Problem stringlengths 5 628 | Rationale stringlengths 1 2.74k | options stringlengths 39 113 | correct stringclasses 5
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you collect baseball cards . suppose you start out with 17 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the en... | "solution start with 17 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 17 + 1 which is 9 , so you ' re left with 17 - 9 = 8 . peter takes 1 baseball card from you : 8 - 1 = 7 baseball cards . paul triples the number of baseball cards you have : 7 ã — 3 ... | a ) 32 % , b ) 1 / 25 , c ) 77 , d ) 21 , e ) 12', ' | d | multiply(subtract(subtract(subtract(17, const_4), const_4), 1), const_3) | subtract(n0,const_4)|subtract(#0,const_4)|subtract(#1,n1)|multiply(#2,const_3)| | general |
a bakery has 6 employees . it pays annual salaries of $ 19000 to each of 2 employees , $ 21000 to 1 employee , and $ 22000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ? | average = 2 ( 19000 ) + ( 21000 ) + 3 ( 22000 ) / 6 = $ 20,833 the answer is c . | a ) $ 336 , b ) 5 / 4 , c ) 9 : 2 , d ) $ 20,800 , e ) 21 - 61 | d | divide(divide(add(multiply(22000, 3), add(multiply(19000, 2), 21000)), const_1000), 6) | multiply(n1,n2)|multiply(n5,n6)|add(n3,#0)|add(#2,#1)|divide(#3,const_1000)|divide(#4,n0) | general |
if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 15.00 / day for each additional week , how much does it cost to stay for 23 days ? | "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 15 = 16 * 15 = 240 $ total charge = 126 + 240 = 366 $ answer a" | a ) 1 , b ) 22 , c ) 108 kmph , d ) $ 336 , e ) 1 : 4', ' | d | add(multiply(18.00, add(const_3, const_4)), multiply(15.00, subtract(23, add(const_3, const_4)))) | add(const_3,const_4)|multiply(n0,#0)|subtract(n2,#0)|multiply(n1,#2)|add(#1,#3)| | general |
one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field . | "other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . ans : a" | a ) 120 , b ) 42 , c ) 1 / 5 , d ) 9 : 5 , e ) 3 | a | rectangle_area(15, sqrt(subtract(power(17, const_2), power(15, const_2)))) | power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)|sqrt(#2)|rectangle_area(n0,#3)| | geometry |
a rainstorm increased the amount of water stored in state j reservoirs from 50 billion gallons to 75 billion gallons . if the storm increased the amount of water in the reservoirs to 37.5 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the... | after the reservoir is filled to 75 gallons the amount of water is at 37.5 % - which means that 62.5 % of the reservoir is empty . to figure out what that 62.5 % is approximate : 75 gallons / 37.5 percent = x gallons / 62.5 percent , therefore , x = 125 gallons , answer choices a , b , c , d are below 125 . we know tha... | a ) 192 , b ) 6400 , c ) 127 , d ) 4 / 5 , e ) 0.1 | c | divide(divide(multiply(75, const_100), 37.5), const_2) | multiply(n1,const_100)|divide(#0,n2)|divide(#1,const_2)| | general |
a certain quantity is measured on two different scales , the t - scale and the s - scale , that are related linearly . measurements on the t - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the t - scale corresponds to a measurement of 100 on the s - scal... | first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ... | a ) 20 % loss , b ) 48 , c ) 12.5', ' , d ) 2 / 7 , e ) 8 | b | add(multiply(subtract(24, 6), divide(subtract(100, 60), subtract(60, 30))), 24) | subtract(n4,n3)|subtract(n3,n2)|subtract(n1,n0)|divide(#0,#1)|multiply(#3,#2)|add(n1,#4) | general |
the sum of two numbers is 184 . if one - third of the one exceeds one - seventh of the other by 8 , find the smaller number . | let the numbers be x and ( 184 - x ) . then , ( x / 3 ) - ( 184 - x ) / 7 = 8 7 x - 3 ( 184 - x ) = 168 10 x = 720 , x = 72 . hence the correct answer is option a ) 72 . | a ) 2 , b ) 2 sqrt ( 6 , c ) 18 m , d ) 3.6 km , e ) 72 | e | divide(add(multiply(184, const_3), multiply(multiply(add(const_3, const_4), const_3), 8)), add(add(const_3, const_4), const_3)) | add(const_3,const_4)|multiply(n0,const_3)|add(#0,const_3)|multiply(#0,const_3)|multiply(n1,#3)|add(#1,#4)|divide(#5,#2) | general |
the sum of the first 50 positive even integers is 2550 . what is the sum q of even integers from 102 to 200 inclusive ? | "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : q = 2550 + ( 100 * 50 ) = 7550 . b" | a ) 480 cm 2 , b ) 7550 , c ) 7 % , d ) 40 miles . , e ) 11.25 ° | b | multiply(divide(add(200, 102), const_2), add(divide(subtract(200, 102), const_2), const_1)) | add(n2,n3)|subtract(n3,n2)|divide(#1,const_2)|divide(#0,const_2)|add(#2,const_1)|multiply(#4,#3)| | general |
how many litres of pure acid are there in 15 litres of a 20 % solution | explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 15 * 20 / 100 = 3 answer : option d | a ) 4 , b ) 48 , c ) 2 , d ) 3 , e ) 55 | d | multiply(divide(20, const_100), 15) | divide(n1,const_100)|multiply(n0,#0)| | gain |
rs . 385 were divided among x , y , z in such a way that x had rs . 20 more than y and z had rs 15 more than x . how much was y ’ s share ? | let y gets rs x . then we can say x gets rs ( x + 20 ) and y gets rs ( x + 35 ) . x + 20 + x + x + 35 = 385 3 x = 330 x = 110 . r ’ s share = rs ( 110 + 35 ) = rs . 145 b | a ) 312 , b ) rs . 145 , c ) s . 7000 , d ) 35 km , e ) 25 % | b | add(15, add(divide(subtract(385, add(15, add(20, 20))), const_3), 20)) | add(n1,n1)|add(n2,#0)|subtract(n0,#1)|divide(#2,const_3)|add(n1,#3)|add(n2,#4) | general |
when n divided by 3 , the remainder is 2 . when n divided by 4 , the remainder is 1 what is the the remainder when divided by 16 | case 1 n = 5,8 , 11,14 , 17,20 case 2 m = 5 , 9,13 , 17,21 therefore n = 17 remainder of 17 / 16 will be 1 a | a ) 1 , b ) 9 , c ) $ 9640 , d ) 0.0375 days , e ) 23 / 29 | a | floor(divide(add(add(const_12, const_3), add(const_2, const_4)), 16)) | add(const_12,const_3)|add(const_2,const_4)|add(#0,#1)|divide(#2,n4)|floor(#3) | general |
a group of men decided to do a work in 20 days , but 8 of them became absent . if the rest of the group did the work in 28 days , find the original number of men ? | "original number of men = 8 * 28 / ( 28 - 20 ) = 28 answer is b" | a ) $ 22,200 , b ) 18 , c ) 4 , d ) 11190 , e ) 28 | e | divide(multiply(8, 28), subtract(28, 20)) | multiply(n1,n2)|subtract(n2,n0)|divide(#0,#1)| | physics |
three walls have wallpaper covering a combined area of 280 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 36 square meters . what is the area that is covered with three layers of wallpaper ? | "280 - 180 = 100 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 100 - 36 = 64 sq m of the wallpaper overlaps in three layers . 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m . answer ( b ) ." | a ) 20 , b ) 20 sec , c ) 32 square meters , d ) 100 coins , e ) $ 5 | c | divide(subtract(subtract(280, 180), 36), const_2) | subtract(n0,n1)|subtract(#0,n2)|divide(#1,const_2)| | geometry |
mr . x , a mathematician , defines a number as ' connected with 6 if it is divisible by 6 or if the sum of its digits is 6 , or if 6 is one of the digits of the number . other numbers are all ' not connected with 6 ' . as per this definition , the number of integers from 1 to 60 ( both inclusive ) which are not connect... | explanation : numbers from 1 to 60 , which are divisible by 6 are : 6 , 1218 , 24 , 30 , 3642 , 48 , 54 , 60 . there are 10 such numbers . numbers from 1 to 60 , the sum of whose digits is 6 are : 6 , 15 , 24 , 33 , 42 , 51 , 60 . there are 7 such numbers of which 4 are common to the above ones . so , there are 3 such ... | a ) 240 , b ) 43 square meters , c ) s . 180 , d ) 280 , e ) 43 | e | subtract(60, add(add(const_10, const_3), const_4)) | add(const_10,const_3)|add(#0,const_4)|subtract(n6,#1) | general |
a camera lens filter kit containing 5 filters sells for $ 67.50 . if the filters are purchased individually , 2 of them are priced at $ 7.45 each , 2 at $ 10.05 each , 1 at $ 14.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ? | "cost of kit = $ 67.50 if filters are purchased individually - $ 7.45 * 2 + $ 10.05 * 2 + $ 14.50 = $ 49.50 amount saved = $ 67.50 - $ 49.50 = $ 18 required % age = ( $ 18 / $ 67.50 ) * 100 = 26.66 % so , the correct answer is b ." | a ) 30 % , b ) 14 , c ) 40 , d ) 54 : 53 , e ) 26.66 % | e | divide(multiply(subtract(67.50, add(14.50, add(multiply(2, 7.45), multiply(2, 10.05)))), const_100), 67.50) | multiply(n2,n3)|multiply(n2,n5)|add(#0,#1)|add(n7,#2)|subtract(n1,#3)|multiply(#4,const_100)|divide(#5,n1)| | general |
the largest 4 digit number exactly divisible by 90 is ? | "largest 4 - digit number = 9999 90 ) 9999 ( 111 9990 - - - - - - - - - - - - largest number divisible by 90 is 9990 answer : e" | a ) 29187 by 1017926 , b ) 158 , c ) 63 , d ) 30 , e ) 9990 | e | square_area(const_pi) | square_area(const_pi)| | general |
if n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2 ^ k is a factor of n ? . | 20 ! = 1 * 2 * 3 * 4 * 5 . . . * 19 * 20 ( this is 20 factorial written as 20 ! ) n = 1 * 2 * 3 * 4 * 5 * 6 * 7 . . . . . * 19 * 20 how many 2 s are there in n ? one 2 from 2 two 2 s from 4 one two from 6 three 2 s from 8 and so on . . . when you count them all , you get 18 . answer : d | a ) 72 , b ) 6.9 , c ) one , d ) 18 , e ) 9 : 5 | d | add(add(add(divide(20, 2), divide(20, power(2, const_2))), floor(divide(20, power(power(2, const_2), 2)))), floor(divide(20, power(2, const_3)))) | divide(n1,n2)|power(n2,const_2)|power(n2,const_3)|divide(n1,#1)|divide(n1,#2)|power(#1,n2)|add(#0,#3)|divide(n1,#5)|floor(#4)|floor(#7)|add(#6,#9)|add(#10,#8) | general |
a man performs 1 / 2 of the total journey by rail , 1 / 4 by bus and the remaining 4 km on foot . his total journey is | "explanation : let the journey be x km then , 1 x / 2 + 1 x / 4 + 4 = x 3 x + 16 = 4 x x = 16 km answer : option b" | a ) 180 , b ) 16 km , c ) 7 , d ) 34 % , e ) 72 | b | multiply(4, 4) | multiply(n3,n4)| | general |
what is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? | "explanation : since every third number starting from 10 will be divisible by 3 , so total number of numbers divisible by 3 are 90 / 3 = 30 numbers which are divisible by 3 and 5 both are numbers which are multiple of 15 . for the range 10 to 99 , 15 is the first number divisible by 15 and 90 is the last number . so to... | a ) 25 π , b ) 9 , c ) 42 , d ) 8000 , e ) 4 / 15 | e | divide(subtract(multiply(multiply(5, const_2), 3), multiply(3, const_2)), multiply(multiply(5, const_2), multiply(3, 3))) | multiply(n1,const_2)|multiply(n0,const_2)|multiply(n0,n0)|multiply(n0,#0)|multiply(#0,#2)|subtract(#3,#1)|divide(#5,#4)| | probability |
bhanu spends 30 % of his income on petrol on scooter 21 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ? | "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 21 % ( 700 ) = rs . 147 answer : e" | a ) 27 / 20 , b ) 44 seconds , c ) 4 , d ) 147 , e ) 52 | d | multiply(subtract(divide(300, divide(30, const_100)), 300), divide(21, const_100)) | divide(n1,const_100)|divide(n0,const_100)|divide(n2,#1)|subtract(#2,n2)|multiply(#0,#3)| | gain |
45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 35 meters deep by working for 6 hours ? | "45 workers * 8 hours / 30 meters = x * 6 / 35 x = 70 total workers 70 - 45 = 30 new workers the answer is c ." | a ) $ 300 , b ) 30 , c ) 30 days . , d ) 10.3 , e ) 72 | b | subtract(multiply(multiply(45, divide(8, 6)), divide(35, 30)), 45) | divide(n3,n2)|divide(n1,n4)|multiply(n0,#1)|multiply(#0,#2)|subtract(#3,n0)| | physics |
one - third less than 25 % of 180 is equal to : | "lots of ways to tackle this . 25 % of 180 = 45 1 / 3 of 45 = 15 so , 1 / 3 less than 45 is equal to 45 - 15 = 30 answer : b" | a ) 30 , b ) 28000 , c ) 151 / 31 , d ) 8 , e ) 315 | a | subtract(multiply(divide(25, const_100), 180), multiply(divide(const_1, const_3), multiply(divide(25, const_100), 180))) | divide(n0,const_100)|divide(const_1,const_3)|multiply(n1,#0)|multiply(#1,#2)|subtract(#2,#3)| | general |
if an object travels at 8 feet per second , how many feet does it travel in forty five minutes ? | "if an object travels at 8 feet per second it covers 8 x 60 feet in one minute , and 8 x 60 x 45 feet in forty five minutes . answer = 21600 answer : c" | a ) 41 sec , b ) 189 , c ) 27.38 % , d ) 21600 , e ) 12.50 % | d | multiply(multiply(const_3, const_60), const_60) | multiply(const_3,const_60)|multiply(#0,const_60)| | physics |
in arun ’ s opinion , his weight is greater than 65 kg but less than 72 kg . his brother doest not agree with arun and he thinks that arun ’ s weight is greater than 60 kg but less than 70 kg . his mother ’ s view is that his weight can not be greater than 68 kg . if all are them are correct in their estimation , what ... | explanation : let arun ’ s weight by x kg . according to arun , 65 < x < 72 according to arun ’ s brother , 60 < x < 70 . according to arun ’ s mother , x < = 68 the values satisfying all the above conditions are 66 , 67 and 68 . required average = [ 66 + 67 + 68 / 3 ] = [ 201 / 3 ] = 67 kg answer b | a ) 48 hours , b ) 2056 , c ) 67 kg , d ) 44 hours , e ) t = 121 | c | divide(add(add(subtract(68, const_1), subtract(subtract(68, const_1), const_1)), 68), const_3) | subtract(n4,const_1)|subtract(#0,const_1)|add(#0,#1)|add(n4,#2)|divide(#3,const_3) | general |
there are 8 books on a shelf , of which 3 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ? | approach 1 at - least 1 paper back = total - no paper back 8 c 4 - 5 c 4 = 65 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 3 c 1 * 5 c 3 + 3 c 2 * 5 c 2 + 3 c 3 * 5 c 1 = 65 answer is e | a ) 90 , b ) 12 , c ) 5 , d ) 3 / 7 , e ) 65 | e | subtract(choose(8, 4), choose(5, 4)) | choose(n0,n3)|choose(n2,n3)|subtract(#0,#1) | probability |
rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 500 . then his monthly salary is | "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 500 â ‡ ” 20 / 100 x = 500 â ‡ ” x = 500 ã — 5 = 2500 . answer a" | a ) 24 , b ) 5.5 % , c ) rs . 2500 , d ) 19 min , e ) 100 coins | c | multiply(500, add(const_4, const_1)) | add(const_1,const_4)|multiply(n4,#0)| | gain |
there are 418 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ? | "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 418 = 242 answer : c" | a ) 35 km , b ) 242 , c ) 38 % , d ) 27,550 , e ) 1 / 24 | b | multiply(multiply(8, subtract(11, 8)), 11) | subtract(n2,n1)|multiply(n1,#0)|multiply(n2,#1)| | other |
robert left from a pvt company . management hold his salary rs . 15000 / - for one month . earlier robert borrowed rs . 7280 / - from company . but robert forget that . after one month robert asked his salary and accountant gives rs . 18500 / - to him . what is the incentive amount given to robert ? | "total salary = rs . 15000 / - borrowed money = 7280 / - balance salary = 15000 - 7280 = 7720 paid amount = 18500 / - incentive amount = 18500 - 7720 = 10780 / - answer is c" | a ) rs . 9000 , b ) 35 : 44 , c ) 10780 , d ) 70 mph , e ) 62 | c | subtract(18500, 7280) | subtract(n2,n1)| | general |
what number has a 3 : 4 ratio to the number 400 ? | "3 : 4 = x : 200 4 x = 3 * 400 x = 300 answer : d" | a ) 200 , b ) 36', ' , c ) 300 , d ) 108 , e ) 1200 | c | multiply(400, 3) | multiply(n0,n2)| | other |
the food in a camp lasts for 40 men for 20 days . if 10 more men join , how many days will the food last ? | one man can consume the same food in 40 * 20 = 800 days . 10 more men join , the total number of men = 50 the number of days the food will last = 800 / 50 = 16 days . answer : d | a ) 25 % , b ) 90 , c ) 16 days , d ) $ 24 , e ) 3 | c | divide(multiply(40, 20), add(40, 10)) | add(n0,n2)|multiply(n0,n1)|divide(#1,#0) | physics |
a trader bought a car at 30 % discount on its original price . he sold it at a 50 % increase on the price he bought it . what percent of profit did he make on the original price ? | "original price = 100 cp = 70 s = 70 * ( 150 / 100 ) = 105 100 - 105 = 5 % answer : e" | a ) 8 , b ) c : 37.5 , c ) 24000 , d ) 5 % , e ) 10 % | d | multiply(subtract(divide(divide(multiply(subtract(const_100, 30), add(const_100, 50)), const_100), const_100), const_1), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|divide(#3,const_100)|subtract(#4,const_1)|multiply(#5,const_100)| | gain |
how many cubes of 5 cm edge can be cut out of a cube of 20 cm edge | "explanation : number of cubes = ( 20 x 20 x 20 ) / ( 5 x 5 x 5 ) = 64 answer : b" | a ) 0 , b ) 64 , c ) 20 , d ) 36 , e ) 1 / 10 | b | divide(volume_cube(20), volume_cube(divide(5, const_100))) | divide(n0,const_100)|volume_cube(n1)|volume_cube(#0)|divide(#1,#2)| | probability |
in a weight - lifting competition , the total weight of joe ' s two lifts was 450 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ? | "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 450 pounds . we sum the two variables to obtain : f +... | a ) 3200 , b ) 23 , c ) 9 : 16 , d ) 11.5 sec , e ) 250 | e | divide(add(450, 300), const_3) | add(n0,n1)|divide(#0,const_3)| | general |
a particular library has 150 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 108 books in the sp... | "the total number of books is 150 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 108 books , thus the number of un - returned books is 150 - 108 = 42 books . 0.35 x = 42 x = 120 the answer is ... | a ) 5 inches', ' , b ) 22 , c ) 120 , d ) 2 , e ) 108 | c | divide(subtract(150, 108), subtract(const_1, divide(65, const_100))) | divide(n1,const_100)|subtract(n0,n2)|subtract(const_1,#0)|divide(#1,#2)| | gain |
ramu rides his bike at an average speed of 45 km / hr and reaches his desitination in 4 hours . somu covers the same distance in 6 hours . if ramu covered his journey at an average speed which was 9 km / hr less and somu covered his journey at an average speed which was 10 km / hr more , then the difference in their ti... | distance travelled by ramu = 45 * 4 = 180 km somu travelled the same distance in 6 hours . his speed = 180 / 6 = 30 km / hr hence in the conditional case , ramu ' s speed = 45 - 9 = 36 km / hr and somu ' s speed = 30 + 10 = 40 km / hr . therefore travel time of ramu and somu would be 5 hours and 4.5 hours respectively ... | a ) 2200 , b ) 320 m , c ) 27 / 19 , d ) 30 minutes , e ) 5 / 4 | d | multiply(subtract(divide(multiply(45, 4), subtract(45, 9)), divide(multiply(45, 4), add(divide(multiply(45, 4), 6), 10))), const_60) | multiply(n0,n1)|subtract(n0,n3)|divide(#0,#1)|divide(#0,n2)|add(n4,#3)|divide(#0,#4)|subtract(#2,#5)|multiply(#6,const_60) | general |
if â € œ * â € is called â € œ + â € , â € œ / â € is called â € œ * â € , â € œ - â € is called â € œ / â € , â € œ + â € is called â € œ - â € . 240 * 80 / 60 + 40 / 10 = ? | "explanation : given : 240 * 80 / 60 + 40 / 10 = ? substituting the coded symbols for mathematical operations , we get , 240 / 80 - 60 * 40 - 10 = ? 3 - 2400 - 10 = - 2407 answer : b" | a ) 40 , b ) - 2407 , c ) 4.2 , d ) 10 , e ) 10 hr | b | add(multiply(divide(60, 40), divide(240, 80)), 10) | divide(n2,n3)|divide(n0,n1)|multiply(#0,#1)|add(n4,#2)| | general |
elena purchased brand x pens for $ 5.00 apiece and brand y for $ 2.80 apiece . if elena purchased a total of 12 of these pens for $ 42.00 , how many brand x pens did she purchase ? | "4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 6 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : c ." | a ) 2,000 , b ) 5 % , c ) $ 214.16 , d ) 6 , e ) 2.5 sec | d | subtract(multiply(const_4.0, 12), 42.00) | multiply(const_4.0,n2)|subtract(#0,n3)| | general |
the l . c . m of two numbers is 48 . the numbers are in the ratio 2 : 3 . the sum of numbers is : | "let the numbers be 2 x and 3 x . then , their l . c . m = 6 x . so , 6 x = 48 or x = 8 . the numbers are 16 and 24 . hence , required sum = ( 16 + 24 ) = 40 . answer : c" | a ) 4 / 1 , b ) 40 , c ) 58 , d ) 20 years , e ) 120 km | b | divide(multiply(2, 48), 3) | multiply(n0,n1)|divide(#0,n2)| | other |
in order to fence a square manish fixed 48 poles . if the distance between two poles , is 2 metres then what will be the area of the square so formed ? | let the side of the square be x m . ∴ perimeter of the square = 48 × 2 = 4 x ∴ x = 24 m ∴ area = ( 24 ) 2 = 576 m 2 answer d | a ) 576 cm 2', ' , b ) 50 . , c ) rs . 90 , d ) 9 , e ) 18 | a | square_area(divide(48, 2)) | divide(n0,n1)|square_area(#0) | physics |
find the area of a parallelogram with base 20 cm and height 10 cm ? | area of a parallelogram = base * height = 20 * 10 = 200 cm 2 answer : e | a ) 0.28 % , b ) 195 cm 2 , c ) 33 , d ) 9 , e ) 200 cm 2' | e | multiply(20, 10) | multiply(n0,n1) | geometry |
a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 84 liters of drink a to convert it to drink b ? | "in 84 liters of drink a , there are 48 liters of milk and 36 liters of juice . with 48 liters of milk , we need a total of 64 liters of juice to make drink b . we need to add 28 liters of juice . the answer is b ." | a ) 5 , b ) 3 , c ) 36100 , d ) 80 % , e ) 28 | e | subtract(divide(multiply(multiply(divide(4, add(4, 3)), 84), 4), 3), multiply(divide(3, add(4, 3)), 84)) | add(n0,n1)|divide(n0,#0)|divide(n1,#0)|multiply(n4,#1)|multiply(n4,#2)|multiply(n0,#3)|divide(#5,n1)|subtract(#6,#4)| | general |
which greatest possible length can be used to measure exactly 12 meter 65 cm , 15 meter 25 cm and 10 meter 65 cm | "explanation : convert first all terms into cm . i . e . 1265 cm , 1525 cm , 1065 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 5 . option b" | a ) 8 / 25 , b ) 5 cm , c ) 2068 , d ) 6 cm', ' , e ) 2 kmph | b | floor(divide(add(multiply(12, const_100), 65), add(multiply(15, const_100), 25))) | multiply(n0,const_100)|multiply(n2,const_100)|add(n1,#0)|add(n3,#1)|divide(#2,#3)|floor(#4)| | physics |
in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive r difference between n and m ? | "we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be eq... | a ) 2 : 1 , b ) $ 23400 , c ) s . 120 , d ) 3 , e ) 66 | d | subtract(5, 2) | subtract(n1,n0)| | general |
in a school with 620 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is | "sol . let the number of grils be x . then , number of boys = ( 620 - x ) . then , ( 11 3 / 4 × 620 ) ⇔ 11 x + 12 ( 620 - x ) ⇔ x = 7440 - 7285 ⇔ 155 . answer c" | a ) 1 , b ) 155 , c ) 80 % , d ) 1.9632 , e ) 16 : 15 | b | subtract(multiply(12, 620), multiply(add(11, divide(9, 12)), 620)) | divide(n4,n1)|multiply(n0,n1)|add(n2,#0)|multiply(n0,#2)|subtract(#1,#3)| | general |
two trains are moving in opposite directions with speed of 60 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds | "relative speed = 60 + 90 = 150 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 150 hr = 1 / / 75 hr = 3600 / 75 seconds = 1200 / 25 = 240 / 5 = 48 seconds answer is e ." | a ) 42 , b ) 31.67 % , c ) 170 m , d ) 48 , e ) 38 | d | multiply(divide(add(1.10, 0.9), add(60, 90)), const_3600) | add(n2,n3)|add(n0,n1)|divide(#0,#1)|multiply(#2,const_3600)| | physics |
the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 14 km / hr respectively . they will meet for the first time in ? | clearly , the two will meet when they are 1000 m apart to be 20 + 14 = 34 km apart , they take 1 hour to be 1000 m apart , they take 34 * 1000 / 1000 = 34 min . answer is c | a ) 1 / 2 , b ) 1000 , c ) 28 , d ) 40 , e ) 34 min | e | add(20, 14) | add(n1,n2) | general |
the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 90 and rs . 80 respectively . the sum is : | "sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 90 * 80 / ( 90 - 80 ) = rs . 720 . answer c" | a ) 3 , b ) 2250 , c ) 720 , d ) 2972 , e ) 2 | c | divide(multiply(90, 80), subtract(90, 80)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | gain |
find the l . c . m of 6 , 15 , 24 and 20 . | "explanation : 2 x 3 x 5 x 2 x 2 = 120 answer : option c" | a ) 16 : 15 , b ) 120 , c ) 170 m , d ) 14 , e ) 4 | b | multiply(multiply(power(const_3, const_3), multiply(power(const_2, const_3), power(add(const_4, const_1), const_2))), divide(divide(divide(divide(divide(24, const_2), const_2), const_3), add(const_4, const_1)), add(const_4, const_1))) | add(const_1,const_4)|divide(n2,const_2)|power(const_2,const_3)|power(const_3,const_3)|divide(#1,const_2)|power(#0,const_2)|divide(#4,const_3)|multiply(#2,#5)|divide(#6,#0)|multiply(#7,#3)|divide(#8,#0)|multiply(#10,#9)| | physics |
if shreehari walks in the speed of 4.5 km / hr from his house , in what time will he reach his school which is 750 m long from his house ? | speed = 4.5 * 5 / 18 = 1.25 m / sec time taken = 750 / 1.25 = 600 sec ie . 10 mins . answer : c | a ) 4 years , b ) 3024 , c ) 10 , d ) 1260 , e ) 2 | c | multiply(divide(divide(750, const_1000), 4.5), const_60) | divide(n1,const_1000)|divide(#0,n0)|multiply(#1,const_60) | physics |
if x is a number such that x ^ 2 + 2 x - 24 = 0 and x ^ 2 - 5 x + 4 = 0 , then x = | x ^ 2 + 2 x - 24 = ( x + 6 ) ( x - 4 ) = 0 then x = - 6 or x = 4 . x ^ 2 - 5 x + 4 = ( x - 4 ) ( x - 1 ) = 0 then x = 4 or x = 1 . thus x = 4 . the answer is a . | a ) 10800 , b ) 30 , c ) 15 sec , d ) 4 , e ) 129 | d | divide(add(4, 24), add(2, 5)) | add(n2,n6)|add(n0,n5)|divide(#0,#1) | general |
a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is | sol . since the month begins with a sunday , so there will be five sundays in the month . ∴ required average = [ 510 x 5 + 240 x 25 / 30 ] = 8550 / 30 = 285 answer d | a ) 7.41 % , b ) 2068 , c ) 285 , d ) 9 , e ) 37 % | c | divide(add(multiply(add(const_4, const_1), 510), multiply(multiply(add(const_4, const_1), add(const_4, const_1)), 240)), 30) | add(const_1,const_4)|multiply(n0,#0)|multiply(#0,#0)|multiply(n1,#2)|add(#1,#3)|divide(#4,n2) | general |
a horse chases a pony 8 hours after the pony runs . horse takes 12 hours to reach the pony . if the average speed of the horse is 320 kmph , what s the average speed of the pony ? | pony take 20 hours and horse take 12 hours . . . then distance chased by them is 320 * 12 . so speed of pony is ( 320 * 12 ) / 20 = 192 kmph . answer is b | a ) 360 , b ) m , c ) 192 kmph , d ) 5.5 mph , e ) 62 mph | c | divide(multiply(12, 320), add(12, 8)) | add(n0,n1)|multiply(n1,n2)|divide(#1,#0) | physics |
a , b and c start a business each investing 10,000 . after 6 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 34,200 was recorded . find the share of b . | "ratio of the capitals of a , b and c = 10000 ã — 6 + 5000 ã — 6 : 10000 ã — 6 + 6000 ã — 6 : 10000 ã — 6 + 16000 ã — 6 = 90000 : 96000 : 156000 = 90 : 96 : 156 b â € ™ s share = ( 34200 ã — 96 â „ 342 ) = 9600 answer a" | a ) 6 , b ) 2 , c ) 250 , d ) 7 / 12 , e ) 9,600 | e | divide(add(multiply(subtract(const_12, 6), 4000), multiply(multiply(const_2, multiply(const_100, const_100)), 6)), multiply(const_100, const_10)) | multiply(const_100,const_100)|multiply(const_10,const_100)|subtract(const_12,n1)|multiply(n3,#2)|multiply(#0,const_2)|multiply(n1,#4)|add(#3,#5)|divide(#6,#1)| | gain |
a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 50 $ for the meal . assuming that they will pay 10 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ? | "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.10 x = 50 x = 39.52 hence , the correct option is a" | a ) 66 , b ) $ 11000 , c ) 1 : 64 .', ' , d ) 39.52 $ , e ) 3024 | d | divide(50, add(divide(add(10, 15), const_100), const_1)) | add(n1,n2)|divide(#0,const_100)|add(#1,const_1)|divide(n0,#2)| | general |
an aeroplane covers a certain distance at a speed of 300 kmph in 6 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of : | "explanation : distance = ( 300 x 6 ) = 1800 km . speed = distance / time speed = 1800 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 1800 x 3 / 5 km / hr = 1080 km / hr . answer : option c" | a ) 1632 , b ) 56 , c ) 1080 kmph , d ) 2 / 9 , e ) 9 | c | divide(divide(multiply(300, 6), add(const_1, divide(const_2, const_3))), const_2) | divide(const_2,const_3)|multiply(n0,n1)|add(#0,const_1)|divide(#1,#2)|divide(#3,const_2)| | physics |
what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 150 ? | "surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 150 / 2 = 75 answer is d" | a ) 100 , b ) 75 , c ) 49 , d ) 75.5 kg , e ) 1300 | b | divide(150, const_2) | divide(n0,const_2)| | general |
two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 25 seconds . the ratio of their speeds is ? | "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 25 = = > 27 x + 17 y = 25 x + 25 y = = > 2 x = 8 y = = > x / y = 4 / 1 . answer : b" | a ) 130 , b ) 11988 , c ) $ 320 , d ) 5 / 4 , e ) 4 / 1 | e | divide(subtract(27, 25), subtract(25, 17)) | subtract(n0,n2)|subtract(n2,n1)|divide(#0,#1)| | physics |
a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ? | "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 15 ) / ( 15 - 0 ) = 3 / 1 1 / x = 3 / 1 x = 1 / 3 answer : b" | a ) 1 / 3 , b ) 5 , c ) 3 , d ) 1000 , e ) 6 / 7 | a | divide(15, subtract(60, 15)) | subtract(n0,n1)|divide(n1,#0)| | gain |
a certain car uses one gallon of gasoline every 32 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ? | "4 miles on the highway = 4 / 32 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 32 + 4 / 20 = 13 / 40 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 13 / 40 - 8 / 32 ) / ( 8 / 32 ) = 0.30 . answer : e ." | a ) 30 % , b ) 15 , c ) 95 , d ) 43 , e ) 4.8 | a | multiply(divide(subtract(add(multiply(divide(const_1, 20), 4), multiply(4, divide(const_1, 32))), multiply(8, divide(const_1, 32))), multiply(8, divide(const_1, 32))), const_100) | divide(const_1,n1)|divide(const_1,n0)|multiply(n2,#0)|multiply(n2,#1)|multiply(n4,#1)|add(#2,#3)|subtract(#5,#4)|divide(#6,#4)|multiply(#7,const_100)| | general |
a retailer sold an appliance for $ 100 . if the retailer ' s gross profit on the appliance was 25 percent of the retailer ' s cost for the appliance , how many dollars was the retailer ' s gross profit ? | let p be the original price paid by the retailer . 1.25 * p = 100 p = 80 the profit is $ 20 . the answer is c . | a ) 60 , b ) $ 20 , c ) 3 , 400,000 , d ) 11 , e ) 16 | b | subtract(100, multiply(divide(const_1, add(divide(25, 100), const_1)), 100)) | divide(n1,n0)|add(#0,const_1)|divide(const_1,#1)|multiply(n0,#2)|subtract(n0,#3) | gain |
24 oz of juice p and 25 oz of juice t are mixed to make smothies x and y . the ratio of p to t in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ? | easy way to solve this question is start from the answer and then conform the information provided in the question . we can start from option d i . e 20 . . . as a quantity of juice p in x because it is the only one option that gets divided by 4 is 20 . . . since in the x the juice p to t ratio is 4 : 1 this gives us t... | a ) 466 , b ) 6 , c ) 7 , d ) 20 , e ) 12 | d | subtract(24, divide(subtract(multiply(4, 25), 24), subtract(multiply(4, 5), 1))) | multiply(n1,n2)|multiply(n2,n5)|subtract(#0,n0)|subtract(#1,n3)|divide(#2,#3)|subtract(n0,#4) | other |
if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 75 percent of the test takers answered the second question correctly , and 15 percent of the test takers answered neither question correctly , what percent answered both correctl... | { total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 75 - { both correctly } + 15 { both correctly } = 75 . answer : d . | a ) 11 / 48,000 , b ) $ 22,200 , c ) $ 330 , d ) 75 % , e ) 180 m | d | subtract(add(add(85, 75), 15), const_100) | add(n0,n1)|add(n2,#0)|subtract(#1,const_100) | other |
the grade point average of one third of the classroom is 69 ; the grade point average of the rest is 60 . what is the grade point average of the whole class ? | "let the number of students in class a be = x 1 + x 2 + . . . . . . + a 1 ( where a 1 = remaining students ) now the remaining avg of the students be a 1 / t = 60 a 1 = 60 t ( we are not sure on the number of students , assuming it as t ) . a = x 1 + x 2 + . . . . . . + a 1 ( first set of students + remaining students ... | a ) s . 1300 , b ) 8 hours , c ) it depends how many people are there in the class . , d ) 6.9 , e ) 125 % | c | add(multiply(divide(60, const_3), const_2), divide(69, const_3)) | divide(n0,const_3)|divide(n1,const_3)|multiply(#1,const_2)|add(#0,#2)| | general |
find the least number of complete years in which a sum of money put out at 25 % compound interest will be more than double of itself ? | "4 years answer : d" | a ) 4 years , b ) 19619 , c ) 22 , d ) 13,400 , e ) 0 | a | floor(add(divide(log(const_2), log(add(const_1, divide(25, const_100)))), const_1)) | divide(n0,const_100)|log(const_2)|add(#0,const_1)|log(#2)|divide(#1,#3)|add(#4,const_1)|floor(#5)| | general |
mrs . evans gave a test to her freshmen economics class , which has 29 students enrolled and 24 of them answered question 1 correctly . if 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ? | "total number of enrolled students = 29 number of students who did not take test = 5 hence , number of students who took test = 29 - 5 = 24 number of students who answered q 2 correctly = 24 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answe... | a ) $ 336 , b ) 308 , c ) 225 , d ) 22.4 hours , e ) 22 | e | subtract(add(add(24, 22), 5), 29) | add(n1,n3)|add(n5,#0)|subtract(#1,n0)| | other |
7 m - 20 = 2 m , then m + 7 is equal to ? | 7 m - 20 = 2 m so , 5 m = 20 so , m + 7 = 11 answer : c | a ) 36000 , b ) 1.6 . , c ) 9 years , d ) 9.9 % , e ) 11 | e | add(divide(20, subtract(7, 2)), 7) | subtract(n0,n2)|divide(n1,#0)|add(n0,#1) | general |
which is greater than 16 | "66 greater than 16 . answer : b" | a ) 1856 , b ) 0.358 , c ) 40 , d ) 66 , e ) 22 | d | divide(divide(divide(divide(divide(divide(16, const_4), const_3), const_4), const_3), const_2), const_2) | divide(n0,const_4)|divide(#0,const_3)|divide(#1,const_4)|divide(#2,const_3)|divide(#3,const_2)|divide(#4,const_2)| | general |
the smallest value of n , for which 2 n + 1 is not a prime number is | "sol . = ( 2 × 1 + 1 ) = 3 , = ( 2 × 3 + 1 ) = 7 , = ( 2 × 4 + 1 ) = 9 , which is not prime . therefore n = 4 . answer b" | a ) 9 / 20 , b ) 50 , c ) 1 / 4 , d ) 4 , e ) 70 | d | add(2, 2) | add(n0,n0)| | general |
two 100 multiples of 7 are chosen at random , and 300 multiples of 8 are chosen at random . approximately what percentage of the 500 selected numbers are odd ? | two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have all even ( being multiple of 8 ) probability of number selected being odd = total odd numbers / total available numbers probability = 100 / 500 = 0.2 = 20 % answer : option a | a ) 36 , b ) 360 , c ) 50 days , d ) 20 % , e ) 1,350 | d | multiply(divide(100, 500), const_100) | divide(n0,n4)|multiply(#0,const_100) | general |
in traveling from a dormitory to a certain city , a student went 1 / 3 of the way by foot , 1 / 4 of the way by bus , and the remaining 5 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ? | "whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 3 / 5 x + 5 x - 1 / 2 x - 3 / 5 x = 5 x = 12 km option : e" | a ) 33.33 % , b ) 12 , c ) 176 , d ) 22 , e ) 1000 m | b | multiply(5, inverse(subtract(1, add(divide(1, 3), divide(1, 4))))) | divide(n0,n1)|divide(n2,n3)|add(#0,#1)|subtract(n0,#2)|inverse(#3)|multiply(n4,#4)| | physics |
the sector of a circle has radius of 14 cm and central angle 108 o . find its perimeter ? | "perimeter of the sector = length of the arc + 2 ( radius ) = ( 108 / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) = 26.4 + 28 = 54.4 cm answer : b" | a ) 10750 , b ) 1 , c ) 54.4 cm , d ) 35 % , e ) rs . 9000 | c | multiply(multiply(const_2, divide(multiply(subtract(14, const_3), const_2), add(const_4, const_3))), 14) | add(const_3,const_4)|subtract(n0,const_3)|multiply(#1,const_2)|divide(#2,#0)|multiply(#3,const_2)|multiply(n0,#4)| | physics |
tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 10 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ? | ( 1 mph + 10 mph ) / 2 = 5.5 mph correct option is : b | a ) 5.5 mph , b ) 28.57 % , c ) 36100 , d ) 3 , e ) 25 | a | divide(add(1, 10), const_2) | add(n0,n1)|divide(#0,const_2) | physics |
j is 25 % less than p and 20 % less than t . t is x % less than p . what is the value of x ? | "let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( x / 100 ) ] * p i . e . 100 - x = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . x = 6.25 answer : option d" | a ) 7200 , b ) 25 , c ) 2 , d ) 65 , e ) 6.25 | e | divide(multiply(25, 25), const_100) | multiply(n0,n0)|divide(#0,const_100)| | general |
denise is trying to open a safe whose combination she does not know . if the safe has 4000 possible combinations , and she can try 75 different possibilities , what is the probability that she does not pick the one correct combination . | when trying the first time the probability denise does n ' t pick the correct combination = 3999 / 4000 second time , as the total number of possible combinations reduced by one , not picking the right one would be 3998 / 3999 . third time 3997 / 3998 . . . and the same 75 times . so we get : 3999 / 4000 ∗ 3998 / 3999 ... | a ) 157 / 160 , b ) 114.28 % , c ) 19 , d ) 140 , e ) 859 | a | divide(subtract(4000, 75), 4000) | subtract(n0,n1)|divide(#0,n0) | probability |
what percent is 36 paisa ' s of 12 rupees ? | "12 rupees = 1200 paisa ' s 36 / 1200 × 100 = 3 / 12 12 / 3 = 3 % b" | a ) 975 , b ) 180 , c ) 60 , d ) 3 % , e ) 2520 | d | multiply(divide(36, 12), const_100) | divide(n0,n1)|multiply(#0,const_100)| | gain |
in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many q cents does a liter of kerosene cost ? [ one dollar has 100 cents . ] | "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer q = 44 . d" | a ) 50 , b ) 14 , c ) 44 , d ) $ 22,200 , e ) 4 | c | multiply(divide(divide(8, divide(const_1, const_2)), const_12), multiply(0.33, 100)) | divide(const_1,const_2)|multiply(n1,n2)|divide(n0,#0)|divide(#2,const_12)|multiply(#3,#1)| | general |
two spheres of their radios in the ratio 4 : 3 . find its volumes ratio ? | sphere volume ( v ) = 4 / 3 π r ( power 3 ) : 4 / 3 π r ( power 3 ) = 4 ( power 3 ) : 3 ( power 3 ) = 64 : 27 answer is d . | a ) 30 , b ) 80 , c ) 64 : 27', ' , d ) 20 , e ) 48 | c | divide(volume_sphere(4), volume_sphere(3)) | volume_sphere(n0)|volume_sphere(n1)|divide(#0,#1) | other |
a train which has 420 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ? | "time taken to cross a moving person = length of train / relative speed time taken = 420 / ( ( 45 - 9 ) ( 5 / 18 ) = 420 / 36 * ( 5 / 18 ) = 420 / 10 = 42 sec answer : b" | a ) 5 / 8 , b ) 9 years , c ) 0.225 , d ) 80 % , e ) 42 sec | e | divide(420, subtract(divide(45, const_3_6), divide(divide(9, const_2), const_3_6))) | divide(n1,const_3_6)|divide(n2,const_2)|divide(#1,const_3_6)|subtract(#0,#2)|divide(n0,#3)| | physics |
danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 1536 , what is the area of the side face of the box ? | "lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 1536 l * 1.5 l * 2 l = 1536 l = 8 side face area = l * d = l * 2 l = 8 * 2 * 8 = 128 e is the answer" | a ) 274 , b ) 6 , c ) - 8 , d ) 1200 m ^ 2', ' , e ) 128 | e | divide(power(multiply(const_3, power(1536, const_2)), divide(const_1, const_3)), 1.5) | divide(const_1,const_3)|power(n1,const_2)|multiply(#1,const_3)|power(#2,#0)|divide(#3,n0)| | geometry |
sum of the squares of 3 no . is 276 and the sum of their products taken two at a time is 150 . find the sum ? | "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 276 + 2 * 150 a + b + c = â ˆ š 576 = 24 answer d" | a ) 20000 , b ) 91.7 , c ) 13122 , d ) 24 , e ) 75 | d | sqrt(add(276, multiply(150, const_2))) | multiply(n2,const_2)|add(n1,#0)|sqrt(#1)| | general |
zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 14 questions , if sterling had answered 2... | i got two equations : 3 x - 2 y = 25 x + y = 14 3 x - 2 ( 14 - x ) = 25 3 x - 28 + 2 x = 25 5 x = 53 x = 10.6 or between 10 and 11 . ( ans e ) | a ) 10 ^ 5 , b ) 3 , 012,121 , c ) 6 2 / 3 days , d ) 10 , e ) 705 | d | divide(add(subtract(multiply(2, subtract(14, 2)), multiply(3, 2)), 31), add(3, 2)) | add(n0,n2)|multiply(n0,n2)|subtract(n1,n2)|multiply(n2,#2)|subtract(#3,#1)|add(n3,#4)|divide(#5,#0) | general |
bhaman travelled for 15 hours . he covered the first half of the distance at 40 kmph and remaining half of the distance at 10 kmph . find the distance travelled by bhaman ? | let the distance travelled be x km . total time = ( x / 2 ) / 40 + ( x / 2 ) / 10 = 15 = > x / 80 + x / 20 = 15 = > ( x + 4 x ) / 80 = 15 = > x = 240 km answer : a | a ) 240 , b ) 6400 , c ) - 5 , d ) 380 , e ) 9 | a | multiply(divide(15, add(divide(multiply(const_2, 40), const_10), divide(multiply(const_2, 10), const_10))), multiply(multiply(divide(multiply(const_2, 40), const_10), divide(multiply(const_2, 10), const_10)), const_10)) | multiply(n1,const_2)|multiply(n2,const_2)|divide(#0,const_10)|divide(#1,const_10)|add(#2,#3)|multiply(#2,#3)|divide(n0,#4)|multiply(#5,const_10)|multiply(#6,#7) | physics |
in a survey of parents , exactly 7 / 8 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ? | fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 8 * 2 / 5 = 1 / 20 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 1 / 20 = 1 / 5 = 20 % the answer is a . | a ) 20 % , b ) 10 : 1 , c ) 4 , d ) 272 , e ) 3 / 2 | a | add(subtract(subtract(const_100, 40), multiply(divide(3, 4), subtract(const_100, 40))), subtract(40, multiply(divide(7, 8), 40))) | divide(n2,n3)|divide(n0,n1)|subtract(const_100,n4)|multiply(#0,#2)|multiply(n4,#1)|subtract(#2,#3)|subtract(n4,#4)|add(#5,#6) | general |
three pipes of same capacity can fill a tank in 8 hours . if there are only two pipes of same capacity , the tank can be filled in . | the part of the tank filled by three pipes in one hour = 1 / 8 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 8 = 1 / 12 . the tank can be filled in 12 hours . answer : b | a ) 100 , b ) 12 hours , c ) $ 480 , d ) 420 , e ) 30 | b | inverse(multiply(divide(const_2, const_3), divide(const_1, 8))) | divide(const_2,const_3)|divide(const_1,n0)|multiply(#0,#1)|inverse(#2) | physics |
each factor of 220 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 55 ? | "the # of factors 220 has is 12 ; so out of 12 factors only three are multiples of 55 : 55 , 110 and 220 , itself ; so , the probability is 3 / 12 = 1 / 4 . answer : e ." | a ) 1 / 4 , b ) 2700 , c ) 1636 , d ) 3 , e ) 240 square units', ' | a | divide(divide(choose(55, const_1), 55), power(const_3, const_2)) | choose(n1,const_1)|power(const_3,const_2)|divide(#0,n1)|divide(#2,#1)| | other |
john makes $ 40 a week from his job . he earns a raise andnow makes $ 70 a week . what is the % increase ? | "increase = ( 30 / 40 ) * 100 = ( 3 / 4 ) * 100 = 75 % . e" | a ) 44 . , b ) 75 % , c ) 7 , d ) 266 cm 2 , e ) 129 | b | multiply(divide(subtract(70, 40), 40), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
an association of mathematics teachers has 1,260 members . only 525 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 72 percent of the votes cast ? | "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 72 percent of the votes cast number of votes for winning candidate = ( 72 / 100 ) * 525 = 378 percent of total membership that voted for winning candidate = ( 378 / 1260 ) * 100 = 30 % answer c" | a ) 30 % , b ) 101 , c ) 375 , d ) 1 , e ) 3108 | a | multiply(divide(multiply(divide(72, const_100), 525), 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 |
a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ? | "let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34009 + x = 39000 = > x = 39000 − 34009 = 4991 answer is c ." | a ) 48 , b ) 4991 , c ) $ 25 , d ) 9 gallons , e ) 80 | b | subtract(multiply(add(5, const_1), 6500), add(add(add(add(6435, 6927), 6855), 7230), 6562)) | add(n5,const_1)|add(n0,n1)|add(n2,#1)|multiply(n6,#0)|add(n3,#2)|add(n4,#4)|subtract(#3,#5)| | general |
one half of a two digit number exceeds its one third by 4 . what is the sum of the digits of the number ? | "explanation : x / 2 – x / 3 = 4 = > x = 24 2 + 4 = 6 a" | a ) 6 , b ) 100 , c ) 30 , d ) 36.48 , e ) 15 | a | add(reminder(multiply(4, const_4), const_10), const_1) | multiply(n0,const_4)|reminder(#0,const_10)|add(#1,const_1)| | general |
calculate the number of bricks , each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10 % of its volume is occupied by mortar ? | explanation : let the number of bricks be ' n ' 10 x 4 / 100 x 6 x 90 / 100 = 25 / 100 x 15 / 100 x 8 / 100 x n 10 x 4 x 6 x 90 = 15 x 2 x n = > n = 720 . answer is a | a ) 6.7 kg . , b ) 120 km , c ) $ 9.60 , d ) 720 , e ) 11 / 3 | d | divide(multiply(multiply(multiply(10, divide(4, const_100)), 6), subtract(const_1, divide(10, const_100))), multiply(multiply(divide(25, const_100), divide(15, const_100)), divide(8, const_100))) | divide(n4,const_100)|divide(n3,const_100)|divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|multiply(n3,#0)|multiply(#3,#4)|subtract(const_1,#1)|multiply(n5,#5)|multiply(#2,#6)|multiply(#8,#7)|divide(#10,#9) | physics |
if the side length of square b is three times that of square a , the area of square b is how many times the area of square a ? | "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 3 x ) ^ 2 = 9 x ^ 2 . the answer is a ." | a ) 100 , b ) 9 , c ) 66 2 / 3 , d ) 120 , e ) $ 54,000 | b | multiply(const_4, const_4) | multiply(const_4,const_4)| | geometry |
the lcm and hcf of two numbers are 8 and 48 respectively . if one of them is 24 , find the other ? | hcf x lcm = product of numbers 8 x 48 = 24 x the other number other number = ( 8 x 48 ) / 24 other number = 16 answer : d | a ) 16 , b ) 77 , c ) 1000', ' , d ) $ 2000 , e ) 63 | a | divide(multiply(8, 48), 24) | multiply(n0,n1)|divide(#0,n2) | physics |
one night a certain hotel rented 3 / 5 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ? | the rooms which were not rented is 2 / 5 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 2 / 5 ) = 1 / 2 = 50 % the answer is a . | a ) $ . 90 , b ) 1 / 3 , c ) $ 32500 , d ) 1122 , e ) 50 % | e | multiply(divide(multiply(subtract(const_1, divide(2, 3)), multiply(divide(3, 5), const_100)), subtract(const_100, multiply(divide(3, 5), const_100))), const_100) | divide(n0,n1)|divide(n2,n0)|multiply(#0,const_100)|subtract(const_1,#1)|multiply(#2,#3)|subtract(const_100,#2)|divide(#4,#5)|multiply(#6,const_100) | gain |
in what time will a train 180 m long cross an electric pole , it its speed be 144 km / hr ? | "speed = 144 * 5 / 18 = 40 m / sec time taken = 180 / 40 = 4.5 sec . answer : d" | a ) 4.5 sec , b ) 36 , c ) $ 24 , d ) 3 kmph , e ) 60 | a | divide(180, multiply(144, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics |
how many 7 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 1234321 . | "take the task of building palindromes and break it intostages . stage 1 : select the 7 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 6 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways stage ... | a ) 5 % , b ) 9000 , c ) 7.94 , d ) 312 , e ) 252 sec | b | multiply(multiply(multiply(multiply(7, const_10), const_10), const_10), const_10) | multiply(n0,const_10)|multiply(#0,const_10)|multiply(#1,const_10)|multiply(#2,const_10)| | general |
the average monthly salary of 25 employees in an organisation is rs . 2500 . if the manager ' s salary is added , then the average salary increases by rs . 200 . what is the manager ' s monthly salary ? | "manager ' s monthly salary = rs . ( 2700 * 26 - 2500 * 25 ) = rs . 7700 answer : a" | a ) 5 % , b ) rs . 7700 , c ) 77 , d ) 3 , e ) 16 | b | subtract(multiply(add(2500, 200), add(25, const_1)), multiply(2500, 25)) | add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | general |
the sum of two consecutive number is 49 . which is the larger number ? | "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 49 2 x + 1 = 49 2 x = 48 x = 24 therefore larger number is x + 1 = 25 answer : c" | a ) 144 min , b ) 1 : 2', ' , c ) 25 , d ) 22 , e ) 240 square units', ' | c | add(add(power(add(add(divide(subtract(subtract(49, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(49, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(49, 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 |
we had $ 1400 left after spending 30 % of the money that we took for shopping . how much money did we start with ? | "let x be the amount of money we started with . 0.7 x = 1400 x = 2000 the answer is a ." | a ) $ 1260 , b ) 480 , c ) 119 , d ) $ 2000 , e ) 80 % | d | divide(1400, subtract(const_1, divide(30, const_100))) | divide(n1,const_100)|subtract(const_1,#0)|divide(n0,#1)| | gain |
each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 94 % water by weight . what is the new weight of the cucumbers , in pounds ? | "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 94 % water and 6 % of non - water , so now 1 pound of non - water composes 6 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.06 = 16 pounds . answer : b ." | a ) 8 , b ) 16 , c ) 30 , d ) 165 , e ) s . 12000 | b | multiply(divide(subtract(100, 99), subtract(100, 94)), 100) | subtract(n0,n1)|subtract(n0,n2)|divide(#0,#1)|multiply(#2,n0)| | gain |
the average of 5 numbers is 6.8 . if one of the numbers is multiplied by a factor of 4 , the average of the numbers increases to 9.2 . what number is multiplied by 4 ? | "the average of 5 numbers is 6.8 the sum of 5 numbers will be 6.8 x 5 = 34 the average of 5 number after one of the number is multiplied by 4 is 9.2 the sum of the numbers will now be 9.2 x 5 = 46 so the sum has increased by 46 - 34 = 12 let the number multiplied by 4 be n then , 4 n = n + 12 or 3 n = 12 or n = 4 answe... | a ) 104 miles , b ) 30 , c ) 3 , d ) 2 / 9 , e ) 4.0 | e | subtract(multiply(9.2, 5), multiply(6.8, 5)) | multiply(n0,n3)|multiply(n0,n1)|subtract(#0,#1)| | general |
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