Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
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a mixture contains milk and water in the ratio 6 : 3 . on adding 10 litters of water , the ratio of milk to water becomes 6 : 5 . the quantity of milk in the original mixture is ? | "explanation : milk : water = 6 : 3 6 x : 3 x + 10 = 6 : 5 5 [ 6 x ] = 6 [ 3 x + 10 ] 30 x = 18 x + 60 30 x - 18 x = 60 12 x = 60 x = 5 the quantity of milk in the original mixture is = 6 : 3 = 6 + 3 = 9 9 x = 45 short cut method - 2 : for only milk problems milk : water 6 : 3 6 : 5 milk ratio same but water ratio 2 pa... | a ) 90 , b ) 45 , c ) 110 , d ) 40 , e ) 50 | b | divide(multiply(10, divide(3, const_3.0)), subtract(divide(5, add(6, 3)), multiply(divide(3, add(6, 3)), divide(3, 6)))) | add(n0,n1)|divide(n3,n4)|divide(n0,#0)|divide(n1,#0)|multiply(n2,#1)|multiply(#3,#1)|subtract(#2,#5)|divide(#4,#6)| | general |
if the numerator of a fraction be increased by 20 % and its denominator be diminished by 10 % , the value of the fraction is 20 / 21 . find the original fraction ? | "let the original fraction be x / y then , 120 % of x / 90 % of y = 20 / 21 120 x / 90 y = 20 / 21 x / y = 5 / 7 answer is d" | a ) 1 / 2 , b ) 3 / 5 , c ) 4 / 7 , d ) 5 / 7 , e ) 7 / 9 | d | divide(multiply(subtract(const_100, 10), 20), multiply(add(const_100, 20), 21)) | add(n0,const_100)|subtract(const_100,n1)|multiply(n2,#1)|multiply(n3,#0)|divide(#2,#3)| | general |
the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 80 percent of b , what is the value of m / x ? | "a / b = 4 / 5 m / x = ( 1 / 5 ) * 5 / ( 5 / 4 ) * 4 = 1 / 5 the answer is a ." | a ) 1 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2 | a | multiply(divide(subtract(const_100, 80), add(const_100, 25)), divide(5, 4)) | add(n2,const_100)|divide(n1,n0)|subtract(const_100,n3)|divide(#2,#0)|multiply(#3,#1)| | general |
a man saves 10 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 10 % , he is only able to save rs . 200 per month . what is his monthly salary ? | "income = rs . 100 expenditure = rs . 90 savings = rs . 10 present expenditure 90 + 90 * ( 10 / 100 ) = rs . 99 present savings = 100 β 99 = rs . 1 if savings is rs . 1 , salary = rs . 100 if savings is rs . 200 , salary = 100 / 1 * 200 = 20000 answer : c" | a ) rs . 22,000 , b ) rs . 21,000 , c ) rs . 20,000 , d ) rs . 23,000 , e ) rs . 24,000 | c | divide(multiply(200, const_100), subtract(const_100, add(subtract(const_100, 10), multiply(subtract(const_100, 10), divide(10, const_100))))) | divide(n1,const_100)|multiply(n2,const_100)|subtract(const_100,n0)|multiply(#0,#2)|add(#3,#2)|subtract(const_100,#4)|divide(#1,#5)| | general |
the median annual household income in a certain community of 21 households is $ 50000 . if the mean w income of a household increases by 10 % per year over the next 2 years , what will the median income in the community be in 2 years ? | answer is e , because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean w is increase by 10 % . it could be the case that small number of higher end incomes increased a little or many low end incomes increased - it can not be identified . | a ) $ 50000 , b ) $ 60000 , c ) $ 60500 , d ) $ 65000 , e ) can not be determined | e | log(subtract(divide(10, 2), 10)) | divide(n2,n3)|subtract(#0,n2)|log(#1) | general |
4 different children have jelly beans : aaron has 5 , bianca has 7 , callie has 8 , and dante has 9 . how many jelly beans must dante give to aaron to ensure that no child has more than 1 fewer jelly beans than any other child ? | since bianca and callie are both within 1 jelly bean of each other and aaron has 5 , dante must provide 3 of his 9 jelly beans so each child has no more than 1 fewer jelly bean than any other child . dante + aaron = 9 + 5 = 14 / 2 = 7 9 - 8 = 1 so dante must provide 3 jelly beans to aaron . answer ( a ) | a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | a | subtract(9, 8) | subtract(n4,n3) | general |
an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 12 - meter platform and caught it after it had traveled 35.65 meters . how many times did the ball bounce ? | "ans : 6 division of total diatance travelled will be 12 + 12 + 6 + 3 + 1.5 + . 75 + 0.4 ans b" | a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9 | b | divide(divide(12, const_2), const_2) | divide(n0,const_2)|divide(#0,const_2)| | general |
a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and b quits 10 days before the project is completed , in how many days total will the project be completed ? | "a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 10 days , a can do 1 / 2 of the project . thus a and b must complete 1 / 2 of the project , which takes 6 days . the total number of days is 6 + 10 = 16 . the ans... | a ) 18 , b ) 27 , c ) 26 , d ) 16 , e ) 12 | d | add(divide(subtract(const_1, multiply(divide(const_1, 30), 10)), add(divide(const_1, 20), divide(const_1, 30))), 10) | divide(const_1,n1)|divide(const_1,n0)|add(#1,#0)|multiply(n2,#0)|subtract(const_1,#3)|divide(#4,#2)|add(n2,#5)| | physics |
a present value of a machine is $ 128000 . its value depletiation rate is 25 % per annum then find the machine value after 3 years ? | "p = $ 128000 r = 25 % t = 3 years machine value after 3 years = p / ( 1 - r / 100 ) ^ t = 128000 * 3 / 4 * 3 / 4 * 3 / 4 = $ 54000 answer is a" | a ) $ 54000 , b ) $ 48000 , c ) $ 36520 , d ) $ 32450 , e ) $ 42500 | a | multiply(128000, power(subtract(const_1, divide(25, const_100)), 3)) | divide(n1,const_100)|subtract(const_1,#0)|power(#1,n2)|multiply(n0,#2)| | gain |
when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction f of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ? | "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution ... | a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14 | a | divide(subtract(divide(2, add(1, 2)), subtract(divide(2, 9), multiply(divide(2, 9), divide(3, 4)))), divide(subtract(9, 2), 9)) | add(n0,n5)|divide(n0,n1)|divide(n2,n3)|subtract(n1,n0)|divide(n0,#0)|divide(#3,n1)|multiply(#1,#2)|subtract(#1,#6)|subtract(#4,#7)|divide(#8,#5)| | general |
when 1 / 20 % of 8000 is subtracted from 1 / 10 of 8000 , the difference is | 1 / 20 % of 8000 = 4 1 / 10 of 8000 = 800 800 - 2 = 798 ans : d | a ) 50 , b ) 200 , c ) 380 , d ) 798 , e ) 400 | d | subtract(divide(8000, 10), divide(8000, multiply(20, const_100))) | divide(n2,n4)|multiply(n1,const_100)|divide(n2,#1)|subtract(#0,#2) | general |
what is the remainder when 47 * 50 is divided by 8 ? | "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 47 * 50 ) / 8 } } = remainder of ( 47 / 8 ) * remainder of ( 50 / 8 ) = 7 * 2 = 14 answer : e" | a ) 1 , b ) 3 , c ) 13 , d ) 5 , e ) 14 | e | subtract(divide(const_100.0, const_2), multiply(47, 47)) | divide(const_100.0,const_2)|multiply(n0,n0)|subtract(#0,#1)| | general |
there are 100 students in a class . if 14 % are absent on a particular day , find the number of students present in the class . | number of students absent on a particular day = 14 % of 100 i . e . , 14 / 100 Γ 100 = 14 therefore , the number of students present = 100 - 14 = 86 students . answer : c | a ) 43 , b ) 36 , c ) 86 , d ) 129 , e ) 11 | c | multiply(subtract(const_1, divide(14, 100)), const_100) | divide(n1,n0)|subtract(const_1,#0)|multiply(#1,const_100) | gain |
the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department take... | "72 Β° divided by 360 Β° equals 0.2 , therefore the sector is equal to 20 % of the total answer : a" | a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 % | a | multiply(divide(72, divide(const_3600, const_10)), const_100) | divide(const_3600,const_10)|divide(n0,#0)|multiply(#1,const_100)| | physics |
if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 28 , 26 , 19 , 33 and 35 ? | "it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 28 , 26 , 19 , 33 and 35 19 , 24 , 26 , 28 , 30 , 33 , 35 , 42 . . . numbers less than median are 19 , 24 , 26 , 28 . . the median of these numbers = center of 24 and 26 =... | a ) 33 , b ) 28 , c ) 27 , d ) 25 , e ) 23 | d | divide(add(24, 26), const_2) | add(n1,n4)|divide(#0,const_2)| | general |
a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1.5 cm when a man gets on it . the mass of man is | "solution volume of water displaced = ( 3 x 2 x 0.015 ) m 3 = 0.09 m 3 . mass of man = volume of water displaced Γ density of water = ( 0.09 Γ 1000 ) kg = 90 kg . answer b" | a ) 12 kg , b ) 90 kg , c ) 72 kg , d ) 96 kg , e ) none | b | multiply(multiply(multiply(3, 2), divide(1.5, const_100)), const_1000) | divide(n2,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(#2,const_1000)| | physics |
three numbers are in the ratio 1 : 3 : 6 and their average is 100 . the largest number is : | "explanation : let the numbers be x , 3 x and 6 x , then , ( x + 3 x + 6 x ) / 3 = 100 = > 10 x = 100 * 3 = > x = 30 largest number 6 x = 6 * 30 = 180 answer : a" | a ) 180 , b ) 98 , c ) 27 , d ) 21 , e ) 22 | a | add(multiply(multiply(1, 6), const_100), multiply(3, 6)) | multiply(n0,n2)|multiply(n1,n2)|multiply(#0,const_100)|add(#2,#1)| | general |
how many 3 digit positive integers r exist that when divided by 7 leave a remainder of 5 ? | "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leave... | a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129 | e | divide(subtract(subtract(multiply(const_100, const_10), const_1), add(multiply(add(const_10, const_4), 7), 5)), 7) | add(const_10,const_4)|multiply(const_10,const_100)|multiply(n1,#0)|subtract(#1,const_1)|add(n2,#2)|subtract(#3,#4)|divide(#5,n1)| | general |
a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 20 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a c... | "let there be g geese , of which 0.3 g are male and 0.7 g are female lets say m geese migrated , 0.2 m are male and 0.8 m are female migration rate male = 0.2 m / 0.3 g = ( 2 / 3 ) * ( m / g ) migration rate female = 0.8 m / 0.7 g = ( 8 / 7 ) * ( m / g ) ratio of migration rates = ( 2 / 3 ) / ( 8 / 7 ) = 7 / 12 answer ... | a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 8 / 7 | b | divide(divide(divide(20, const_100), divide(30, const_100)), divide(divide(multiply(multiply(const_2, const_4), const_10), const_100), divide(30, const_100))) | divide(n1,const_100)|divide(n0,const_100)|multiply(const_2,const_4)|divide(#0,#1)|multiply(#2,const_10)|divide(#4,const_100)|divide(#5,#1)|divide(#3,#6)| | general |
the average weight of a group of persons increased from 48 kg to 51 kg , when two persons weighing 88 kg and 93 kg join the group . find the initial number of members in the group ? | "let the initial number of members in the group be n . initial total weight of all the members in the group = n ( 48 ) from the data , 48 n + 88 + 93 = 51 ( n + 2 ) = > 51 n - 48 n = 79 = > n = 26 therefore there were 26 members in the group initially . answer : d" | a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27 | d | divide(subtract(add(88, 93), multiply(51, const_2)), subtract(51, 48)) | add(n2,n3)|multiply(n1,const_2)|subtract(n1,n0)|subtract(#0,#1)|divide(#3,#2)| | general |
what percent of 60 is 25 ? | "the phrasing of the question is difficult for some students . ` ` what percent of 60 is 25 ? ' ' is the same question as ` ` 25 is what percent of 60 ? ' ' many students find this later way of phrasing the question easier to work with . if x is y percent of z , then x / z = y / 100 ; for example , 10 is 50 % of 20 ; x... | a ) 60 % , b ) 50 % , c ) 42 % , d ) 25 % , e ) 10 % | c | multiply(divide(60, 25), const_100) | divide(n0,n1)|multiply(#0,const_100)| | gain |
two trains 121 meters and 153 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ? | "t = ( 121 + 153 ) / ( 80 + 65 ) * 18 / 5 t = 6.8 answer : b" | a ) 7.19 , b ) 6.8 , c ) 7.2 , d ) 7.15 , e ) 7.11 | b | divide(add(121, 153), multiply(add(80, 65), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | physics |
find the average of first 4 multiples of 15 ? | "average = ( 15 + 30 + 45 + 60 ) / 4 = 37.5 answer is e" | a ) 10 , b ) 12.6 , c ) 22.5 , d ) 31.3 , e ) 37.5 | e | divide(add(add(add(4, const_1), add(add(4, const_1), const_2)), add(subtract(15, 4), subtract(15, const_2))), 4) | add(n0,const_1)|subtract(n1,n0)|subtract(n1,const_2)|add(#0,const_2)|add(#1,#2)|add(#0,#3)|add(#5,#4)|divide(#6,n0)| | general |
the price of 3 chudi and 6 tops is rs . 1500 . with the same money one can buy 1 chudi and 12 tops . if one wants to buy 5 tops , how much shall she have to pay ? | let the price of a chudi and a top be rs . x and rs . y respectively . then , 3 x + 6 y = 1500 . . . . ( i ) and x + 12 y = 1500 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 500 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 1500 ( - ) x + 2 y = 500 - - - - - - - - - ... | a ) 500 , b ) 1000 , c ) 1200 , d ) 1300 , e ) 1500 | a | multiply(const_100, 5) | multiply(n5,const_100) | general |
the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 10 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ? | "take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 10 % then output equals 121 to restore new holidy demand output to original 100 . final - initial / final * 100 = 21 / 121 * 100 = 8 / 33 * 100 = 17 % approxiamately . option a is co... | a ) 17 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 % | a | multiply(divide(subtract(multiply(divide(add(const_100, 10), const_100), divide(add(const_100, 10), const_100)), const_1), multiply(divide(add(const_100, 10), const_100), divide(add(const_100, 10), const_100))), const_100) | add(n0,const_100)|add(n1,const_100)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|subtract(#4,const_1)|divide(#5,#4)|multiply(#6,const_100)| | general |
a bag contains 3 red , 4 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ? | "p ( both are red ) , = 3 c 211 c 2 = 3 c 211 c 2 = 3 / 55 c" | a ) 2 / 15 , b ) 2 / 21 , c ) 3 / 55 , d ) 3 / 29 , e ) 4 / 27 | c | divide(choose(3, 2), choose(add(add(3, 4), 4), 2)) | add(n0,n1)|choose(n0,n3)|add(n2,#0)|choose(#2,n3)|divide(#1,#3)| | other |
tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 39 pages per hour . if tom starts reading a novel at 4 : 30 , and jan begins reading an identical copy of the same book at 5 : 06 , at what time will they be reading the same page ? | "since tom reads an average of 1 page every 2 minutes , tom will read 18 pages in the first 36 minutes . jan can catch tom at a rate of 9 pages per hour , so it will take 2 hours to catch tom . the answer is c ." | a ) 6 : 06 , b ) 6 : 36 , c ) 7 : 06 , d ) 7 : 36 , e ) 8 : 06 | c | divide(add(5, divide(multiply(add(subtract(5, 4), divide(subtract(06, 30), const_60)), 30), subtract(39, 30))), 06) | subtract(n5,n3)|subtract(n4,n2)|subtract(n1,n0)|divide(#0,const_60)|add(#3,#1)|multiply(n0,#4)|divide(#5,#2)|add(n4,#6)|divide(#7,n5)| | general |
let f ( x , y ) be defined as the remainder when ( x β y ) ! is divided by x . if x = 24 , what is the maximum value of y for which f ( x , y ) = 0 ? | "the question is finding y such that ( 24 - y ) ! is a multiple of 24 . that means we need to have 2 ^ 3 * 3 in ( 24 - y ) ! 4 ! is the smallest factorial number with 2 ^ 3 * 3 as a factor . 24 - y = 4 y = 20 the answer is d ." | a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 21 | d | subtract(24, multiply(const_2, divide(divide(24, const_2), add(const_1, const_4)))) | add(const_1,const_4)|divide(n0,const_2)|divide(#1,#0)|multiply(#2,const_2)|subtract(n0,#3)| | general |
for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.5 ? | "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.5 = 6 * 0 + 2 * 7.2 + 8 - 6.5 = 0 + 14.4 + 1.5 15.7 answer d" | a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 15.7 . , e ) 16.4 . | d | subtract(add(multiply(2, 7.2), subtract(8.4, divide(const_4, const_10))), 6.5) | divide(const_4,const_10)|multiply(n1,n4)|subtract(n5,#0)|add(#1,#2)|subtract(#3,n6)| | general |
15 girls can complete a rangoli in 12 days , and 10 boys can complete the same work in 15 days . to complete the work earlier 10 boys and 15 girls are employed , in how many days will this work get completed ? | work done by 15 girls per day = 1 / 12 work done by 10 boys per day = 1 / 15 work done by 15 girls and 10 boys per day = 1 / 12 + 1 / 15 = 3 / 20 = 6 2 / 3 10 boys and 15 girls will complete the work in = 6 2 / 3 days d | a ) 6 , b ) 7 , c ) 6.5 , d ) 6 2 / 3 , e ) 6 1 / 4 | d | inverse(add(divide(const_1, 15), divide(const_1, 12))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|inverse(#2) | physics |
when a certain number x is divided by 63 , the remainder is 27 . what is the remainder when x is divided by 8 ? | "when a certain number x is divided by 63 , the remainder is 27 . what is the remainder when x is divided by 8 ? putting a value say x = 27 we get remainder as 27 when divided by 63 . when 27 divided by 8 we get 3 as remainder . b is the answer ." | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | b | reminder(27, 8) | reminder(n1,n2)| | general |
on dividing 100 by a number , the quotient is 9 and the remainder is 1 . find the divisor ? | "d = ( d - r ) / q = ( 100 - 1 ) / 9 = 99 / 9 = 11 b )" | a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14 | b | floor(divide(100, 9)) | divide(n0,n1)|floor(#0)| | general |
a can do a work in 15 days and b in 20 days . if they work on it together for 5 days , then the fraction of the work that is left is : | "ans is : c a ' s 1 day ' s work = 1 / 15 b ' s 1 day ' s work = 1 / 20 ( a + b ) ' s 1 day ' s work = ( 1 / 15 + 1 / 20 ) = 7 / 60 ( a + b ) ' s 5 day ' s work = ( 7 / 60 * 5 ) = 7 / 12 therefore , remaining work = ( 1 - 7 / 12 ) = 5 / 12 . answer : c" | a ) 1 / 3 , b ) 7 / 12 , c ) 5 / 12 , d ) 2 / 3 , e ) 1 / 2 | c | subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 5)) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)|subtract(const_1,#3)| | physics |
a monkey ascends a greased pole 6 meters high . he ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute . if this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ? | "the money is climbing 1 meter in 2 min . this pattern will go on till he reaches 4 meters . i mean this will continue for first 4 * 2 = 8 mins . he would have reached 4 meters . after that he will climb 2 meters and he will reach the pole . so total time taken = 8 + 1 = 9 mins . so , asnwer will be a" | a ) 9 th minute , b ) 21 st minute , c ) 11 th minute , d ) 22 nd minute , e ) 13 th minute | a | add(multiply(multiply(const_4, 2), 2), 1) | multiply(n1,const_4)|multiply(n1,#0)|add(n2,#1)| | physics |
what will be the reminder when ( 67 ^ 67 + 67 ) is divided by 68 ? | "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 67 ^ 67 + 1 ) will be divisible by ( 67 + 1 ) ; ( 67 ^ 67 + 1 ) + 66 when divided by 68 will give 66 as remainder . correct option : c" | a ) 1 , b ) 63 , c ) 66 , d ) 67 , e ) none of these | c | subtract(add(power(67, 67), 67), multiply(68, floor(divide(add(power(67, 67), 67), 68)))) | power(n0,n0)|add(n0,#0)|divide(#1,n3)|floor(#2)|multiply(n3,#3)|subtract(#1,#4)| | general |
if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 140 pounds . what is leo ' s current weight ? | "l + k = 140 and so k = 140 - l l + 10 = 1.5 k = 1.5 ( 140 - l ) 2.5 l = 200 l = 80 the answer is a ." | a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120 | a | divide(subtract(multiply(140, divide(add(const_100, 50), const_100)), 10), add(divide(add(const_100, 50), const_100), const_1)) | add(n1,const_100)|divide(#0,const_100)|add(#1,const_1)|multiply(n2,#1)|subtract(#3,n0)|divide(#4,#2)| | gain |
aunt marge is giving candy to each of her nephews and nieces . she has 20 pieces of candy and she gives all the candy to the children according to her wish . if robert gets 2 more pieces than kate , bill gets 6 less than mary , mary gets 2 more pieces than robert , and kate gets 2 more pieces than bill , how many piece... | use the initial letter of each name as a variable : r = k + 2 b = m β 6 m = r + 2 k = 2 + bk = = r β 2 b = k β 2 = ( r β 2 ) β 2 = r β 4 m = r + 2 r + b + m + k = 20 r + r β 4 + r + 2 + r β 2 = 20 r = 6 k = r β 2 = 6 β 2 = 4 answer : b | a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10 | b | subtract(subtract(20, 6), multiply(add(divide(6, 2), 2), 2)) | divide(n2,n1)|subtract(n0,n2)|add(n1,#0)|multiply(n1,#2)|subtract(#1,#3) | general |
in the list 3 , 3 , 4 , 4 , 5 , 5 , 5 , 5 , 7 , 11 , 21 , what fraction of the data is less than the mode ? | mode : the mode of any set is the term which has the highest frequency ( occurrence ) highest frequent term in the set is 5 ( with frequency 4 ) hence mode = 5 two terms ( 3 , 3 , 4 , 4 ) out of a total of 11 terms are less than mode of the set . fraction of set that are less than mode of set = 4 / 11 answer : option c | a ) 2 / 9 , b ) 1 / 3 , c ) 4 / 11 , d ) 2 / 3 , e ) 7 / 9 | c | divide(4, 11) | divide(n2,n9) | general |
how many multiples of 4 are less than 3200 , and also multiples of 16 ? | the lcm of 4 and 16 is 16 . divide 3200 / 16 = 200 . xxx . so b is your answer . | a ) 104 , b ) 200 , c ) 625 , d ) 832 , e ) 833 | b | add(divide(subtract(16, 3200), 4), const_1) | subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)| | general |
a man can row a boat at 10 kmph in still water and the speed of the stream is 8 kmph . what is then time taken to row a distance of 90 km down the stream ? | speed in down stream = 10 + 8 = 18 time taken to cover 90 km down stream = 90 / 18 = 5 hrs . answer : b | a ) 8 hrs , b ) 5 hrs , c ) 15 hrs , d ) 15 hrs , e ) 20 hrs | b | divide(90, add(10, 8)) | add(n0,n1)|divide(n2,#0) | physics |
the sum of two consecutive number is 109 . which is the larger number ? | "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 109 2 x + 1 = 109 2 x = 108 x = 54 therefore larger number is x + 1 = 55 answer : e" | a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 55 | e | add(add(power(add(add(divide(subtract(subtract(109, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(109, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(109, const_10), const_2), const_4), const_2), power(... | 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 |
what is the least number to be added to 1480 to make it a perfect square ? | "the numbers greater than 1480 and are square of number is 1600 . the least number that should be added 1480 to make it perfect square = 1600 - 1480 = 120 . answer : e" | a ) 105 , b ) 160 , c ) 200 , d ) 71 , e ) 120 | e | subtract(multiply(divide(add(add(const_12, const_4), const_2), const_100), divide(add(add(const_12, const_4), const_2), const_100)), 1480) | add(const_12,const_4)|add(#0,const_2)|divide(#1,const_100)|multiply(#2,#2)|subtract(#3,n0)| | general |
a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.00 . if the company β s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ? | "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 7.5 $ then total value is 300 * 7.0 = 2100 . imo option d is correct answer . ." | a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,100 , e ) $ 2,250 | d | divide(multiply(divide(multiply(add(add(multiply(const_3, const_100), multiply(8, 10)), const_4), const_1000), multiply(multiply(8, 10), 12)), 7.00), const_1000) | multiply(const_100,const_3)|multiply(n0,n1)|multiply(n0,n1)|add(#0,#1)|multiply(n2,#2)|add(#3,const_4)|multiply(#5,const_1000)|divide(#6,#4)|multiply(n3,#7)|divide(#8,const_1000)| | general |
in order to obtain an income of rs . 15000 from 80 % stock at rs . 200 , one must make an investment of | "explanation : market value = rs . 200 . required income = rs . 15000 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 80 ( ie , 80 % of the face value 100 ) , investment = rs . 200 to obtain rs . 15000 , investment = 200 / 80 Γ£ β 15000 = rs . 37500 answer :... | a ) rs . 30000 , b ) rs . 37000 , c ) rs . 37500 , d ) rs . 40000 , e ) rs . 40500 | c | multiply(divide(200, 80), 15000) | divide(n2,n1)|multiply(n0,#0)| | gain |
the area of sector of a circle whose radius is 12 metro and whose angle at the center is 40 Β° is ? | "40 / 360 * 22 / 7 * 12 * 12 = 50.2 m 2 answer : c" | a ) 53 m 2 , b ) 51 m 2 , c ) 50.2 m 2 , d ) 45 m 2 , e ) 40 m 2 | c | multiply(multiply(power(12, const_2), divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), divide(40, divide(const_3600, const_10))) | add(const_3,const_4)|divide(const_3600,const_10)|multiply(const_10,const_2)|power(n0,const_2)|add(#2,const_2)|divide(n1,#1)|divide(#4,#0)|multiply(#6,#3)|multiply(#5,#7)| | geometry |
the average runs scored by a batsman in 22 matches is 28 . in the next 13 matches the batsman scored an average of 15 runs . find his average in all the 35 matches ? | total score of the batsman in 22 matches = 616 . total score of the batsman in the next 13 matches = 195 . total score of the batsman in the 35 matches = 811 . average score of the batsman = 811 / 35 = 23.17 . answer : d | a ) 31.23 , b ) 25.12 , c ) 36.25 , d ) 23.17 , e ) 27.66 | d | divide(add(multiply(28, 22), multiply(15, 13)), add(22, 13)) | add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)| | general |
the sum of the numbers is 330 . if the first number be twice the second and third number be one - third of the first , then the second number is : | "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 330 11 x / 3 = 330 x = 90 answer : e" | a ) 48 , b ) 54 , c ) 72 , d ) 84 , e ) 90 | e | divide(multiply(330, const_3), add(const_10, const_1)) | add(const_1,const_10)|multiply(n0,const_3)|divide(#1,#0)| | general |
a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 150 kg . what is the maximum weight of the crates on a single trip ? | "max no . of crates = 5 . max weight = 150 kg max . weight carried = 5 * 150 = 750 kg = d" | a ) 1250 , b ) 625 , c ) 600 , d ) 750 , e ) 375 | d | multiply(5, 150) | multiply(n2,n3)| | general |
the weight of a glass of jar is 20 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ? | "let weight of jar filled with beans = 100 g weight of jar = 20 g weight of coffee beans = 80 g weight of jar and remaining beans = 60 g weight of remaining beans = 40 g fraction remaining = 40 / 80 = 1 / 2 answer is d ." | a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 2 / 3 | d | divide(subtract(60, 20), subtract(const_100, 20)) | subtract(n1,n0)|subtract(const_100,n0)|divide(#0,#1)| | gain |
the diagonals of a rhombus are 16 cm and 20 cm . find its area ? | "1 / 2 * 16 * 20 = 160 answer : a" | a ) 160 , b ) 288 , c ) 150 , d ) 238 , e ) 31 | a | rhombus_area(16, 20) | rhombus_area(n0,n1)| | geometry |
the points a ( 0 , 0 ) , b ( 0 , 4 a - 5 ) and c ( 2 a + 1 , 2 a + 4 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ? | "1 / 2 bh = 1 / 2 ( 2 a + 1 ) ( 2 a + 4 ) now 4 a - 5 = 2 a + 4 2 a = 9 therefore , a ( 0,0 ) ; b ( 0,13 ) ; c ( 10,13 ) 1 / 2 * 10 * 13 = 65 answer : e" | a ) 80 , b ) 75 , c ) 70 , d ) 60 , e ) 65 | e | divide(multiply(subtract(multiply(divide(add(4, 5), 5), 4), 5), add(multiply(divide(add(4, 5), 5), subtract(4, 5)), 1)), 5) | add(n4,n8)|subtract(n3,n4)|divide(#0,n4)|multiply(#2,#1)|multiply(n3,#2)|add(#3,n6)|subtract(#4,n4)|multiply(#5,#6)|divide(#7,n4)| | geometry |
carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 6 inches tall . how tall are the sculpture andbase together ? | "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 6 = 40 40 / 12 = 3.3 feet answer : c" | a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.5 feet | c | divide(add(add(multiply(add(2, 10), 2), 10), 6), add(2, 10)) | add(n0,n1)|multiply(n0,#0)|add(#1,n1)|add(n2,#2)|divide(#3,#0)| | geometry |
xy = 2 then what is ( 2 ^ ( x + y ) ^ 2 ) / ( 2 ^ ( x - y ) ^ 2 ) | ( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 8 2 ^ 8 = 256 answer e | a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 256 | e | power(2, multiply(const_4, 2)) | multiply(n0,const_4)|power(n0,#0) | general |
in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 5.5 ) , ( 8 , 0 ) , ( 0 , - 5.5 ) , ( - 8 , 0 ) ? | ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 5.5 + 5.5 = 11 area = 1 / 2 * 16 * 11 = 88 b is the answer | ['a ) 56', 'b ) 88', 'c ) 112', 'd ) 116', 'e ) 120'] | b | rhombus_area(multiply(8, const_2), multiply(5.5, const_2)) | multiply(n2,const_2)|multiply(n1,const_2)|rhombus_area(#0,#1) | geometry |
a sum of money becomes 7 / 6 of itself in 5 years at a certain rate of simple interest . the rate per annum is ? | "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 5 years . rate = ( 100 * x ) / ( x * 6 * 5 ) = 10 / 3 % . answer : d" | a ) 20 / 7 , b ) 20 / 3 , c ) 23 / 6 , d ) 10 / 3 , e ) 10 / 7 | d | multiply(divide(subtract(divide(7, 6), const_1), 5), const_100) | divide(n0,n1)|subtract(#0,const_1)|divide(#1,n2)|multiply(#2,const_100)| | gain |
a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , then how old is b ? | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 5 x = 20 = > x = 4 hence , b ' s age = 2 x = 8 years . answer : d" | a ) 17 years , b ) 19 years , c ) 29 years , d ) 8 years , e ) 12 years | d | divide(multiply(subtract(22, const_2), const_2), add(const_4, const_1)) | add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)| | general |
all the students of class are told to sit in circle shape . here the boy at the 6 th position is exactly opposite to 16 th boy . total number of boys in the class ? | as half the circle shape consist of 16 - 6 = 10 boys , so total number of boys in full circle = 2 * 10 = 20 answer : c | a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30 | c | multiply(subtract(16, 6), const_2) | subtract(n1,n0)|multiply(#0,const_2) | general |
the area of a square is 4624 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square . | "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4624 a 68 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 44 : 136 = 11 : 34 answer : e" | a ) 5 : 28 , b ) 5 : 19 , c ) 5 : 12 , d ) 5 : 13 , e ) 11 : 34 | e | divide(subtract(sqrt(4624), 24), multiply(sqrt(4624), const_2)) | sqrt(n0)|multiply(#0,const_2)|subtract(#0,n1)|divide(#2,#1)| | geometry |
in what time will a train 100 meters long cross an electric pole , if its speed is 162 km / hr | "first convert speed into m / sec speed = 162 * ( 5 / 18 ) = 45 m / sec time = distance / speed = 100 / 45 = 2.22 seconds answer : b" | a ) 8.5 seconds , b ) 2.22 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds | b | divide(100, multiply(162, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics |
a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint t , in gallons , that must be purchased in order to measure... | "given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , l... | a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4 | b | add(multiply(const_0_25, 2), multiply(2, 5)) | multiply(const_0_25,n2)|multiply(n1,n2)|add(#0,#1)| | general |
find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 2120 ? | "2120 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1892.85 answer : c" | a ) rs . 1000.15 , b ) rs . 1100.95 , c ) rs . 1892.85 , d ) rs . 1050.85 , e ) rs . 1200.25 | c | divide(2120, add(divide(multiply(divide(add(multiply(2, 5), 2), 5), 5), const_100), const_1)) | multiply(n1,n3)|add(n1,#0)|divide(#1,n3)|multiply(n0,#2)|divide(#3,const_100)|add(#4,const_1)|divide(n4,#5)| | general |
the average age of an adult class is 40 years . 8 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ? | "let original strength = y then , 40 y + 8 x 32 = ( y + 8 ) x 36 Γ’ β‘ β 40 y + 256 = 36 y + 288 Γ’ β‘ β 4 y = 32 Γ’ Λ Β΄ y = 8 a" | a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18 | a | divide(subtract(multiply(8, subtract(40, 4)), multiply(8, 32)), 4) | multiply(n1,n2)|subtract(n0,n3)|multiply(n1,#1)|subtract(#2,#0)|divide(#3,n3)| | general |
what is the ratio of two no . 5 xy and 8 xy . | "5 xy / 8 xy = 5 : 8 answer c" | a ) 2 : 5 , b ) 3 : 4 , c ) 5 : 8 , d ) 2 : 3 , e ) 1 : 2 | c | divide(5, const_60) | divide(n0,const_60)| | other |
how many positive integers less than 17 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ? | "the number = 2 a + 3 b < 17 when a = 1 , b = 1 , 2 , 3 , 4 , 5 - > 2 a = 2 ; 3 b = 3 , 6 , 9 , 12 , 15 - > the number = 5 , 8 , 11 , 14 - - > 4 numbers when a = 2 , b = 1,2 , 3,4 - > . . . . - - > 4 numbers when a = 3 , b = 1 , 2,3 - - > . . . . - - > 3 numbers total number is already 11 . look at the answer there is ... | a ) 14 , b ) 13 , c ) 12 , d ) 11 , e ) 10 | d | subtract(subtract(subtract(17, 2), const_4), const_1) | subtract(n0,n1)|subtract(#0,const_4)|subtract(#1,const_1)| | general |
what least number should be added to 1056 , so that the sum is completely divisible by 23 ? | "that is 1056 / 23 = 45 remainder = 21 = > 21 + 2 = 23 hence 2 should be added to 1056 so that the sum will be divisible by 23 answer is option b" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | subtract(23, reminder(1056, 23)) | reminder(n0,n1)|subtract(n1,#0)| | general |
at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses t at the restaurant ? ( assume that all boxes are fille... | "most test takers would recognize the system of equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong ... | a ) 96 , b ) 240 , c ) t = 256 , d ) t = 384 , e ) t = 480 | e | multiply(multiply(16, const_2), 15) | multiply(n1,const_2)|multiply(n2,#0)| | general |
a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 200 before any discount ... | "since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 20 % off of the discounted price . . . . we '... | a ) $ 112.00 , b ) $ 145.60 , c ) $ 163.80 , d ) $ 182.00 , e ) $ 100.00 | a | multiply(200, divide(add(30, 20), const_100)) | add(n1,n2)|divide(#0,const_100)|multiply(n3,#1)| | gain |
a train 550 m long is running with a speed of 60 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 = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 550 * 3 / 55 = 30 sec . answer : option e" | a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 30 | e | divide(550, multiply(add(60, 6), const_0_2778)) | add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 186 cms . what was the ratio of men to women ? | "we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 186 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 186 m ) / ( w + m ) = 180 170 w + 186 m = 180 w + 1... | a ) 5 : 2 , b ) 5 : 1 , c ) 5 : 3 , d ) 4 : 1 , e ) 3 : 1 | c | divide(subtract(180, 170), subtract(186, 180)) | subtract(n0,n1)|subtract(n2,n0)|divide(#0,#1)| | general |
a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 50 minutes . the total distance is ? | "c 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 50 / 60 47 x / 60 = 50 / 60 = > x = 1.06 . total distance = 3 * 1.06 = 3.19 km ." | a ) 1 km , b ) 2 km , c ) 3.19 km , d ) 4 km , e ) 5 km | c | multiply(multiply(divide(divide(50, const_60), add(add(divide(const_1, 3), divide(const_1, 4)), divide(const_1, 5))), const_3), const_1000) | divide(n3,const_60)|divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#1,#2)|add(#4,#3)|divide(#0,#5)|multiply(#6,const_3)|multiply(#7,const_1000)| | physics |
how many digits are used to number a book containg 300 pages . | explanation : number of digits in 1 digit numbers = 1 to 9 = 9 number of digits in 2 digit numbers = 10 to 99 = 90 ( 2 ) = 180 number of digits in 3 digit numbers = 100 to 300 = 201 ( 3 ) = 603 total = 792 answer : option b | a ) 694 , b ) 792 , c ) 698 , d ) 784 , e ) 789 | b | add(add(multiply(300, const_2), const_100), subtract(subtract(const_100, const_4), const_4)) | multiply(n0,const_2)|subtract(const_100,const_4)|add(#0,const_100)|subtract(#1,const_4)|add(#2,#3) | general |
barbata invests $ 2800 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ? | "let the additional invested amount for 8 % interest be x ; equation will be ; 2800 + 0.05 * 2800 + x + 0.08 x = 2800 + x + 0.06 ( 2800 + x ) 0.05 * 2800 + 0.08 x = 0.06 x + 0.06 * 2800 0.02 x = 2800 ( 0.06 - 0.05 ) x = 2800 * 0.01 / 0.02 = 1400 ans : ` ` d ' '" | a ) 1200 , b ) 3000 , c ) 1000 , d ) 1400 , e ) 2400 | d | divide(subtract(multiply(divide(6, const_100), 2800), multiply(2800, divide(5, const_100))), subtract(divide(8, const_100), divide(6, const_100))) | divide(n3,const_100)|divide(n1,const_100)|divide(n2,const_100)|multiply(n0,#0)|multiply(n0,#1)|subtract(#2,#0)|subtract(#3,#4)|divide(#6,#5)| | general |
at what rate percent on simple interest will rs . 600 amount to rs . 950 in 5 years ? | "350 = ( 600 * 5 * r ) / 100 r = 11.67 % answer : e" | a ) 3.33 % , b ) 5.93 % , c ) 4.33 % , d ) 9.33 % , e ) 11.67 % | e | multiply(divide(divide(subtract(950, 600), 600), 5), const_100) | subtract(n1,n0)|divide(#0,n0)|divide(#1,n2)|multiply(#2,const_100)| | gain |
a , b and c can do a work in 90 , 45 and 6 days respectively . if they work together , in how many days will they complete the work ? | one days ' s work of a , b and c = 1 / 90 + 1 / 45 + 1 / 6 = ( 1 + 2 + 15 ) / 90 = 1 / 5 a , b and c together can do the work in 5 days . answer : a | a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 11 | a | inverse(add(divide(const_1, 6), add(divide(const_1, 90), divide(const_1, 45)))) | divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|add(#3,#2)|inverse(#4) | physics |
a man can row upstream at 25 kmph and downstream at 41 kmph , and then find the speed of the man in still water ? | "us = 25 ds = 41 m = ( 41 + 25 ) / 2 = 33 answer : a" | a ) 33 , b ) 67 , c ) 30 , d ) 15 , e ) 17 | a | divide(add(25, 41), const_2) | add(n0,n1)|divide(#0,const_2)| | physics |
i bought two books ; for rs . 450 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ? | "x * ( 85 / 100 ) = ( 450 - x ) 119 / 100 x = 262.5 answer : b" | a ) 337 , b ) 262.5 , c ) 299.5 , d ) 266.5 , e ) 299 | b | divide(multiply(450, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19))) | add(n2,const_100)|subtract(const_100,n1)|add(#0,#1)|multiply(n0,#0)|divide(#3,#2)| | gain |
how many multiples of 5 are there between 1 and 100 ( both are inclusive ) ? | "the answer is ( 100 - 1 ) / 5 + 1 = 20.8 answer is b" | a ) 1.2 , b ) 20.8 , c ) 2.3 , d ) 6.7 , e ) 8.2 | b | add(divide(subtract(100, 1), 5), const_1) | subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)| | other |
when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 2 / 5 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ? | "say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 2 / 5 ) ( 4 + 4 x ) or , x = 4 answer d" | a ) 3 / 10 , b ) 2 / 5 , c ) 1 / 2 , d ) 4 , e ) 6 / 5 | d | divide(4, subtract(multiply(subtract(6, 4), 5), 4)) | subtract(n1,n0)|multiply(n4,#0)|subtract(#1,n0)|divide(n0,#2)| | general |
in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 30 percent , but profits were 14 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ? | 0,098 r = x / 100 * 0.1 r answer e | a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 98 % | e | multiply(divide(multiply(subtract(const_1, divide(30, const_100)), divide(14, const_100)), divide(10, const_100)), const_100) | divide(n4,const_100)|divide(n3,const_100)|divide(n1,const_100)|subtract(const_1,#1)|multiply(#0,#3)|divide(#4,#2)|multiply(#5,const_100) | gain |
the speed of a train is 110 kmph . what is the distance covered by it in 11 minutes ? | "110 * 11 / 60 = 20 kmph answer : d" | a ) 15 kmph , b ) 11 kmph , c ) 88 kmph , d ) 20 kmph , e ) 12 kmph | d | multiply(divide(11, const_60), 110) | divide(n1,const_60)|multiply(n0,#0)| | physics |
a sum of money at simple interest amounts to rs . 2240 in 2 years and to rs . 2600 in 5 years . the sum is : | "s . i . for 3 years = rs . ( 2600 - 2240 ) = rs . 360 . s . i . for 1 year = rs . 360 / 3 = rs . 120 . s . i . for 2 years = rs . ( 120 x 2 ) = rs . 240 . principal = rs . ( 2240 - 240 ) = rs . 2000 . answer : option b" | a ) rs . 1500 , b ) rs . 2000 , c ) rs . 1000 , d ) rs . 1200 , e ) rs . 1800 | b | subtract(2240, divide(multiply(subtract(2600, 2240), 2), 5)) | subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)| | gain |
mother , her daughter and her grand child weighs 120 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ? | "mother + daughter + child = 120 kg daughter + child = 60 kg mother = 120 - 60 = 60 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 60 = 12 kg so now daughter = 120 - ( mother + child ) = 120 - ( 60 + 12 ) = 48 kg answer : c" | a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50 | c | subtract(60, divide(subtract(120, 60), 5)) | subtract(n0,n1)|divide(#0,n3)|subtract(n1,#1)| | general |
a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 8 managers , if 2 managers will not attend the meeting together . | "8 managers , but two of them can not attend the meeting together . we can split it into two cases . 1 . meeting without these two managers in it . that would mean selecting 5 , from the remaining 6 which is 6 c 5 = 6 2 . meeting with one of the two managers . select 1 manager from two , and then select 4 from the rema... | a ) 1.35 , b ) 2.91 , c ) 3.12 , d ) 4.36 , e ) 5.15 | d | subtract(choose(8, 5), choose(subtract(8, 2), 2)) | choose(n1,n0)|subtract(n1,n2)|choose(#1,n2)|subtract(#0,#2)| | probability |
150 is what percent of 60 ? | "60 * x = 150 - - > x = 2.5 - - > 2.5 expressed as percent is 250 % . answer : a ." | a ) 250 % , b ) 20 % , c ) 50 % , d ) 200 % , e ) 500 % | a | multiply(divide(150, 60), const_100) | divide(n0,n1)|multiply(#0,const_100)| | gain |
if each edge of cube increased by 25 % , the percentage increase in | "100 Γ ( 125 ) / 100 Γ ( 125 ) / 100 = 156.25 = > 56.25 % answer is e ." | a ) 55 , b ) 52.25 , c ) 59.75 , d ) 51.75 , e ) 56.25 | e | multiply(const_100, divide(subtract(power(add(const_100, 25), const_3), power(const_100, const_3)), power(const_100, const_3))) | add(n0,const_100)|power(const_100,const_3)|power(#0,const_3)|subtract(#2,#1)|divide(#3,#1)|multiply(#4,const_100)| | gain |
in a class of students , 1 / 2 of the number of girls is equal to 1 / 5 of the total number of students . what is the ratio of boys to girls in the class ? | "( 1 / 2 ) g = ( 1 / 5 ) ( b + g ) 5 g = 2 b + 2 g 3 g = 2 b b / g = 3 / 2 . the answer is b ." | a ) 1 / 2 , b ) 3 / 2 , c ) 1 / 3 , d ) 2 / 3 , e ) 4 / 3 | b | divide(subtract(divide(1, 2), divide(1, 5)), divide(1, 5)) | divide(n0,n1)|divide(n2,n3)|subtract(#0,#1)|divide(#2,#1)| | general |
how many 3 - digit positive integers are there , where each digit is positive , and no 3 adjacent digits are same ? | "first digit . . 9 posibilities second digit , 8 possibilities third digit , 7 possibilities 9 * 8 * 7 = 504 . b" | a ) 1236 , b ) 504 , c ) 4096 , d ) 4608 , e ) 6561 | b | multiply(multiply(add(3, 3), add(3, 3)), multiply(add(3, 3), multiply(3, 3))) | add(n1,n0)|add(n0,n0)|multiply(n1,n1)|multiply(#0,#0)|multiply(#1,#2)|multiply(#3,#4)| | general |
if n = ( 33 ) ^ 43 + ( 23 ) ^ 33 what is the units digit of n ? | "first of all , the units digit of ( 33 ) ^ 23 is the same as that of 3 ^ 23 and the units digit of ( 23 ) ^ 33 is the same as that of 3 ^ 33 . so , we need to find the units digit of 3 ^ 23 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the un... | a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8 | d | subtract(reminder(add(power(reminder(33, const_10), reminder(43, const_4)), power(reminder(43, const_10), const_4)), const_100), multiply(const_2, const_3)) | multiply(const_2,const_3)|reminder(n0,const_10)|reminder(n1,const_4)|reminder(n1,const_10)|power(#1,#2)|power(#3,const_4)|add(#4,#5)|reminder(#6,const_100)|subtract(#7,#0)| | general |
for a positive integer n , if 5 ^ n is a factor of 20 ! , but 5 ^ n + 1 is not a factor of 20 ! , what is the value of n ? | 20 ! has four 5 ' s 20 / 5 = 4 thus 5 ^ 4 can completely divide 20 ! and 5 ^ 5 can not divide 20 ! so , answer will be ( a ) 4 | a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9 | a | subtract(subtract(multiply(5, 5), 20), 1) | multiply(n0,n0)|subtract(#0,n1)|subtract(#1,n3) | other |
a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 570 pounds after processing , how many pounds did it weigh before processing ? | "let weight of side of beef before processing = x ( 65 / 100 ) * x = 570 = > x = ( 570 * 100 ) / 65 = 876 answer d" | a ) 191 , b ) 355 , c ) 737 , d ) 876 , e ) 1,560 | d | divide(multiply(570, const_100), subtract(const_100, 35)) | multiply(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)| | gain |
the volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate r , in cubic meters per minutes , at which the water is flowing into the swimming pool ? | "the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and ... | a ) 0.125 , b ) 0.25 , c ) 0.5 , d ) 0.75 , e ) not enough information to determine the rate | e | divide(840, 0.5) | divide(n0,n1)| | geometry |
in what time will a railway train 96 m long moving at the rate of 45 kmph pass a telegraph post on its way ? | "t = 96 / 45 * 18 / 5 = 8 sec answer : b" | a ) 3 sec , b ) 8 sec , c ) 5 sec , d ) 6 sec , e ) 7 sec | b | divide(96, multiply(45, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics |
what is x if x + 2 y = 10 and y = 3 ? | "substitute y by 3 in x + 2 y = 10 x + 2 ( 3 ) = 10 x + 6 = 10 if we substitute x by 4 in x + 6 = 10 , we have 4 + 6 = 10 . hence x = 4 correct answer d" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | d | subtract(10, multiply(2, 3)) | multiply(n0,n2)|subtract(n1,#0)| | general |
if 10 a = 6 b = 20 , then 120 ab = | "10 a * 6 b = 20 * 20 = 400 60 ab = 400 i . e . 120 ab = 800 answer : option a" | a ) 800 , b ) 1000 , c ) 1200 , d ) 1400 , e ) 1600 | a | multiply(120, multiply(divide(20, 10), divide(20, 6))) | divide(n2,n0)|divide(n2,n1)|multiply(#0,#1)|multiply(n3,#2)| | general |
which number need to add to 7844213 to get a number exactly divisible by 549 ? | "7844213 / 549 = 14288 and reminder = 101 . 549 - 101 = 448 so , the next number divisible by 549 is 448 places in front of 7844213 which means 448 + 7844213 = 7844661 448 should be added to 7844213 c" | a ) 418 , b ) 148 , c ) 448 , d ) 248 , e ) 348 | c | multiply(549, subtract(add(floor(divide(7844213, 549)), const_1), divide(7844213, 549))) | divide(n0,n1)|floor(#0)|add(#1,const_1)|subtract(#2,#0)|multiply(n1,#3)| | general |
a scale 7 ft . 12 inches long is divided into 4 equal parts . find the length of each part . | "explanation : total length of scale in inches = ( 7 * 12 ) + 12 = 96 inches length of each of the 4 parts = 96 / 4 = 24 inches answer : c" | a ) 20 inches , b ) 77 inches , c ) 24 inches , d ) 97 inches , e ) 66 inches | c | divide(add(multiply(7, const_12), 12), 4) | multiply(n0,const_12)|add(n1,#0)|divide(#1,n2)| | general |
the population of a town increases 10 % and 20 % respectively in two consecutive years . after the growth the present population of the town is 1320 . then what is the population of the town 2 years ago ? | "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1320 * 100 / 110 * 100 / 120 = 1000 answer : option d" | a ) 1100 , b ) 1001 , c ) 1010 , d ) 1000 , e ) 1002 | d | divide(1320, multiply(add(const_1, divide(10, const_100)), add(const_1, divide(20, const_100)))) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(#2,#3)|divide(n2,#4)| | gain |
there were two candidates in an election . winner candidate received 62 % of votes and won the election by 408 votes . find the number of votes casted to the winning candidate ? | "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 408 62 % - - - - - - - - ? = > 1054 answer : b" | a ) 288 , b ) 1054 , c ) 788 , d ) 298 , e ) 177 | b | divide(multiply(divide(408, divide(subtract(62, subtract(const_100, 62)), const_100)), 62), const_100) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)| | gain |
balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 1104 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the ... | "as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 110... | a ) 2145 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560 | a | multiply(subtract(1104, multiply(const_4, const_100)), add(multiply(subtract(1104, multiply(const_4, const_100)), 2), const_1)) | multiply(const_100,const_4)|subtract(n1,#0)|multiply(n0,#1)|add(#2,const_1)|multiply(#3,#1)| | general |
20 beavers , working together in a constant pace , can build a dam in 3 hours . how many v hours will it take 12 beavers that work at the same pace , to build the same dam ? | "c . 5 hrs if there were 10 beavers it qould have taken double v = 6 hrs . . so closest to that option is 5 ." | a ) 2 . , b ) v = 4 . , c ) v = 5 . , d ) v = 6 . , e ) 8 . | c | divide(multiply(3, 20), 12) | multiply(n0,n1)|divide(#0,n2)| | physics |
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