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mathqa_shuffle_question_test

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a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 30 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?

32 / ( 2 * 2 ) = 8 days answer : e

a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8

e

multiply(multiply(32, divide(const_1, const_2)), divide(const_1, const_2))

divide(const_1,const_2)|multiply(n0,#0)|multiply(#0,#1)

physics

if x / y = 7 / 4 , then ( x + y ) / ( x - y ) = ?

"the units digit of 33 ^ 2 is the units digit of 3 * 3 = 9 which is 9 . the units digit of 17 ^ 3 is the units digit of 7 * 7 * 7 = 343 which is 3 . the units digit of 39 ^ 2 is the units digit of 9 * 9 = 81 which is 1 . the units digit of 9 * 3 * 1 = 27 is 7 . the answer is d ."

a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9

d

divide(add(multiply(factorial(33), factorial(2)), multiply(factorial(33), factorial(3))), 33)

factorial(n0)|factorial(n1)|factorial(n3)|multiply(#0,#1)|multiply(#0,#2)|add(#3,#4)|divide(#5,n0)|

general

15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container h ?

they can make a team of 3 men and 2 women . the number of ways to do this is 6 c 3 * 4 c 2 = 20 * 6 = 120 they can make a team of 2 men and 3 women . the number of ways to do this is 6 c 2 * 4 c 3 = 15 * 4 = 60 the total number of distinct groups is 180 . the answer is c .

a ) 120 , b ) 150 , c ) 180 , d ) 210 , e ) 240

c

add(add(multiply(multiply(6, 5), 4), multiply(6, 5)), multiply(6, 5))

multiply(n1,n3)|multiply(n2,#0)|add(#1,#0)|add(#2,#0)

general

the sum of the squares of three consecutive natural number is 2030 . what is the middle number ?

"percentage error in calculated area = ( 3 + 3 + ( 3 ã — 3 ) / 100 ) % = 9.09 % answer : a"

a ) 9.09 % , b ) 4.02 % , c ) 4 % , d ) 3 % , e ) 2 %

a

divide(multiply(subtract(square_area(add(const_100, 3)), square_area(const_100)), const_100), square_area(const_100))

add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)|

gain

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 special collection at that time , how many books of the special collection were loaned out during that month ?

"first , you must find the total weight of the mixture given that 80 % of it will be dough . 75 % * total = 40 = > ( 75 / 100 ) total = 40 = > total = 4000 / 75 = > total = 53.33 oz , from there , you must find 25 % of the total 53.33 oz of the mixture . 25 % * total = > ( 25 / 100 ) ( 53.33 ) = 13.33 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 20 - 13.3 = 6.7 oz chocolate left over . answer : d"

a ) 8.5 , b ) 9.5 , c ) 10.5 , d ) 6.7 , e ) 6.5

d

multiply(divide(25, const_100), 25)

divide(n2,const_100)|multiply(n2,#0)|

gain

if 0.5 : x : : 5 : 8 , then x is equal to :

"1 / 10 + 1 / 15 - 1 / x = 1 / 15 x = 10 10 * 20 = 200 answer : c"

a ) 150 liters , b ) 540 liters , c ) 200 liters , d ) 560 liters , e ) 580 liters

c

multiply(multiply(inverse(subtract(add(add(divide(const_1, 10), divide(const_1, 15)), divide(const_1, 20)), divide(const_1, 15))), const_3), 15)

divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|divide(const_1,n3)|add(#0,#1)|add(#4,#2)|subtract(#5,#3)|inverse(#6)|multiply(#7,const_3)|multiply(n1,#8)|

physics

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 37 , the how old is b ?

"a : b = 90000 : 25000 = 90 : 25 = 18 : 5 answer : d"

a ) 9 : 2 , b ) 3 : 2 , c ) 18 : 20 , d ) 18 : 5 , e ) 17 : 4

d

divide(add(multiply(multiply(const_3, const_3), add(multiply(const_3, const_3), const_1)), 2), multiply(2, add(multiply(const_3, const_3), const_1)))

multiply(const_3,const_3)|add(#0,const_1)|multiply(#1,#0)|multiply(n2,#1)|add(n2,#2)|divide(#4,#3)|

gain

how many 1 / 6 s are there in 37 1 / 2 ?

"let x be the money invested at 3 % . 1.03 x + 1.04 ( 1000 - x ) = 1036.70 . 0.01 x = 1040 - 1036.70 . 0.01 x = 3.30 . x = 330 . the answer is b ."

a ) $ 300 , b ) $ 330 , c ) $ 360 , d ) $ 390 , e ) $ 420

b

divide(subtract(multiply(multiply(const_100, multiply(add(const_2, const_3), const_2)), add(divide(4, const_100), const_1)), add(add(multiply(const_100, multiply(add(const_2, const_3), const_2)), multiply(multiply(add(const_2, const_3), const_2), 3)), multiply(const_2, const_3))), subtract(add(divide(4, const_100), const_1), add(divide(3, const_100), const_1)))

add(const_2,const_3)|divide(n2,const_100)|divide(n1,const_100)|multiply(const_2,const_3)|add(#1,const_1)|add(#2,const_1)|multiply(#0,const_2)|multiply(#6,const_100)|multiply(#6,n1)|subtract(#4,#5)|add(#7,#8)|multiply(#4,#7)|add(#10,#3)|subtract(#11,#12)|divide(#13,#9)|

gain

the least number which must be subtracted from 6709 to make it exactly divisible by 9 is :

"notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 3 5 5 number of possibilities = 4 * 4 * 4 = 64 . then , just add up the number of 1 digits numbers = 4 , so total is 64 + 4 = 68 . answer : e"

a ) 48 , b ) 52 , c ) 66 , d ) 84 , e ) 68

e

divide(factorial(subtract(add(const_4, 1), const_1)), multiply(factorial(1), factorial(subtract(const_4, const_1))))

add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)|

probability

what is the product of all the possible values of x if x ^ 2 + 5 x + 6 ?

explanation : let forks = 4 x , spoons = 4 x & knives = 3 x . now , 4 x = 16 hence x = 4 . number of knives = 3 x = 12 . answer : c

a ) 8 , b ) 4 , c ) 12 , d ) 16 , e ) 14

c

multiply(divide(16, 4), 3)

divide(n3,n0)|multiply(n2,#0)

other

the length of a rectangular floor is more than its breadth by 200 % . if rs . 324 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?

"450 = 2 x 3 ^ 2 x 5 ^ 2 now we need two 2 s , one 3 and one 5 to make it perfect cube . so x = 2 ^ 2 x 3 x 5 = 60 . answer is c ."

a ) 2 , b ) 15 , c ) 30 , d ) 60 , e ) 120

c

add(const_3, const_4)

add(const_3,const_4)|

geometry

by how much is 70 % of 120 greater than 35 % of 200 .

"c number of valid votes = 80 % of 6000 = 4800 . valid votes polled by other candidate = 45 % of 4800 = ( 45 / 100 x 4800 ) = 2160 ."

a ) 2800 , b ) 2700 , c ) 2160 , d ) 2200 , e ) 2300

c

multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 6000)

divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|multiply(#2,#3)|multiply(n2,#4)|

gain

john left home and drove at the rate of 50 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ?

"10 * 6 = 4 * x x = 15 answer : b"

a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30

b

multiply(6, divide(10, 4))

divide(n0,n1)|multiply(n2,#0)|

physics

if x and y are integers , what is the least positive number of 24 x + 21 y ?

"speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 36 = > 300 + l = 15 × 36 = 540 = > l = 540 - 300 = 240 meter answer is a ."

a ) 240 , b ) 250 , c ) 260 , d ) 230 , e ) 220

a

multiply(multiply(const_0_2778, 54), subtract(36, 20))

multiply(n2,const_0_2778)|subtract(n0,n1)|multiply(#0,#1)|

physics

a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 3 students left over . what is the sum of the two smallest possible values of n ?

"let the amount lent at 2 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 2 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 450 = > x = 1875 amount lent at 10 % = 4125 required ratio = 5 : 11 answer : a"

a ) 5 : 11 , b ) 5 : 6 , c ) 5 : 2 , d ) 5 : 8 , e ) 5 : 2

a

divide(divide(subtract(multiply(450, const_100), multiply(6000, 2)), subtract(10, 2)), divide(subtract(multiply(450, const_100), multiply(6000, 2)), subtract(10, 2)))

multiply(n3,const_100)|multiply(n0,n1)|subtract(n2,n1)|subtract(#0,#1)|divide(#3,#2)|divide(#4,#4)|

gain

if the number is divided by 3 , it reduced by 34 . the number is

"the number of exhaustive outcomes is 36 . let e be the event of getting doublet on the dies is 6 / 36 = 1 / 6 p ( e ) = 1 / 6 . a )"

a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2

a

divide(const_6, multiply(const_6, const_6))

multiply(const_6,const_6)|divide(const_6,#0)|

probability

if $ 120 invested at a certain rate of simple interest amounts to $ 180 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?

"8 × 8 = 4 ^ 2 × 2 ^ 2 so total factors = ( 3 + 1 ) ( 3 + 1 ) = 16 answer : d"

a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18

d

add(power(const_2, const_2), const_2)

power(const_2,const_2)|add(#0,const_2)|

other

a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 18 seconds . due to some problem , two boggies were detached . the train now crosses a telegraph post in

"ratio of the sides = â ³ â ˆ š 343 : â ³ â ˆ š 512 = 7 : 8 ratio of surface areas = 49 : 64 answer : e"

a ) 12 : 24 , b ) 8 : 16 , c ) 45 : 25 , d ) 18 : 56 , e ) 49 : 64

e

power(divide(343, 512), divide(const_1, const_3))

divide(n0,n1)|divide(const_1,const_3)|power(#0,#1)|

geometry

in what time will a railway train 110 m long moving at the rate of 36 kmph pass a telegraph post on its way ?

"explanation : for an income of rs . 9 , investment = rs . 100 . for an income of rs 6 , investment = rs . 100 / 9 x 6 = rs 66.66 market value of rs . 100 stock = rs . 66.66 answer is e"

a ) rs 66.55 , b ) rs 68.55 , c ) rs 69.55 , d ) rs 65.55 , e ) rs 66.66

e

multiply(divide(const_100, 9), 6)

divide(const_100,n1)|multiply(n0,#0)|

gain

the price of an item is discounted 6 percent on day 1 of a sale . on day 2 , the item is discounted another 6 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?

"the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 25 / 36 = ( 5 / 6 ) * ( 5 / 6 ) therefore probability that the next one she draws is pink = 1 / 6 option ( a )"

a ) 1 / 6 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49

a

subtract(const_1, sqrt(divide(25, 36)))

divide(n0,n1)|sqrt(#0)|subtract(const_1,#1)|

general

a train 400 m long can cross an electric pole in 10 sec and then find the speed of the train ?

"let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 253 n * ( n - 1 ) = 506 = 23 * 22 ( trial and error ) the answer is c ."

a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25

c

divide(add(sqrt(add(multiply(multiply(253, const_2), const_4), const_1)), const_1), const_2)

multiply(n0,const_2)|multiply(#0,const_4)|add(#1,const_1)|sqrt(#2)|add(#3,const_1)|divide(#4,const_2)|

general

what is the angle between the hands of a clock when time is 10 : 30 ?

more days , more length ( direct ) less breadth , more length ( indirect ) more depth , less length ( indirect days 10 : 30 ; breadth 25 : 50 ; : : 100 : x depth 15 : 10 ; : . 10 * 25 * 15 * x = 30 * 50 * 10 * 100 x = ( 30 * 50 * 10 * 100 ) / 10 * 25 * 15 = 400 so the required length = 400 m answer : a

a ) 400 m , b ) 200 m , c ) 100 m , d ) 89 m , e ) 79 m

a

divide(multiply(multiply(multiply(30, 50), 10), 100), multiply(15, multiply(10, 25)))

multiply(n2,n6)|multiply(n0,n4)|multiply(n0,#0)|multiply(n5,#1)|multiply(n1,#2)|divide(#4,#3)

physics

0.05 x 0.03 = ?

"explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 3 : 3 : : 56 : x therefore ( 20 x 3 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 60 = 98 hence , the required length is 98 m . answer : e"

a ) 40 m , b ) 64 m , c ) 77 m , d ) 89 m , e ) 98 m

e

multiply(divide(56, multiply(20, 3)), multiply(35, 3))

multiply(n0,n2)|multiply(n3,n4)|divide(n1,#0)|multiply(#2,#1)|

physics

what least value should be replaced by * in 2551112 * so the number become divisible by 6

p = ( 2 / 9 ) * p + 63 ( 7 / 9 ) * p = 63 p = 81 the answer is e .

a ) $ 69 , b ) $ 72 , c ) $ 75 , d ) $ 78 , e ) $ 81

e

divide(63, subtract(const_1, multiply(divide(1, 9), const_2)))

divide(n1,n2)|multiply(#0,const_2)|subtract(const_1,#1)|divide(n0,#2)

general

in the set of positive integers from 1 to 100 , what is the sum of all the odd multiples of 5 ?

"speed = 110 * 5 / 18 = 275 / 9 m / sec length of the train = speed * time = 275 / 9 * 9 = 275 m answer : b"

a ) 298 m , b ) 275 m , c ) 208 m , d ) 988 m , e ) 299 m

b

multiply(divide(multiply(110, const_1000), const_3600), 9)

multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|

physics

on average , the boys in the class have 20 pencils and the girls have 38 pencils . if the overall class average is 30 pencils , what is the ratio of boys to girls in the class ?

2 ^ y = 4 ^ ( 5 x + 3 ) 2 ^ y = 2 ^ 2 ( 5 x + 3 ) y = 10 x + 6 . . . . . . . . . . . 1 3 ^ ( x - 7 ) = 9 ^ y 3 ^ ( x - 7 ) = 3 ^ 2 y x - 7 = 2 y . . . . . . . . . . . . . 2 put value of y = 10 x + 6 in eq 2 x - 7 = 2 ( 10 x + 6 ) x - 7 = 20 x + 12 19 x = - 19 x = - 1 therefore , y = - 10 + 6 y = - 4 x + y = - 1 - 4 = - 5 answer : b

a ) - 10 , b ) - 5 , c ) - 4 , d ) 3 , e ) 7

b

add(divide(add(divide(add(negate(7), negate(multiply(multiply(2, 3), 2))), subtract(multiply(2, const_10), const_1)), negate(7)), 2), divide(add(negate(7), negate(multiply(multiply(2, 3), 2))), subtract(multiply(2, const_10), const_1)))

multiply(n0,n3)|multiply(n0,const_10)|negate(n5)|multiply(n0,#0)|subtract(#1,const_1)|negate(#3)|add(#2,#5)|divide(#6,#4)|add(#7,#2)|divide(#8,n0)|add(#9,#7)

general

how long does a train 150 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?

"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 140 = 380 m . time taken = 380 / 10 = 38 sec . answer : c"

a ) 28 sec , b ) 16 sec , c ) 38 sec , d ) 18 sec , e ) 17 sec

c

divide(add(240, 140), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2))))

add(n1,n2)|divide(const_10,const_2)|subtract(n3,n0)|divide(#2,const_2)|divide(#1,#3)|multiply(#4,#2)|divide(#0,#5)|

general

in a company of 11 employees , 5 employees earn $ 32,000 , 4 employees earn $ 45,000 , and the 2 highest - paid employees earn the same amount . if the average annual salary for the 11 employees is $ 48,000 , what is the annual salary for each of the highest - paid employees ?

"neither car nor garage = total - garage - ( swim - common ) = 75 - 50 - ( 40 - 35 ) = 75 - 55 = 20 answer c"

a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30

c

subtract(75, add(add(subtract(50, 35), subtract(40, 35)), 35))

subtract(n1,n3)|subtract(n2,n3)|add(#0,#1)|add(n3,#2)|subtract(n0,#3)|

other

a train 1200 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?

"before price increase price = a after 30 % price increase price = a + ( 30 / 100 ) * a = 1.3 a = 351 ( given ) i . e . a = 351 / 1.3 = $ 270 i . e . 2 a = 2 * 270 = 540 answer : option a"

a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700

a

multiply(divide(351, divide(add(const_100, 30), const_100)), 2)

add(n0,const_100)|divide(#0,const_100)|divide(n1,#1)|multiply(n2,#2)|

general

if 2 ^ 5 , 4 ^ 3 , and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?

"in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability w of cgd / ( cg ) - > 3 / 19 answer d"

a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43

d

divide(divide(divide(1, 8), divide(2, 3)), add(divide(divide(1, 8), divide(2, 3)), 1))

divide(n0,n1)|divide(n2,n3)|divide(#0,#1)|add(#2,n0)|divide(#2,#3)|

other

if f ( f ( n ) ) + f ( n ) = 2 n + 3 and f ( 0 ) = 1 , what is the value of f ( 2012 ) ?

"sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 75 2 / 3 sp 1 = 75 sp 1 = 112.50 100 - - - 12.5 = > 12.5 % answer : e"

a ) 20 % , b ) 26 % , c ) 42 % , d ) 27 % , e ) 12.5 %

e

subtract(divide(subtract(const_100, 25), divide(2, 3)), const_100)

divide(n0,n1)|subtract(const_100,n2)|divide(#1,#0)|subtract(#2,const_100)|

gain

if the sum of two numbers is 22 and the sum of their squares is 386 , then the product of the numbers is

n = ( 4 * 5 - 1 ) * 5 * 5 * 5 = 2375 where 4 cases of first digit { 2,4 , 6,8 } 5 cases of second digit { 0 , 2,4 , 6,8 } 1 case of 22 for two leftmost digit 5 cases of third digit { 1 , 3,5 , 7,9 } 5 cases of fourth digit { 1 , 3,5 , 7,9 } 5 cases of fifth digit { 1 , 3,5 , 7,9 } c

a ) 2200 , b ) 2295 , c ) 2375 , d ) 2380 , e ) 2385

c

multiply(add(multiply(const_3, const_4), add(const_3, const_4)), power(5, const_3))

add(const_3,const_4)|multiply(const_3,const_4)|power(n0,const_3)|add(#0,#1)|multiply(#3,#2)

general

if 40 % of a certain number is 160 , then what is 90 % of that number ?

"in one hour , the crow eats 1 / 24 of the nuts . ( 1 / 4 ) / ( 1 / 24 ) = 6 hours the answer is a ."

a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14

a

divide(divide(const_1, const_4), divide(divide(const_1, add(const_2, const_3)), 4))

add(const_2,const_3)|divide(const_1,const_4)|divide(const_1,#0)|divide(#2,n0)|divide(#1,#3)|

general

the general hospital is comprised of , 3 / 5 pediatricians , 1 / 4 surgeons , and the rest are gp doctors . if 1 / 4 of the surgeons are heart surgeons , and the hospital doubles the number of gp doctors , what proportion of the hospital are now heart surgeons ?

"let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1081 96 + 225 + 490 + 6 x = 1081 6 x = 270 = > x = 45 . answer : e"

a ) 25 , b ) 66 , c ) 77 , d ) 99 , e ) 45

e

divide(subtract(subtract(subtract(1081, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6)

multiply(n0,n3)|multiply(n1,n5)|multiply(n2,n6)|subtract(n7,#0)|subtract(#3,#1)|subtract(#4,#2)|divide(#5,n3)|

general

how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ?

"explanation : marked price = rs . 30 c . p . = 100 / 140 * 30 = rs . 21.42 sale price = 90 % of rs . 30 = rs . 27 required gain % = 5.57 / 21.42 * 100 = 26 % . answer : e"

a ) 8 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 26 %

e

multiply(divide(subtract(multiply(divide(30, const_100), subtract(const_100, 10)), divide(multiply(30, const_100), add(40, const_100))), divide(multiply(30, const_100), add(40, const_100))), const_100)

add(n1,const_100)|divide(n0,const_100)|multiply(n0,const_100)|subtract(const_100,n2)|divide(#2,#0)|multiply(#1,#3)|subtract(#5,#4)|divide(#6,#4)|multiply(#7,const_100)|

gain

joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 36400 , how many months will it take joan to pay back her mortgage ?

"prime factors of 30 are 2 ^ 1,3 ^ 1,5 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3,5 , ) = ( 1 + 1 ) ( 1 + 1 ) = 4 since we need odd divisors other than 1 = > 4 - 1 = 3 odd divisors b is the answer"

a ) 3 , b ) 3 , c ) 5 , d ) 6 , e ) 7

b

divide(30, multiply(const_10, const_2))

multiply(const_10,const_2)|divide(n0,#0)|

other

subtracting 30 from a number , the remainder is one fourth of the number . find the number ?

"withoutusing the formula , we can see that today the restaurant served 40 customers above the average . the total amount above the average must equal total amount below the average . this additional 40 customers must offset the “ deficit ” below the average of 80 created on the x days the restaurant served only 75 customers per day . 40 / 5 = 8 days . choice ( a ) . withthe formula , we can set up the following : 80 = ( 75 x + 120 ) / ( x + 1 ) 80 x + 80 = 75 x + 120 5 x = 40 x = 8 answer choice ( d )"

a ) 2 , b ) 5 , c ) 7 , d ) 8 , e ) 20

d

subtract(divide(subtract(120, 80), subtract(80, 75)), divide(subtract(120, const_100), const_100))

subtract(n1,n2)|subtract(n2,n0)|subtract(n1,const_100)|divide(#0,#1)|divide(#2,const_100)|subtract(#3,#4)|

general

two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?

"say x / 3 / 6 * 5 / 6 = x * 6 / 3 * 5 / 6 = x * 5 / 3 e"

a ) 31 ⁄ 5 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 9 ⁄ 20 , e ) 5 ⁄ 3

e

multiply(divide(6, 3), divide(5, 6))

divide(n1,n0)|divide(n2,n3)|multiply(#0,#1)|

general

a boat can travel with a speed of 12 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 68 km downstream .

"then , 15 % of x = 15 ( 15 / 100 ) x = 15 x = ( 15 * 100 * ) / 15 = 100 answer is a"

a ) a ) 100 , b ) b ) 120 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160

a

divide(multiply(15, const_100), 15)

multiply(n1,const_100)|divide(#0,n0)|

gain

a man is walking at a speed of 10 km per hour . after every kilometre , he takes rest for 6 minutes . how much time will be take to cover a distance of 6 kilometres ?

"in one cycle they fill 40 + 30 - 20 = 50 liters 700 = 50 * n = > n = 14 here n = number of cycles . total time = 14 * 3 = 42 as in one cycle there are 3 minutes . thus 42 minutes answer : a"

a ) 42 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these

a

multiply(divide(700, subtract(add(40, 30), 20)), const_3)

add(n1,n2)|subtract(#0,n3)|divide(n0,#1)|multiply(#2,const_3)|

physics

if ( a – b ) is 15 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :

"2 x * x = 72 = > x = 6 answer : a"

a ) 6 , b ) 16 , c ) 8 , d ) 36 , e ) none

a

sqrt(divide(72, const_2))

divide(n0,const_2)|sqrt(#0)|

geometry

a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 26 per kg , then his gain percent is

"us = 20 ds = 30 m = ( 30 + 20 ) / 2 = 25 answer : c"

a ) 11 , b ) 77 , c ) 25 , d ) 88 , e ) 34

c

divide(add(10, 20), const_2)

add(n0,n1)|divide(#0,const_2)|

physics

a man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes . if the ratio between the length and breadth of the park be 3 : 2 , then its area is :

here lcm of 12 and 16 is taken as total work . ( becomes easy to solve ) assume total work = 48 units then workdone by ( a + b ) in one day = 48 / 12 = 4 units similarly , by ( b + c ) in one day = 48 / 16 = 3 units now according to question , a works 5 days , b for 7 days and c for 13 days to complete total work so , 5 a + 7 b + 13 c = 48 units 5 ( a + b ) + 2 ( b + c ) + 11 c = 48 units 5 * 4 + 2 * 3 + 11 c = 48 units 11 c = 22 units c = 2 units ( c does 2 units of work daily ) therefore , 48 / 2 = 24 days c requires 24 days to complete the work alone . answer d

a ) 22 days , b ) 21 days , c ) 25 days , d ) 24 days , e ) 23 days

d

divide(const_1, divide(subtract(const_1, add(divide(5, 12), divide(const_2, 16))), subtract(add(5, 13), 7)))

add(n2,n4)|divide(n2,n0)|divide(const_2,n1)|add(#1,#2)|subtract(#0,n3)|subtract(const_1,#3)|divide(#5,#4)|divide(const_1,#6)

physics

a car going at 40 miles per hour set out on an 60 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ?

let their ages be x and ( x + 20 ) years ( x - 5 ) * 5 = ( x + 20 - 5 ) after solving this we get x = 10 years the age of elder one = 10 + 20 = 30 years so the present ages are 30 and 10 years answer : a

a ) 30 , 10 , b ) 2010 , c ) 3515 , d ) 5117 , e ) 20,17

a

add(20, const_10)

add(n0,const_10)

general

dan can do a job alone in 15 hours . annie , working alone , can do the same job in just 10 hours . if dan works alone for 12 hours and then stops , how many hours will it take annie , working alone , to complete the job ?

( 100 % + 8 % ) * ( 100 % - 6 % ) = 1.08 * 0.94 = 1.0152 = 101.52 % . the net percentage change in the price of the stock is ( + ) 1.52 % the answer is d

a ) 0.2 % , b ) 0.8 % , c ) 1.2 % , d ) 1.52 % , e ) 2 %

d

subtract(multiply(multiply(divide(add(const_100, 8), const_100), divide(subtract(const_100, 6), const_100)), const_100), const_100)

add(n0,const_100)|subtract(const_100,n1)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|multiply(#4,const_100)|subtract(#5,const_100)

general

what is the smallest integer t greater than 1 that leaves a remainder of 1 when divided by any of the integers 6 , 8 , and 10 ?

"400 kg - 1 cubic meter ; 400,000 g - 1 cubic meter ; 400,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 400,000 = 10 / 4 = 2.5 cubic centimeters . answer : b ."

a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5

b

divide(multiply(1,000, 1,000), multiply(400, 1,000))

multiply(n4,n4)|multiply(n1,n4)|divide(#0,#1)|

geometry

the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 4.4 miles in the sixth 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?

"for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 5 k ) ^ 2 - 4 * 2 k * 1 = 0 by solving this equation we get k = 0 , k = 8 / 25 answer : c"

a ) 2 / 7 , b ) 9 / 4 , c ) 8 / 25 , d ) 7 / 1 , e ) 7 / 2

c

divide(power(2, add(2, 2)), power(5, 2))

add(n0,n0)|power(n2,n0)|power(n0,#0)|divide(#2,#1)|

general

the population of a town is 10000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?

"the average number of books per student was 2 means that total of 2 * 25 = 50 books were borrowed ; 2 + 10 + 8 = 20 students borrowed total of 2 * 0 + 10 * 1 + 8 * 2 = 26 books ; so 50 - 26 = 24 books are left to distribute among 25 - 20 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 4 books per student , so total number of books they could have borrowed is 4 * 3 = 12 books . so the 5 th student could have borrowed is 24 - 12 = 12 books . answer : c ."

a ) 8 , b ) 10 , c ) 12 , d ) 13 , e ) 15

c

add(subtract(multiply(25, 2), add(add(10, multiply(8, 2)), multiply(2, 3))), 3)

multiply(n0,n5)|multiply(n4,n5)|multiply(n1,n6)|add(n2,#1)|add(#3,#2)|subtract(#0,#4)|add(n6,#5)|

general

what least number must besubtracted from 427398 so that remaining no . is divisible by 15 ?

"volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 24 ) ^ 2 * h = ( 4 / 3 ) π ( 12 ) ^ 3 = > h = 4 cm answer : b"

a ) 6 cm , b ) 4 cm , c ) 8 cm , d ) 3 cm , e ) 9 cm

b

divide(multiply(const_4, divide(power(12, const_3), power(24, const_2))), const_3)

power(n0,const_3)|power(n1,const_2)|divide(#0,#1)|multiply(#2,const_4)|divide(#3,const_3)|

physics

little john had $ 8.50 . he spent $ 1.25 on sweets and gave to his two friends $ 1.20 and $ 2.20 . how much money was left ?

there are twice as many girls as boys in the class - - > g = 2 b . each girl writes 3 more letters than each boy - - > boys write x letters , girls write x + 3 letters . boys write 24 letters - - > bx = 24 . girls write 90 - 24 = 66 letters - - > ( 2 b ) ( x + 3 ) = 66 - - > 2 bx + 6 b = 66 - - > 2 * 24 + 6 b = 66 - - > b = 3 . bx = 24 - - > 3 x = 24 - - > x = 8 . answer : d .

a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12

d

divide(24, divide(subtract(90, multiply(3, 24)), multiply(3, const_2)))

multiply(n0,n1)|multiply(n0,const_2)|subtract(n2,#0)|divide(#2,#1)|divide(n1,#3)

general

9.009 / 1.001

"speed = ( 5 * 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 * 15 * 60 ) m = 1250 m . correct option : d"

a ) 600 , b ) 750 , c ) 1000 , d ) 1250 , e ) none of these

d

multiply(divide(multiply(5, const_1000), const_60), 15)

multiply(n0,const_1000)|divide(#0,const_60)|multiply(n1,#1)|

physics

if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 23 , find the value of ab .

"let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 14 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 2 m / s a"

a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10

a

divide(add(multiply(6, 3), 14), 10)

multiply(n1,n3)|add(n2,#0)|divide(#1,n0)|

physics

a man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes . if the ratio between the length and breadth of the park be 3 : 2 , then its area is :

"explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8010 = p + ( 54 p / 100 ) 8010 = ( 100 p + 54 p ) / 100 8010 = 154 p / 100 p = ( 8010 * 100 ) / 154 = rs . 5201.298 answer : d"

a ) s . 5266 , b ) s . 5269 , c ) s . 5228 , d ) s . 5201 , e ) s . 52192

d

divide(8010, add(const_1, divide(multiply(6, 9), const_100)))

multiply(n0,n1)|divide(#0,const_100)|add(#1,const_1)|divide(n3,#2)|

gain

two mechanics were working on your car . one can complete the given job in six hours , but the new guy takes 10 hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?

"d number of valid votes = 80 % of 6500 = 5200 . valid votes polled by other candidate = 45 % of 5200 = ( 45 / 100 x 5200 ) = 2340 ."

a ) 2800 , b ) 2700 , c ) 2900 , d ) 2340 , e ) 2300

d

multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 6500)

divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|multiply(#2,#3)|multiply(n2,#4)|

gain

evaluate 35 % of 450 + 45 % of 350

9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 4 is allowed . imo b .

a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7

b

add(divide(9, 3), divide(3, divide(9, 3)))

divide(n0,n1)|divide(n1,#0)|add(#0,#1)

general

in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 5 years older than b , the present age of b is

"21 - 7 * 3 18 - 3 * 3 * 2 15 - 5 * 3 12 - 4 * 3 9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 9 is allowed . imo d ."

a ) 3 , b ) 4 , c ) 5 , d ) d , e ) 7

d

add(divide(21, 3), divide(3, divide(21, 3)))

divide(n0,n1)|divide(n1,#0)|add(#0,#1)|

general

5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3443 , how much was it in the beginning ?

sum of all the 13 results = 13 * 60 = 780 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 780 = 46 . c

a ) 35 , b ) 37 , c ) 46 , d ) 48 , e ) 50

c

subtract(add(multiply(7, 57), multiply(7, 61)), multiply(13, 60))

multiply(n2,n3)|multiply(n2,n5)|multiply(n0,n1)|add(#0,#1)|subtract(#3,#2)

general

50 men shake hands with each other . maximum no of handshakes without cyclic handshakes .

"explanation : all are prime numbers in their order , starting from 23 hence , next number is 67 answer : b"

a ) 53 , b ) 67 , c ) 48 , d ) 59 , e ) 45

b

multiply(43, 23)

multiply(const_3.0,n0)|

general

chocolate bars are sold in packages of 4 or 9 only . if mark bought 97 chocolate bars exactly , what could be the number of large packs mark bought ?

"x / ( 11 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 11 * lowest value of p = 2 * 11 * 2 = 44 answer c"

a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 99

c

multiply(multiply(9, const_2), const_2)

multiply(n0,const_2)|multiply(#0,const_2)|

general

after 6 games , team b had an average of 75 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?

"cp * ( 75 / 100 ) = 1500 cp = 20 * 100 = > cp = 2000 answer : d"

a ) 1400 , b ) 1300 , c ) 1200 , d ) 2000 , e ) 1500

d

divide(1500, subtract(const_1, divide(25, const_100)))

divide(n0,const_100)|subtract(const_1,#0)|divide(n1,#1)|

gain

a trader sells 23 meters of cloth for rs . 529 at the profit of rs . 5 per metre of cloth . what is the cost price of one metre of cloth ?

"the triangle with sides 52 cm , 48 cm and 20 cm is right angled , where the hypotenuse is 52 cm . area of the triangle = 1 / 2 * 48 * 20 = 480 cm 2 answer : a"

a ) 480 cm 2 , b ) 765 cm 2 , c ) 216 cm 2 , d ) 197 cm 2 , e ) 275 cm 2

a

divide(multiply(48, 20), const_2)

multiply(n1,n2)|divide(#0,const_2)|

geometry

what is the average of xx , 2 x 2 x , and 66 ?

"x * ( 95 / 100 ) * ( 85 / 100 ) = 3443 x = 4264 answer : a"

a ) 4264 , b ) 2776 , c ) 4400 , d ) 2871 , e ) 881

a

floor(divide(3443, multiply(divide(subtract(const_100, 5), const_100), divide(subtract(const_100, 15), const_100))))

subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|divide(n2,#4)|floor(#5)|

general

the length of rectangle is thrice its breadth and its perimeter is 72 m , find the area of the rectangle ?

let the sum borrowed be x . then , ( x × 6 × 21 / 00 ) + ( x × 9 × 3 / 100 ) + ( x × 14 × 4 / 100 ) = 11900 ⇒ ( 3 ⁄ 25 x + 27 ⁄ 100 x + 14 ⁄ 25 x ) = 11400 ⇒ 95 ⁄ 100 x = 11900 ⇒ x = ( 11900 × 100 / 95 ) = 12526 hence , sum borrowed = 12,526 answer b

a ) 10,526 , b ) 12,526 , c ) 14,000 , d ) 16,000 , e ) 16,536

b

subtract(divide(11900, add(add(divide(multiply(6, const_2), const_100), divide(multiply(9, 3), const_100)), divide(multiply(14, 4), const_100))), multiply(const_12, const_1000))

multiply(n0,const_2)|multiply(n1,n2)|multiply(n3,n4)|multiply(const_1000,const_12)|divide(#0,const_100)|divide(#1,const_100)|divide(#2,const_100)|add(#4,#5)|add(#7,#6)|divide(n5,#8)|subtract(#9,#3)

gain

what quantity of water should be added to reduce 20 liters of 80 % acidic liquid to 20 % acidic liquid ?

"explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 6 men ’ s 1 day ’ s work = 1 × 6 / 96 = 1 / 16 1 woman ’ s 1 day ’ s work = 1 / 192 4 women ’ s 1 day ’ s work = 1 / 192 × 4 = 1 / 48 1 child ’ s 1 day ’ s work = 1 / 240 10 children ’ s 1 day ’ s work = 1 / 24 therefore , ( 6 men + 4 women + 10 children ) ’ s 1 day ’ s work = 1 / 16 + 1 / 48 + 1 / 24 = 1 / 8 the required no . of days = 8 days answer : option d"

a ) 5 days , b ) 15 days , c ) 28 days , d ) 8 days , e ) 7 days

d

inverse(add(multiply(10, inverse(multiply(24, 10))), add(multiply(inverse(multiply(12, 8)), 6), multiply(inverse(multiply(48, 4)), 4))))

multiply(n0,n1)|multiply(n2,n3)|multiply(n4,n5)|inverse(#0)|inverse(#1)|inverse(#2)|multiply(n6,#3)|multiply(n2,#4)|multiply(n4,#5)|add(#6,#7)|add(#9,#8)|inverse(#10)|

physics

after decreasing 15 % in the price of an article costs rs . 915 . find the actual cost of an article ?

"7 / 8 x - 3 / 4 x = 6 galls 1 / 8 * x = 6 gallons x = 48 gallons answer b"

a ) 25 , b ) 48 , c ) 64 , d ) 80 , e ) 96

b

multiply(6, divide(const_1, subtract(divide(7, 8), divide(3, 4))))

divide(n3,n4)|divide(n1,n2)|subtract(#0,#1)|divide(const_1,#2)|multiply(n0,#3)|

general

the number 150 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?

"t = 120 / 70 * 18 / 5 = 6 sec answer : d"

a ) 3 sec , b ) 4 sec , c ) 5 sec , d ) 6 sec , e ) 7 sec

d

divide(120, multiply(70, const_0_2778))

multiply(n1,const_0_2778)|divide(n0,#0)|

physics

what is the area of a square field whose sides have a length of 16 meters ?

"there are 396 managers and 4 others . the 4 others would compose 2 % of the total number of people if there were 200 people in the room . thus 200 managers must leave . the answer is d ."

a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250

d

divide(subtract(multiply(400, divide(99, const_100)), multiply(400, divide(98, const_100))), subtract(const_1, divide(98, const_100)))

divide(n1,const_100)|divide(n2,const_100)|multiply(n0,#0)|multiply(n0,#1)|subtract(const_1,#1)|subtract(#2,#3)|divide(#5,#4)|

gain

if a wholesaler distributes items to several outlets ( a , b , c and d ) in the ratio of 1 / 12 : 1 / 13 : 1 / 15 : 1 / 2 , then find the total number of items the wholesaler distributes ?

"out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 97 % water and 3 % of non - water , so now 1 pound of non - water composes 3 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.03 = 34 pounds . answer : b ."

a ) 2 , b ) 33 , c ) 92 , d ) 96 , e ) 98

b

multiply(divide(subtract(100, 99), subtract(100, 97)), 100)

subtract(n0,n1)|subtract(n0,n2)|divide(#0,#1)|multiply(#2,n0)|

gain

a fruit seller had some oranges . he sells 40 % oranges and still has 600 oranges . how many oranges he had originally ?

length of the two trains = 600 m + 400 m speed of the first train = x speed of the second train = 48 kmph 1000 / x - 48 = 180 1000 / x - 48 * 5 / 18 = 180 50 = 9 x - 120 x = 68 kmph answer : b

a ) 76 kmph , b ) 68 kmph , c ) 87 kmph , d ) 56 kmph , e ) 10 kmph

b

add(48, multiply(divide(add(400, 600), 180), const_3_6))

add(n0,n1)|divide(#0,n2)|multiply(#1,const_3_6)|add(n3,#2)

physics

a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 18 seconds . due to some problem , two boggies were detached . the train now crosses a telegraph post in

"1 flash = 5 sec for 1 min = 12 flashes so for 1 hour = 12 * 60 = 720 flashes . answer : a"

a ) 720 , b ) 600 , c ) 650 , d ) 700 , e ) 750

a

divide(const_3600, 5)

divide(const_3600,n0)|

physics

if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 23 , find the value of ab .

"each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits . here ' s another way to organize the information . we ' re given [ ( 2222 ) ^ 333 ] [ ( 3333 ) ^ 222 ] we can ' combine ' some of the pieces and rewrite this product as . . . . ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) [ ( 2222 ) ^ 111 ] ( 2222 ) ( 3333 ) = a big number that ends in a 6 taking a number that ends in a 6 and raising it to a power creates a nice pattern : 6 ^ 1 = 6 6 ^ 2 = 36 6 ^ 3 = 216 etc . thus , we know that ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) will be a gigantic number that ends in a 6 . 2 ^ 111 requires us to figure out thecycleof the units digit . . . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 so , every 4 powers , the pattern of the units digits repeats ( 2 , 4 , 8 , 6 . . . . . 2 , 4 , 8 , 6 . . . . ) . 111 = 27 sets of 4 with a remainder of 3 . . . . this means that 2 ^ 111 = a big number that ends in an 8 so we have to multiply a big number that ends in a 6 and a big number that ends in an 8 . ( 6 ) ( 8 ) = 48 , so the final product will be a gigantic number that ends in an 6 . final answer : d"

a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8

d

add(add(const_4, const_3), const_2)

add(const_3,const_4)|add(#0,const_2)|

general

a piece of work can finish by a certain number of men in 100 days . if however , there were 10 men less , it would take 10 days more for the work to be finished . how many men were there originally ?

"40 % of 6 = 2.4 50 % of 6 = 3 shortage is 0.6 so we need to have 0.6 / 50 % to get 50 % alcohol content . = 1.2 b"

a ) a . 0.6 , b ) b . 1.2 , c ) c . 2.1 , d ) d . 3 , e ) e . 5.4

b

subtract(6, multiply(const_2, multiply(divide(40, const_100), 6)))

divide(n1,const_100)|multiply(n0,#0)|multiply(#1,const_2)|subtract(n0,#2)|

gain

a goods bullet train runs at the speed of 72 km / hr and crosses a 250 m long platform in 26 seconds . what is the length of the goods bullet train ?

"54 = ( 3 ^ 3 ) * 2 since 54 is not a perfect square , no of ways = 4 answer d"

a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2

d

subtract(divide(divide(54, const_1), const_3), const_3)

divide(n0,const_1)|divide(#0,const_3)|subtract(#1,const_3)|

general

when x is multiplied by 3 , the result is 18 more than the result of subtracting x from 70 . what is the value of x ?

"explanation : l . c . m of 2400 = 3 x 2 x 2 x 2 x 2 x 2 x 5 x 5 3 , 2 , 5 number of different prime factors is 3 . answer : option c"

a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6

c

add(const_2, const_2)

add(const_2,const_2)|

other

john purchased some shirts and trousers for $ 800 . he paid $ 400 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?

"let arun ' s weight be x kg . according to arun , 63 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 66 . the values satisfying all the above conditions are 64 and 65 . required average = ( 64 + 65 ) / 2 = 64.5 kg answer : b"

a ) 86.5 kg , b ) 64.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg

b

divide(add(66, add(63, const_1)), const_2)

add(n0,const_1)|add(n4,#0)|divide(#1,const_2)|

general

a and b start walking towards each other at 4 pm at speed of 2 kmph and 3 kmph . they were initially 15 km apart . at what time do they meet ?

given ; 2 dog = 3 cat ; or , dog / cat = 3 / 2 ; let cat ' s 1 leap = 2 meter and dogs 1 leap = 3 meter . then , ratio of speed of cat and dog = 2 * 5 / 3 * 4 = 5 : 6 . ' ' answer : 5 : 6 ;

a ) 5 : 6 , b ) 3 : 2 , c ) 4 : 8 , d ) 1 : 2 , e ) 7 : 8

a

divide(multiply(divide(2, 3), 5), 4)

divide(n2,n3)|multiply(n0,#0)|divide(#1,n1)

other

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 ?

"let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 115 % of rs . 1600 = 115 / 100 * 1600 = rs . 1840 . answer : c"

a ) 2000 , b ) 2778 , c ) 1840 , d ) 2778 , e ) 2771

c

multiply(divide(add(const_100, 15), const_100), divide(add(1920, 1280), const_2))

add(n2,const_100)|add(n0,n1)|divide(#0,const_100)|divide(#1,const_2)|multiply(#2,#3)|

gain

a can finish a work in 36 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?

"min value of a / b will be when b is highest and a is lowest - - - > a = 20 and b = 40 so , a / b = 1 / 2 max value of a / b will be when b is lowest and a is highest - - - > a = 30 and b = 30 so , a / b = 1 range is 1 - ( 1 / 2 ) = 1 / 2 . answer should be b"

a ) 1 / 4 , b ) 1 / 2 , c ) 3 / 4 , d ) 1 , e ) 5 / 4

b

subtract(divide(subtract(32, const_1), add(29, const_1)), divide(add(19, const_1), subtract(42, const_1)))

add(n2,const_1)|add(n0,const_1)|subtract(n1,const_1)|subtract(n3,const_1)|divide(#2,#0)|divide(#1,#3)|subtract(#4,#5)|

general

a train 300 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 150 m long ?

"( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 125 x = 2500 answer : e"

a ) 2333 , b ) 2777 , c ) 2688 , d ) 1000 , e ) 2500

e

divide(subtract(125, divide(multiply(6, 2500), const_100)), subtract(divide(5, const_100), divide(6, const_100)))

divide(n1,const_100)|divide(n2,const_100)|multiply(n0,n2)|divide(#2,const_100)|subtract(#0,#1)|subtract(n3,#3)|divide(#5,#4)|

gain

a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 25 hour to row to a place and come back , how far is the place ?

"total time taken by jerry = ( 8 / 40 ) * 60 minutes + 13 minutes + ( 20 / 60 ) * 60 minutes = 35 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 35 / 60 ) hours = 28 * 60 / 35 = 48 miles per hour answer : option a"

a ) 48 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5

a

divide(add(8, 20), add(add(divide(8, 40), divide(13, 60)), divide(20, 60)))

add(n0,n3)|divide(n0,n1)|divide(n2,n4)|divide(n3,n4)|add(#1,#2)|add(#4,#3)|divide(#0,#5)|

physics

in the manufacture of a certain product , 9 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?

first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 18 and c = 1 / 2 into the equation and simplify to get the answer 2109 . option e .

a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 1,316 , e ) 2,109

e

divide(divide(multiply(multiply(18, add(18, const_1)), add(multiply(18, const_2), const_1)), 6), divide(multiply(multiply(18, add(18, const_1)), add(multiply(18, const_2), const_1)), 6))

add(n4,const_1)|multiply(n4,const_2)|add(#1,const_1)|multiply(n4,#0)|multiply(#2,#3)|divide(#4,n3)|divide(#5,#5)

general

how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 1 m x 2 m x 20 cm ?

1 : 8 answer : b

['a ) 1 : 9', 'b ) 1 : 8', 'c ) 1 : 3', 'd ) 1 : 4', 'e ) 1 : 5']

b

power(sqrt(divide(1, 4)), const_3)

divide(n0,n1)|sqrt(#0)|power(#1,const_3)

geometry

the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area e of that hemisphere ?

"if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 30 ) % = ( 100 − 10 √ 70 ) % = 100 - 84 = 16 % answer b"

a ) 20 % , b ) 16 % , c ) 36 % , d ) 64 % , e ) none of these

b

multiply(subtract(const_1, sqrt(divide(subtract(const_100, 30), const_100))), const_100)

subtract(const_100,n0)|divide(#0,const_100)|sqrt(#1)|subtract(const_1,#2)|multiply(#3,const_100)|

geometry

33 1 / 3 % of 240 ?

"s = { hh , tt , ht , th } e = event of getting at most one head . e = { tt , ht , th } . p ( e ) = n ( e ) / n ( s ) = 3 / 4 answer is option c"

a ) 2 / 3 , b ) 1 , c ) 3 / 4 , d ) 2 , e ) 1 / 2

c

negate_prob(divide(const_1, power(const_2, const_3)))

power(const_2,const_3)|divide(const_1,#0)|negate_prob(#1)|

probability

two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 27 seconds . find the length of the faster train ?

"let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 25 = 2 r a = 12 / 5 r and r = 75 a = 180 required total cost = 4 * 180 + 3 * 75 + 5 * 25 = 720 + 225 + 125 = $ 1070 c"

a ) 347 , b ) 987 , c ) 1070 , d ) 1371 , e ) 1667

c

add(add(multiply(4, multiply(divide(24, 10), divide(multiply(25, 6), 2))), multiply(3, divide(multiply(25, 6), 2))), multiply(5, 25))

divide(n1,n0)|multiply(n2,n4)|multiply(n4,n7)|divide(#1,n3)|multiply(#0,#3)|multiply(n6,#3)|multiply(n5,#4)|add(#6,#5)|add(#7,#2)|

general

what is 120 % of 13 / 24 of 600 ?

"percent of students who are 25 years old or older is 0.4 * 48 + 0.2 * 52 = ~ 30 , so percent of people who are less than 25 years old is 100 - 30 = 70 . answer : b ."

a ) 0.9 , b ) 0.7 , c ) 0.45 , d ) 0.3 , e ) 0.25

b

subtract(const_1, multiply(divide(40, const_100), divide(subtract(const_100, 20), const_100)))

divide(n2,const_100)|subtract(const_100,n3)|divide(#1,const_100)|multiply(#0,#2)|subtract(const_1,#3)|

general

after decreasing 90 % in the price of an article costs rs . 320 . find the actual cost of an article ?

"speed = 54 * 5 / 18 = 15 m / sec time taken = 300 * 1 / 15 = 20 sec answer : c"

a ) 17 sec , b ) 16 sec , c ) 20 sec , d ) 14 sec , e ) 12 sec

c

multiply(divide(300, multiply(54, const_1000)), const_3600)

multiply(n1,const_1000)|divide(n0,#0)|multiply(#1,const_3600)|

physics

the average age of 20 men in the class is 15.6 years . 5 new men join and the new average becomes 14.56 years . what was the average age of 5 new men ?

"12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 899 = 279 answer : b"

a ) 270 , b ) 279 , c ) 267 , d ) 255 , e ) 552

b

multiply(divide(899, add(add(multiply(12, 8), multiply(16, 9)), multiply(18, 6))), multiply(16, 9))

multiply(n1,n2)|multiply(n3,n4)|multiply(n5,n6)|add(#0,#1)|add(#3,#2)|divide(n0,#4)|multiply(#5,#1)|

general

find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder

"explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 27 3 x = 27 x = 9 . answer : d"

a ) 12 , b ) 16 , c ) 18 , d ) 9 , e ) 12

d

divide(27, add(const_1, const_2))

add(const_1,const_2)|divide(n0,#0)|

general

a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 325,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?

explanation : given that simple interest for 2 years is rs . 800 i . e . , simple interest for 1 st year is rs . 400 and simple interest for 2 nd year is also rs . 400 compound interest for 1 st year will be 400 and compound interest for 2 nd year will be 832 - 400 = 432 you can see that compound interest for 2 nd year is more than simple interest for 2 nd year by 432 - 400 = rs . 32 i . e , rs . 32 is the interest obtained for rs . 400 for 1 year rate , r = 100 × si / pt = ( 100 × 32 ) / ( 400 × 1 ) = 8 % difference between compound and simple interest for the 3 rd year = simple interest obtained for rs . 832 = prt / 100 = ( 832 × 8 × 1 ) / 100 = rs . 66.56 total difference between the compound and simple interest for 3 years = 32 + 66.56 = rs . 98.56 answer : option b

a ) rs . 48 , b ) rs . 98.56 , c ) rs . 66.56 , d ) rs . 66.58 , e ) none of these

b

add(subtract(832, 800), multiply(832, divide(subtract(832, 800), divide(800, 2))))

divide(n2,n0)|subtract(n1,n2)|divide(#1,#0)|multiply(n1,#2)|add(#3,#1)

general

in a class of 25 students , 2 students did not borrow any books from the library , 10 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?

let x be the value in excess of $ 1,000 . 0.07 x = 94.5 x = $ 1,350 the total value was $ 1,350 + $ 1,000 = $ 2,350 . the answer is a .

a ) $ 2,350 , b ) $ 2,850 , c ) $ 3,250 , d ) $ 3,400 , e ) $ 3,750

a

floor(divide(add(divide(94.5, divide(7, const_100)), 1000), const_1000))

divide(n0,const_100)|divide(n2,#0)|add(n1,#1)|divide(#2,const_1000)|floor(#3)

general

a , b and c start a business each investing 20,000 . after 10 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 71400 was recorded . find the share of b .

": cp = sp * ( 100 / ( 100 + profit % ) ) = 8463 ( 100 / 124 ) = rs . 6825 . answer : b"

a ) 6727 , b ) 6825 , c ) 6728 , d ) 6725 , e ) 2871

b

divide(8463, add(const_1, divide(24, const_100)))

divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)|

gain

yesterday it took robert 4 hours to drive from city a to city b . today it took robert 2.5 hours to drive back from city в to city a along the same route . if he had saved 15 minutes in both trips , the speed for the round trip would be 70 miles per hour . what is the distance between city a and city b ?

"total work = 15 * 4 = 60 beaver hours 20 beaver * x = 60 beaver hours x = 60 / 20 = 3 answer : e"

a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 3 .

e

divide(multiply(4, 15), 20)

multiply(n0,n1)|divide(#0,n2)|

physics

the two trains of lengths 400 m , 600 m respectively , running at same directions . the faster train can cross the slower train in 180 sec , the speed of the slower train is 48 km . then find the speed of the faster train ?

"area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 14 ) = 266 cm 2 answer : c"

a ) 178 cm 2 , b ) 179 cm 2 , c ) 266 cm 2 , d ) 167 cm 2 , e ) 197 cm 2

c

quadrilateral_area(14, 18, 20)

quadrilateral_area(n2,n1,n0)|

physics

if 20 men take 15 days to to complete a job , in how many days can 25 men finish that work ?

a prime number is a number that has only two factors : 1 and itself . therefore , a prime number is divisible by two numbers only . let ' s list the numbers from 61 to 69 . 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 immediately we can eliminate the even numbers because they are divisible by 2 and thus are not prime . we are now left with : 61 , 63 , 65 , 67 , 69 we can next eliminate 65 because 65 is a multiple of 5 . we are now left with 61 , 63 , 67 , 69 . to eliminate any remaining values , we would look at those that are multiples of 3 . if you don ’ t know an easy way to do this , just start with a number that is an obvious multiple of 3 , such as 60 , and then keep adding 3 . we see that 60 , 63 , 66 , 69 are all multiples of 3 and therefore are not prime . thus , we can eliminate 63 and 69 from the list because they are not prime . finally , we are left with 61 and 67 , and we must determine whether they are divisible by 7 . they are not , and therefore they must be both prime . thus , the sum q of 61 and 67 is 128 . answer b .

a ) 67 , b ) 128 , c ) 191 , d ) 197 , e ) 260

b

add(add(60, const_1), subtract(70, const_3))

add(n0,const_1)|subtract(n1,const_3)|add(#0,#1)

general

the distance between 2 cities a and b is 1000 km . a train starts from a at 12 p . m . and travels towards b at 100 km / hr . another starts from b at 1 p . m . and travels towards a at 150 km / hr . at what time do they meet ?

"we have $ 200 and we have to maximize the number of hot dogs that we can buy with this amount . let ' s try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money , which in this case is 400 for $ 22.95 . for the sake of calculation , let ' s take $ 23 . 23 x 8 gives 184 , i . e . a total of 400 x 8 = 3200 hot dogs . we are left with ~ $ 16 . similarly , let ' s use $ 3 for calculation . we can buy 5 20 - pack hot dogs ( 3 x 5 ) , a total of 20 x 5 = 100 hot dogs . so we have 3300 hot dogs . 2108 looks far - fetched ( since we are not likely to be left with > $ 1.55 ) . hence , ( b ) 3300 ( answer b )"

a ) 1,108 , b ) 3,300 , c ) 2,108 , d ) 2,124 , e ) 2,256

b

multiply(divide(200, 22.95), 400)

divide(n6,n5)|multiply(n4,#0)|

general

you need to print a document of the area 216 sq cm . condition is 3 cm margin is to be left at both top & bottom and 2 cm at the sides . what is the optimized size of your paper ?

"you need to primarily find the primes of 990 : 2 , 3,3 , 5,11 the integer must contain all these primes by knowing 11 is an prime , we know the answer can be b , c , d or e as these all contain 11 . 11 = 1 , 2,3 , 4,5 , 6,7 , 8,9 , 10,11 11 contains the 2 , 3,5 and 11 explicitly and the second 3 comes from the 6 ( 2 * 3 ) , therefore the answer is 11 . this is because we know a number that contains all the primes of 990 will be a multiple of 990 . answer : b"

a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14

b

divide(divide(divide(divide(990, const_2), const_3), const_4), divide(const_10, const_2))

divide(n1,const_2)|divide(const_10,const_2)|divide(#0,const_3)|divide(#2,const_4)|divide(#3,#1)|

general

excluding stoppages , the speed of a bus is 80 km / hr and including stoppages , it is 70 km / hr . for how many minutes does the bus stop per hour ?

"sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 3 ans . ( c )"

a ) 1 / 2 , b ) 1 , c ) 1 / 3 , d ) 3 / 4 , e ) 2

c

multiply(subtract(1, divide(1, 2)), subtract(1, divide(1, 3)))

divide(n1,n2)|divide(n1,n5)|subtract(n1,#0)|subtract(n1,#1)|multiply(#2,#3)|

general

each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 3 and the 24 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?

3 * 5 + 5 * 3 = ( 2 x 3 - 3 x 5 + 3 x 5 ) + ( 2 x 5 - 3 x 3 + 5 x 3 ) = 22 answer a 22

a ) 22 , b ) 25 , c ) 26 , d ) 28 , e ) 23

a

add(multiply(2, 3), multiply(3, 5))

multiply(n0,n1)|multiply(n1,n3)|add(#0,#1)

general

if w / x = 1 / 3 and w / y = 4 / 15 , then ( x + y ) / y =

answer : d , ( with different approach ) : the 200 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 200 therefore x = 100,000 total = 200,000 + x = 300,000

a ) $ 180,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 300,000 , e ) $ 2 , 200,000

d

multiply(multiply(200, const_100), const_10)

multiply(n3,const_100)|multiply(#0,const_10)

general