answer : d" | a ) 7 min , b ) 6 min , c ) 9 min , d ) 8 min , e ) 11 min | d | multiply(const_60, divide(subtract(52, 45), 52)) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_60)| | physics |
what is the smallest positive integer x , such that √ 392 x is an integer ? | "for a perfect square , the powers of prime factors should be even . 392 can be broken up as 2 ^ 3 * 7 ^ 2 . you just need 2 to be multiplied to this number so that the number finally becomes 2 ^ 4 * 7 ^ 2 which is a perfect square . therefore x = 2 . answer : a" | a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 14 | a | add(const_3, const_4) | add(const_3,const_4)| | general |
the cost of an article is decreased by 10 % . if the original cost is $ 60 , find the decrease cost . | "original cost = $ 60 decrease in it = 10 % of $ 60 = 10 / 100 ã — 60 = 600 / 100 = $ 6 therefore , decrease cost = $ 60 - $ 6 = $ 54 answer : e" | a ) 33 , b ) 12 , c ) 68 , d ) 36 , e ) 54 | e | divide(multiply(60, 10), const_100) | multiply(n0,n1)|divide(#0,const_100)| | gain |
if 4 people are selected from a group of 5 married couples , what is the probability that none of them would be married to each other ? | "if we are to select 4 people from 5 couples without any restriction , how many ways can we make the selection ? 10 ! / 4 ! 6 ! = 210 if we are to select 4 people from 5 couples with restriction that no married couple can both make it to the group , only a representative ? 5 ! / 4 ! 1 ! = 5 but we know that to select a... | a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 8 / 21 | e | multiply(multiply(multiply(divide(multiply(5, const_2), multiply(5, const_2)), divide(multiply(4, 4), subtract(multiply(5, const_2), const_1))), divide(subtract(multiply(4, 4), const_2), multiply(4, 4))), divide(subtract(subtract(multiply(4, 4), const_2), const_2), subtract(multiply(4, 4), const_1))) | multiply(n0,n0)|multiply(n1,const_2)|divide(#1,#1)|subtract(#0,const_2)|subtract(#0,const_1)|subtract(#1,const_1)|divide(#3,#0)|divide(#0,#5)|subtract(#3,const_2)|divide(#8,#4)|multiply(#2,#7)|multiply(#6,#10)|multiply(#9,#11)| | probability |
a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 2.5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ? | "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 2.5 = 3600 . answer : d" | a ) 5729 , b ) 5760 , c ) 2889 , d ) 3600 , e ) 2799 | d | divide(multiply(2.5, multiply(8, const_60)), subtract(divide(multiply(8, const_60), multiply(6, const_60)), const_1)) | multiply(n2,const_60)|multiply(n0,const_60)|divide(#0,#1)|multiply(n1,#0)|subtract(#2,const_1)|divide(#3,#4)| | physics |
the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ? | "correct avg marks = 100 + ( 10 - 50 ) / 10 avg = 100 - 4 = 96 answer is c" | a ) a ) 78 , b ) b ) 82 , c ) c ) 96 , d ) d ) 91 , e ) e ) 85 | c | divide(add(subtract(multiply(100, 10), 50), 10), 10) | multiply(n0,n1)|subtract(#0,n2)|add(n3,#1)|divide(#2,n0)| | general |
find the simple interest on $ 2500 for 3 years at 10 % per annum ? | "si = ptr / 100 = 2500 * 3 * 10 / 100 = $ 750 answer is c" | a ) $ 250 , b ) $ 300 , c ) $ 750 , d ) $ 600 , e ) $ 1000 | c | multiply(2500, divide(3, const_100)) | divide(n1,const_100)|multiply(n0,#0)| | gain |
due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 40 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? | "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 40 = 10 * 3 / 2 = 15 time difference = 4.1 ans : b" | a ) a ) 6.24 , b ) b ) 4.1 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24 | b | max(multiply(subtract(add(55, 10), const_1), subtract(divide(10, 40), divide(10, 55))), const_4) | add(n0,n1)|divide(n0,n2)|divide(n0,n1)|subtract(#0,const_1)|subtract(#1,#2)|multiply(#3,#4)|max(#5,const_4)| | physics |
p and q can complete a work in 40 days and 24 days respectively . p alone started the work and q joined him after 16 days till the completion of the work . how long did the work last ? | "explanation : work done by p in 1 day = 1 / 40 work done by q in 1 day = 1 / 24 work done by p in 16 days = 16 ã — ( 1 / 40 ) = 2 / 5 remaining work = 1 â € “ 2 / 5 = 3 / 5 work done by p and q in 1 day = 1 / 40 + 1 / 24 = 1 / 15 number of days p and q take to complete the remaining work = ( 3 / 5 ) / ( 1 / 15 ) = 9 t... | a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 25 days | e | add(16, divide(subtract(const_1, divide(16, 40)), add(inverse(40), inverse(24)))) | divide(n2,n0)|inverse(n0)|inverse(n1)|add(#1,#2)|subtract(const_1,#0)|divide(#4,#3)|add(n2,#5)| | physics |
in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 360 vote ’ s majority . what is the total number of votes polled ? | "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 360 ( 40 * 9 = 360 ) 100 % - - - - - > 900 ( 100 * 9 = 900 ) answer : option c" | a ) 750 , b ) 700 , c ) 900 , d ) 850 , e ) none of these | c | divide(multiply(const_100, 360), subtract(70, subtract(const_100, 70))) | multiply(n1,const_100)|subtract(const_100,n0)|subtract(n0,#1)|divide(#0,#2)| | gain |
if the price of petrol increases by 25 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ? | "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 25 ) i . e 125 . now , his consumption should be reduced to : - = 125 − 100125 ∗ 100 . hence , the consumption should be reduced to 20 % . answer : b" | a ) 25 % , b ) 20 % , c ) 16.67 % , d ) 33.33 % , e ) none of these | b | multiply(subtract(const_1, divide(const_100, add(const_100, 25))), const_100) | add(n0,const_100)|divide(const_100,#0)|subtract(const_1,#1)|multiply(#2,const_100)| | general |
an association of mathematics teachers has 1,260 members . only 640 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ? | "total number of members = 1260 number of members that cast votes = 640 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 640 = 384 percent of total membership that voted for winning candidate = ( 384 / 1260 ) * 100 = 30.47 % answer a" | a ) 30.47 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25 % | a | multiply(divide(multiply(divide(60, const_100), 640), multiply(const_100, power(const_4, const_2))), const_100) | divide(n2,const_100)|power(const_4,const_2)|multiply(n1,#0)|multiply(#1,const_100)|divide(#2,#3)|multiply(#4,const_100)| | gain |
there are 10 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ? | "10 players are there . two players play one game with one another . so 10 c 2 = 10 * 9 / 2 = 45 so option c is correct" | a ) 10 , b ) 30 , c ) 45 , d ) 60 , e ) 90 | c | divide(multiply(10, subtract(10, const_1)), const_2) | subtract(n0,const_1)|multiply(n0,#0)|divide(#1,const_2)| | general |
by selling 24 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ? | "80 % - - - 24 120 % - - - ? 80 / 120 * 24 = 16 answer : c" | a ) 8 , b ) 9 , c ) 16 , d ) 6 , e ) 4 | c | multiply(divide(const_1, multiply(add(const_100, 20), divide(const_1, subtract(const_100, 20)))), 24) | add(n2,const_100)|subtract(const_100,n1)|divide(const_1,#1)|multiply(#0,#2)|divide(const_1,#3)|multiply(n0,#4)| | gain |
ramesh purchased a refrigerator for rs . 13500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ? | "price at which the tv set is bought = rs . 13,500 discount offered = 20 % marked price = 13500 * 100 / 80 = rs . 16875 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no di... | a ) 34778 , b ) 26888 , c ) 2899 , d ) 18975 , e ) 12778 | d | divide(multiply(add(const_100, 10), add(divide(multiply(13500, const_100), subtract(const_100, 20)), add(125, 250))), const_100) | add(n4,const_100)|add(n2,n3)|multiply(n0,const_100)|subtract(const_100,n1)|divide(#2,#3)|add(#1,#4)|multiply(#0,#5)|divide(#6,const_100)| | gain |
suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 15 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ? | "the part of job that suresh completes in 9 hours = 9 â „ 15 = 3 â „ 5 remaining job = 1 - 3 â „ 5 = 2 â „ 5 remaining job can be done by ashutosh in 2 â „ 5 ã — 15 = 6 hours answer c" | a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) none of these | c | multiply(subtract(const_1, divide(9, 15)), 15) | divide(n2,n0)|subtract(const_1,#0)|multiply(n1,#1)| | physics |
water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 4 meters . what is value of the radius ? | "10 * 0.31 = 3.1 m ^ 3 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 4 ) which is about 1 / 4 r = 1 / 2 the answer is a ." | a ) 0.5 , b ) 1.0 , c ) 1.5 , d ) 2.0 , e ) 2.5 | a | divide(multiply(10, 0.31), 4) | multiply(n0,n2)|divide(#0,n3)| | physics |
in a family 4 people eat only vegetarian , 3 people eat only non veg . , 2 people eat both veg and non veg . . how many people are in the family ? | "total number of people in family = veg + non veg + ( both veg and non veg ) total = 4 + 3 + 2 = 9 answer is e" | a ) 4 , b ) 3 , c ) 10 , d ) 2 , e ) 9 | e | add(4, 2) | add(n0,n2)| | other |
how many of the positive factors of 36 are not factors of 72 | "factors of 36 - 1 , 2,3 , 4,6 , 9,12 , 18,36 , factors of 72 - 1,2 , 3,4 , 6,8 , 9,12 , 18,24 , 36,72 , comparing both , we have no factors of 36 which are not factors of 72 - 0 answer ( a )" | a ) 0 , b ) 3 , c ) 4 , d ) 5 , e ) 1 | a | divide(72, 36) | divide(n1,n0)| | other |
trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 1 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 1 ) . what is its perimeter ? | "jk = 2 lm = 11 kl = using distance formula 10 jm = using distance formula 8 sum of all is 31 c" | a ) 34 , b ) 36 , c ) 31 , d ) 40 , e ) ( f ) 42 | c | add(add(add(const_10, add(1, 1)), add(2, 6)), add(7, 1)) | add(n1,n3)|add(n0,n4)|add(n1,n5)|add(#0,const_10)|add(#3,#1)|add(#4,#2)| | physics |
noelle walks from point a to point b at an average speed of 4 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 6 kilometers per hour ? | "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 6 = 2 * 4 * x / 4 + x x = 12 d is the answer" | a ) 6.75 , b ) 7 , c ) 8 , d ) 12 , e ) 14 | d | divide(multiply(6, 4), subtract(multiply(const_2, 4), 6)) | multiply(n0,n1)|multiply(n0,const_2)|subtract(#1,n1)|divide(#0,#2)| | physics |
the sum of all two digit numbers divisible by 4 is | "required numbers are 12 , 16,20 . . . . . 96 this is an a . p . in which a = 12 , d = 4 and l = 96 . let the number of terms in it be n . then t = 96 so a + ( n - 1 ) d = 96 . 12 + ( n - 1 ) * 6 = 96 , 12 + 4 n - 4 = 96 4 + 4 n = 96 4 n = 96 - 4 n = 92 / 4 then n = 23 . required sum = n / 2 ( a + l ) = 23 / 2 ( 12 + 9... | a ) 1242 , b ) 1542 , c ) 1742 , d ) 1610 , e ) 1842 | a | multiply(divide(divide(subtract(multiply(4, add(const_10, const_1)), multiply(const_1, 4)), subtract(multiply(4, const_2), multiply(const_1, 4))), const_2), add(multiply(4, const_2), multiply(4, add(const_10, const_1)))) | add(const_1,const_10)|multiply(n0,const_2)|multiply(n0,const_1)|multiply(n0,#0)|subtract(#1,#2)|add(#1,#3)|subtract(#3,#2)|divide(#6,#4)|divide(#7,const_2)|multiply(#5,#8)| | general |
the profits of qrs company rose 35 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ? | assume 100 in march , then 135 in april as 35 % increase , then 108 in may as 20 % decrease from april , and then 162 in june which is 150 % of 108 . so overall increase is from 100 to 162 is 62 % answer d | a ) 15 % , b ) 32 % , c ) 40 % , d ) 62 % , e ) 80 % | d | multiply(const_100, subtract(multiply(add(const_1, divide(50, const_100)), multiply(add(const_1, divide(35, const_100)), subtract(const_1, divide(20, const_100)))), const_1)) | divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|add(#1,const_1)|subtract(const_1,#2)|multiply(#4,#5)|multiply(#3,#6)|subtract(#7,const_1)|multiply(#8,const_100) | gain |
find the area of a parallelogram with base 36 cm and height 24 cm ? | "area of a parallelogram = base * height = 36 * 24 = 864 cm 2 answer : d" | a ) 760 , b ) 284 , c ) 288 , d ) 864 , e ) 820 | d | multiply(36, 24) | multiply(n0,n1)| | geometry |
what quantity of water should taken out to concentrate 18 liters of 40 % acidic liquid to 60 % acidic liquid ? | "required answer is = 18 ( 60 - 40 ) / 60 = 6 liters answer is e" | a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters | e | subtract(18, divide(multiply(18, 40), 60)) | multiply(n0,n1)|divide(#0,n2)|subtract(n0,#1)| | gain |
if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 26 , what is the value of r - p ? | "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 52 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 32 hence , the correct answer is c" | a ) 20 , b ) 10 , c ) 32 , d ) 40 , e ) 5 | c | subtract(multiply(26, const_2), multiply(10, const_2)) | multiply(n1,const_2)|multiply(n0,const_2)|subtract(#0,#1)| | general |
a can do a work in 6 days . b can do the same work in 4 days . both a & b together will finish the work and they got $ 2000 from that work . find their shares ? | "ratio of their works a : b = 6 : 4 ratio of their wages a : b = 2 : 3 a ' s share = ( 2 / 5 ) 2000 = 800 b ' s share = ( 3 / 5 ) 2000 = 1200 correct option is d" | a ) 600,400 , b ) 500,500 , c ) 300,700 , d ) 800,1200 , e ) 550,1450 | d | divide(multiply(6, 4), add(6, 4)) | add(n0,n1)|multiply(n0,n1)|divide(#1,#0)| | physics |
3.00001 unbiased coins are tossed . what is the probability of getting 2 tails ? | "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 2 tails then e = { tth , tht , htt } p ( e ) = n ( e ) / n ( s ) = 3 / 8 answer is c" | a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8 | c | negate_prob(divide(const_1, power(const_2, const_3))) | power(const_2,const_3)|divide(const_1,#0)|negate_prob(#1)| | probability |
veena ranks 73 rd from the top in a class of 182 . what is her rank from the bottom if 35 students have failed the examination ? | "total student = 182 failed = 35 paasd student = 182 - 35 = 160 from bottom her rank is = 147 - 73 + 1 = 75 answer : d" | a ) 88 , b ) 108 , c ) 110 , d ) 75 , e ) 93 | d | subtract(subtract(subtract(182, 35), subtract(73, const_1)), const_4) | subtract(n1,n2)|subtract(n0,const_1)|subtract(#0,#1)|subtract(#2,const_4)| | other |
the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 20 ? | "$ 20 = 3 * $ 6 + $ 2 the number of doughnuts is 3 * 12 + 2 = 38 the answer is e ." | a ) 30 , b ) 32 , c ) 34 , d ) 36 , e ) 38 | e | multiply(divide(20, 6), const_12) | divide(n2,n1)|multiply(#0,const_12)| | general |
a bowl was half full of water . 4 cups of water were then added to the bowl , filling the bowl to 70 % of its capacity . how many cups of water are now in the bowl ? | lets say total volume of the container = v initial water content is half of total volume = v / 2 then 4 cups of water were added . current water content = ( v / 2 ) + 4 cups = ( 70 / 100 ) v = > v = 20 cups = > current water content is equivalent to = v / 2 + 4 cups = 20 / 2 + 4 = 14 cups ; answer : a | a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | a | multiply(divide(70, const_100), divide(multiply(4, const_100), multiply(subtract(divide(70, const_100), divide(divide(const_100, const_2), const_100)), const_100))) | divide(n1,const_100)|divide(const_100,const_2)|multiply(n0,const_100)|divide(#1,const_100)|subtract(#0,#3)|multiply(#4,const_100)|divide(#2,#5)|multiply(#0,#6) | gain |
two numbers are in the ratio of 5 : 7 . if 25 be subtracted from each , they are in the ratio of 35 : 59 . find the numbers ? | "( 5 x - 25 ) : ( 7 x - 25 ) = 35 : 59 x = 12 = > 60,84 answer : d" | a ) 60,88 , b ) 60,86 , c ) 60,82 , d ) 60,84 , e ) 60,83 | d | multiply(5, 25) | multiply(n0,n2)| | other |
the number 189 is equal to the sum of the cubes of two integers . what is the product of those integers ? | "4 ^ 3 + 5 ^ 3 = 189 the number is 4 * 5 = 20 c" | a ) 8 , b ) 15 , c ) 20 , d ) 27 , e ) 39 | c | multiply(floor(power(divide(189, const_2), divide(const_1, const_3))), power(subtract(189, power(floor(power(divide(189, const_2), divide(const_1, const_3))), const_3)), divide(const_1, const_3))) | divide(n0,const_2)|divide(const_1,const_3)|power(#0,#1)|floor(#2)|power(#3,const_3)|subtract(n0,#4)|power(#5,#1)|multiply(#3,#6)| | general |
in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 36000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ? | "0.037 * 10 ^ 5 can be written as 3600 74000 * 10 ^ ( - 3 ) can be written as 36 required = 3600 / 36 = 100 answer : a" | a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500 | a | divide(multiply(multiply(const_1000, const_100), 0.036), divide(36000, const_1000)) | divide(n3,const_1000)|multiply(const_100,const_1000)|multiply(n0,#1)|divide(#2,#0)| | general |
in 120 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by : | "distance covered by b in 9 sec . = 120 / 45 x 9 m = 24 m . a beats b by 24 metres . answer : option a" | a ) 24 m , b ) 25 m , c ) 22.5 m , d ) 9 m , e ) 12 m | a | multiply(divide(120, 45), subtract(45, 36)) | divide(n0,n2)|subtract(n2,n1)|multiply(#0,#1)| | physics |
how many seconds will a 450 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ? | "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 450 * 3 / 50 = 27 sec . answer : option b" | a ) 20 , b ) 27 , c ) 42 , d ) 32 , e ) 60 | b | divide(450, multiply(subtract(63, 3), const_0_2778)) | subtract(n2,n1)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
fox jeans regularly sell for $ 10 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22... | "x discount on pony jeans , ( 0.22 - x ) discount on fox jeans . set the equation : 3 * 10 ( 0.22 - x ) + 2 * 18 x = 9 - - > x = 0.4 = 40 % answer : e ." | a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 40 % | e | multiply(subtract(divide(22, const_100), divide(subtract(9, multiply(divide(22, const_100), multiply(18, 2))), subtract(multiply(10, 3), multiply(18, 2)))), const_100) | divide(n6,const_100)|multiply(n1,n5)|multiply(n0,n4)|multiply(#0,#1)|subtract(#2,#1)|subtract(n2,#3)|divide(#5,#4)|subtract(#0,#6)|multiply(#7,const_100)| | gain |
a taxi leaves point a 3 hours after a bus left the same spot . the bus is traveling 30 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in three hours . | let the speed of bus be v - 30 , speed of taxi be v the bus travelled a total of 6 hrs and taxi a total of 3 hrs . hence 6 * ( v - 30 ) = 3 v 6 v - 180 = 3 v 3 v = 180 v = 60 mph a | a ) 60 , b ) 72 , c ) 48 , d ) 36 , e ) 64 | a | divide(add(multiply(3, 30), multiply(3, 30)), subtract(add(3, 3), 3)) | add(n0,n0)|multiply(n0,n1)|add(#1,#1)|subtract(#0,n0)|divide(#2,#3) | physics |
a single reservoir supplies the petrol to the whole city , while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume . when the reservoir is full and if 40,000 liters of petrol is used daily , the suply fails in 90 days . if 32,000 liters of petrol is used daily , it fails ... | explanation : let x liter be the per day filling and v litr be the capacity of the reservoir , then 90 x + v = 40000 × 90 - - - - - ( 1 ) 60 x + v = 32000 × 60 - - - - - - ( 2 ) solving eq . ( 1 ) and ( 2 ) , we get x = 56000 hence , 56000 liters per day can be used without the failure of supply . answer : b | ['a ) 64000 liters', 'b ) 56000 liters', 'c ) 78000 liters', 'd ) 60000 liters', 'e ) none of these'] | b | add(add(add(multiply(60, 90), surface_rectangular_prism(const_180, 60, 60)), const_180), multiply(const_2, const_10)) | multiply(n1,n3)|multiply(const_10,const_2)|surface_rectangular_prism(n3,n3,const_180)|add(#0,#2)|add(#3,const_180)|add(#4,#1) | physics |
a train 100 m long crosses a platform 250 m long in 7 sec ; find the speed of the train ? | "d = 100 + 250 = 350 t = 7 s = 350 / 7 * 18 / 5 = 180 kmph answer : d" | a ) 94 kmph , b ) 58 kmph , c ) 54 kmph , d ) 180 kmph , e ) 59 kmph | d | subtract(multiply(7, multiply(const_60.0, const_0_2778)), 100) | multiply(const_60.0,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)| | physics |
what is the greatest positive integer x such that 6 ^ x is a factor of 216 ^ 10 ? | "216 ^ 10 = ( 6 ^ 3 ) ^ 10 = 6 ^ 30 answer : e" | a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30 | e | multiply(subtract(216, 10), 10) | subtract(n1,n2)|multiply(n2,#0)| | general |
the length of the bridge , which a train 100 metres long and travelling at 45 km / hr can cross in 30 seconds , is ? | "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 100 + x ) / 30 = 25 / 2 = > 2 ( 100 + x ) = 750 = > x = 275 m . answer : c" | a ) 10 m , b ) 16 m , c ) 275 m , d ) 19 m , e ) 27 m | c | subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 100) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | physics |
simple interest on a certain sum at a certain annual rate of interest is 1 / 4 of the sum . if the numbers representing rate percent and time in years be equal , then the rate of interest is : | "explanation : let sum = x . then , s . i . = x / 4 let rate = r % and time = r years . [ x * r * r / 100 ] = x / 4 ? r ^ 2 = 100 / 4 = 25 r = 5 hence , rate of interest = 5 % . answer : c" | a ) 4 % . , b ) 25 / 4 % . , c ) 5 % , d ) 6 % . , e ) 3 % . | c | divide(add(multiply(floor(sqrt(multiply(divide(1, 4), const_100))), const_10), 1), const_3) | divide(n0,n1)|multiply(#0,const_100)|sqrt(#1)|floor(#2)|multiply(#3,const_10)|add(#4,n0)|divide(#5,const_3)| | gain |
ravish has to secure 40 % marks to clear his board exam of class 10 th . he got 40 marks and failed by 40 marks . what is the maximum marks ? | d 200 to pass the exam ravish needs 40 + 40 = 80 marks . = > ( 80 / 40 ) * 100 = 200 | a ) 150 , b ) 135 , c ) 160 , d ) 200 , e ) 155 | d | divide(add(40, 40), divide(40, const_100)) | add(n0,n0)|divide(n0,const_100)|divide(#0,#1) | gain |
there are 172 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off ... | "editing my solution : number of switches = 172 number of switches turned on by a : 3 , 6 , . . . 171 = 57 number of switches turned on by b : 5 , 10 , . . . . 170 = 34 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a a... | a ) 83 , b ) 85 , c ) 87 , d ) 79 , e ) 89 | d | subtract(add(floor(divide(172, const_3)), floor(divide(172, add(const_1, const_4)))), multiply(floor(divide(172, multiply(const_3, add(const_1, const_4)))), const_2)) | add(const_1,const_4)|divide(n0,const_3)|divide(n0,#0)|floor(#1)|multiply(#0,const_3)|divide(n0,#4)|floor(#2)|add(#3,#6)|floor(#5)|multiply(#8,const_2)|subtract(#7,#9)| | other |
car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 41 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ? | "in 72 minutes , car x travels 42 miles . car y gains 6 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is d ." | a ) 140 , b ) 175 , c ) 210 , d ) 245 , e ) 280 | d | multiply(35, divide(multiply(divide(72, const_60), 35), subtract(41, 35))) | divide(n1,const_60)|subtract(n2,n0)|multiply(n0,#0)|divide(#2,#1)|multiply(n0,#3)| | physics |
a man swims downstream 36 km and upstream 48 km taking 6 hours each time , what is the speed of the man in still water ? | "36 - - - 6 ds = 6 ? - - - - 1 48 - - - - 6 us = 8 ? - - - - 1 m = ? m = ( 6 + 8 ) / 2 = 7 answer : c" | a ) 5 , b ) 24 , c ) 7 , d ) 42 , e ) 6 | c | divide(add(divide(48, 6), divide(36, 6)), const_2) | divide(n1,n2)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)| | physics |
a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 17 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neithe... | c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 17 - 2 cmb = 100 b - cb - mb - 2 cmb = 27 hence the... | a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 27 / 100 , e ) 9 / 100 | d | divide(subtract(100, subtract(add(50, 40), 17)), 100) | add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)|divide(#2,n0) | other |
the original price of a suit is $ 150 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ? | "0.8 * ( 1.2 * 150 ) = $ 144 the answer is c ." | a ) $ 130 , b ) $ 136 , c ) $ 144 , d ) $ 150 , e ) $ 160 | c | subtract(add(150, divide(multiply(150, 20), const_100)), divide(multiply(add(150, divide(multiply(150, 20), const_100)), 20), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)|multiply(n1,#2)|divide(#3,const_100)|subtract(#2,#4)| | general |
convert 350 inches into centimeter ? | "1 inch = 2.54 cm 350 inches = 100 * 2.54 = 889 cm answer is d" | a ) 812 cm , b ) 820 cm , c ) 850 cm , d ) 889 cm , e ) 854 cm | d | divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 350), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2))) | add(const_2,const_3)|multiply(#0,const_2)|multiply(#1,#1)|multiply(n0,#2)|divide(#3,#2)| | physics |
the length of a rectangular floor is more than its breadth by 200 % . if rs . 624 is required to paint the floor at the rate of rs . 4 per sq m , then what would be the length of the floor ? | "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 624 / 4 = 156 sq m l b = 156 i . e . , l * l / 3 = 156 l 2 = 468 = > l = 21.6 m . answer : b" | a ) 22.8 m . , b ) 21.6 m . , c ) 21.1 m . , d ) 20.6 m . , e ) 22.5 m . | b | multiply(sqrt(divide(divide(624, 4), const_3)), const_3) | divide(n1,n2)|divide(#0,const_3)|sqrt(#1)|multiply(#2,const_3)| | gain |
a is twice as fast as b . if b alone can do a piece of work in 10 days , in what time can a and b together complete the work ? | "a can do the work in 10 / 2 i . e . , 5 days . a and b ' s one day ' s work = 1 / 5 + 1 / 10 = ( 2 + 1 ) / 10 = 10 / 3 so a and b together can do the work in 10 / 3 days . answer : a" | a ) 10 / 3 , b ) 8 , c ) 9 , d ) 7 / 3 , e ) 12 | a | inverse(add(divide(const_1, 10), multiply(divide(const_1, 10), const_2))) | divide(const_1,n0)|multiply(#0,const_2)|add(#0,#1)|inverse(#2)| | physics |
two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.4 km respectively . the time taken by the slower train to cross the faster train in seconds is ? | "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.4 = 1.5 km = 1500 m . required time = 1500 * 3 / 125 = 36 sec . answer : b" | a ) 65 sec , b ) 36 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec | b | subtract(divide(multiply(1.10, const_1000), divide(multiply(60, const_1000), const_3600)), divide(multiply(0.4, const_1000), divide(multiply(90, const_1000), const_3600))) | multiply(n2,const_1000)|multiply(n0,const_1000)|multiply(n3,const_1000)|multiply(n1,const_1000)|divide(#1,const_3600)|divide(#3,const_3600)|divide(#0,#4)|divide(#2,#5)|subtract(#6,#7)| | physics |
how much time does a train 225 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 = 225 / t t = 9 s answer : d" | a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 9 s , e ) 7.4 s | d | multiply(divide(divide(225, const_1000), 90), const_3600) | divide(n0,const_1000)|divide(#0,n1)|multiply(#1,const_3600)| | general |
of the goose eggs laid at a certain pond , 1 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many ... | "let x be the number of eggs that were laid . ( 2 / 5 ) ( 3 / 4 ) ( 1 / 3 ) x = 120 ( 6 / 60 ) x = 120 x = 1200 the answer is b ." | a ) 1000 , b ) 1200 , c ) 1400 , d ) 1600 , e ) 1800 | b | divide(divide(divide(120, subtract(const_1, divide(3, 5))), divide(3, 4)), divide(1, 3)) | divide(n1,n5)|divide(n1,n3)|divide(n0,n1)|subtract(const_1,#0)|divide(n6,#3)|divide(#4,#1)|divide(#5,#2)| | general |
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