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mathqa_shuffle_question_test

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on a partly cloudy day , milton decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction of the total distance did he cover while the sun was shining on him ?

"a 410 a = ( 72 * 5 / 18 ) * 28 - 150 = 410"

a ) 410 m , b ) 354 m , c ) 450 m , d ) 350 m , e ) 250 m

a

subtract(multiply(28, multiply(72, const_0_2778)), 150)

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

physics

a profit of rs . 900 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?

"explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 170 x + ( x - 170 ) = 208 2 x = 378 x = 189 runs answer : c"

a ) 179 , b ) 367 , c ) 189 , d ) 177 , e ) 191

c

divide(add(170, subtract(multiply(60, 46), multiply(58, subtract(46, const_2)))), const_2)

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

"x 13 : ( t , d , s ) y 14 : ( t , 3 d , s + 1000 mi / hour ) z 15 : ( t + 2 seconds , s , 5 d ) d = ? distance = speed * time x 13 : d = s * t x 14 : 3 d = ( s + 1000 ) * t = = = > 3 d = ts + 1000 t z 15 : 5 d = s * ( t + 2 t ) = = = > 5 d = st + 2 st = = = > 5 d - 2 st = st 3 d = 5 d - 2 st + 1000 t - 2 d = - 2 st + 1000 t 2 d = 2 st - 1000 t d = st - 500 t x 13 : d = s * t st - 500 t = s * t s - 500 = s - 250 = s i got to this point and could n ' t go any further . this seems like a problem where i can set up individual d = r * t formulas and solve but it appears that ' s not the case . for future reference how would i know not to waste my time setting up this problem in the aforementioned way ? thanks ! ! ! the distance of z 15 is equal to five times the distance of x 13 ( we established that x 13 is the baseline and thus , it ' s measurements are d , s , t ) s ( t + 2 ) = 5 ( s * t ) what clues would i have to know to set up the equation in this fashion ? is it because i am better off setting two identical distances together ? st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 1000 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 1000 2 = 500 d = s * t d = 500 * ( 1 / 2 ) d = 250 answer : a"

a ) 250 , b ) 1,600 / 3 , c ) 1,000 , d ) 1,500 , e ) 2,500

a

multiply(divide(1000, 2), divide(const_1, 2))

divide(n8,n3)|divide(const_1,n3)|multiply(#0,#1)|

physics

two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 90 kmph and 70 kmph respectively . in what time will they cross each other completely ?

"we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 35 are employed males , hence 29 % are employed females . ( employed females ) / ( total employed people ) = 29 / 64 = 45 % answer : d ."

a ) 16 % , b ) 25 % , c ) 32 % , d ) 45 % , e ) 52 %

d

multiply(divide(subtract(64, 35), 64), const_100)

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

gain

country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 9 % . if ron imported a $ 18,000 imported car and ended up paying $ 1950 in taxes , what is the first tier ' s price level ?

"in a room of n people , the number of possible handshakes is c ( n , 2 ) or n ( n - 1 ) / 2 so n ( n - 1 ) / 2 = 91 or n ( n - 1 ) = 182 or n = 14 answer is ( a )"

a ) 14 , b ) 12 , c ) 11 , d ) 15 , e ) 16

a

divide(divide(multiply(91, const_2), const_3), const_4)

multiply(n0,const_2)|divide(#0,const_3)|divide(#1,const_4)|

general

a man can do a job in 15 days . his father takes 20 days and his son finishes it in 15 days . how long will they take to complete the job if they all work together ?

"answer given expression = 12008 - 50 ÷ 10.00 = 12008 - 5 = 12003 correct option : d"

a ) 1195 , b ) 120 , c ) 12000 , d ) 12003 , e ) none

d

subtract(multiply(divide(12008, const_100), 50), multiply(divide(const_1, const_3), multiply(divide(12008, const_100), 50)))

divide(n0,const_100)|divide(const_1,const_3)|multiply(n1,#0)|multiply(#1,#2)|subtract(#2,#3)|

general

find the missing figures : ? % of 25 = 20125

"we can write the above in terms of ( a + b ) ( a - b ) 6 ^ 4 − 4 ^ 4 = ( 6 ^ 2 ) 2 - ( 4 ^ 2 ) 2 = ( 6 ^ 2 − 4 ^ 2 ) * ( 6 ^ 2 + 4 ^ 2 ) = ( 36 − 16 ) * ( 36 + 16 ) = > 20 * 52 = 1040 ans option e ."

a ) 20 , b ) 52 , c ) 104 , d ) 520 , e ) 1040

e

divide(power(6, 4), power(6, 4))

power(n0,n1)|power(n0,n3)|divide(#0,#1)|

general

chris age after 13 years will be 5 times his age 5 years back . what is the present age of chris ?

"( 855000 + 220 ) / 900 * 900 = 855000 + 220 = 855220 answer : d"

a ) 854542 , b ) 856945 , c ) 758965 , d ) 855220 , e ) 826450

d

multiply(add(divide(220, 900), 950), 900)

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

general

for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 2 / 3 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?

if a + b = 4.6 assuming a and b are positive then a * b < 10 ( they could be either 1,2 , 3,4 ) therefore a * b = c 2 * b = c a + b = 4.6 three simple equations - divide the 1 st / 2 nd - - > a = 2 plug it the 3 rd - - > b = 2.6 - - > c = 5.2 ( answer b )

a ) 6 , b ) 5.2 , c ) 4 , d ) 3 , e ) 2

b

divide(multiply(subtract(4.6, 2), const_10), add(const_4, const_1))

add(const_1,const_4)|subtract(n1,n0)|multiply(#1,const_10)|divide(#2,#0)

general

renu can do a piece of work in 6 days , but with the help of her friend suma , she can do it in 5 days . in what time suma can do it alone ?

let t be the tier price , p be total price = 18000 per the given conditions : 0.12 t + 0.09 ( p - t ) = 1950 0.12 t + 0.09 * 18000 - 0.09 t = 1950 0.03 t + 1620 = 1950 0.03 t = 1950 - 1620 = 330 t = 330 / 0.03 = 11000 answer b

a ) $ 11500 , b ) $ 11000 , c ) $ 12000 , d ) $ 12100 , e ) $ 12500

b

divide(subtract(1950, multiply(multiply(multiply(const_3, multiply(const_2, const_3)), const_1000), divide(9, const_100))), subtract(divide(12, const_100), divide(9, const_100)))

divide(n1,const_100)|divide(n0,const_100)|multiply(const_2,const_3)|multiply(#2,const_3)|subtract(#1,#0)|multiply(#3,const_1000)|multiply(#0,#5)|subtract(n3,#6)|divide(#7,#4)

general

the product of x and y is a constant . if the value of x is increased by 60 % , by what percentage must the value of y be decreased ?

"( 4 - x ) = x * ( 3 + x ) ( 4 - x ) = 3 x + x ^ 2 0 = x ^ 2 + 4 x - 4 the answer is c ."

a ) - 4 , b ) - 1 , c ) 0 , d ) 1 , e ) 4

c

subtract(multiply(4, 2), 4)

multiply(n2,n0)|subtract(#0,n0)|

general

what is the remainder when 17 ^ 200 is divided by 18 ?

"by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 8 + 7 ) × 12 = 90 . the answer is a ."

a ) 90 , b ) 95 , c ) 104 , d ) 117 , e ) 182

a

divide(multiply(add(add(2, 6), add(2, 6)), subtract(14, 2)), 2)

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

geometry

a and b can do a piece of work in 7 days , b and c in 8 days , c and a in 9 days . how long will c take to do it ?

"time taken to reach = 3000 / 40 = 75 minutes answer : c"

a ) 70 minutes , b ) 72 minutes , c ) 75 minutes , d ) 76 minutes , e ) 77 minutes

c

divide(3000, 40)

divide(n1,n0)|

gain

set a contains all the even numbers between 12 and 50 inclusive . set b contains all the even numbers between 112 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?

"explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 18 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 18 = 2 / 9 therefore , 1 woman ’ s 1 day ’ s work = 1 / 3 – 2 / 9 = 3 - 2 / 9 = 1 / 9 therefore , the woman alone can finish the work in 9 days . answer : option a"

a ) 9 days , b ) 21 days , c ) 24 days , d ) 27 days , e ) 28 days

a

inverse(subtract(inverse(3), add(inverse(6), inverse(18))))

inverse(n0)|inverse(n1)|inverse(n2)|add(#1,#2)|subtract(#0,#3)|inverse(#4)|

physics

by weight , liquid x makes up 1.5 percent of solution p and 6.5 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?

"explanation : let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 | | : : 270 : x time 1 : 4 | = > 6 * 1 * x = 10 * 4 * 270 = > x = ( 10 * 4 * 270 ) / 6 = > x = 1800 answer : d"

a ) 1500 , b ) 1545.6 , c ) 1640.33 , d ) 1800 , e ) none of these

d

multiply(multiply(divide(270, 6), 4), 10)

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

gain

a 14 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?

"the tank is emptied at this rate : 14 + 6 - 5 = 15 cubic inches / min the tank has a volume of 45 * 12 * 12 * 12 = 77760 cubic inches . the time it takes to empty the tank is 77760 / 15 = 5184 minutes . the answer is a ."

a ) 5184 , b ) 5276 , c ) 5368 , d ) 5460 , e ) 5552

a

divide(multiply(45, power(14, 5)), subtract(add(12, 6), 5))

add(n4,n5)|power(n8,n6)|multiply(n0,#1)|subtract(#0,n2)|divide(#2,#3)|

physics

what is rate of interest if principal . amount be 400 , simple interest 80 and time 2 year .

"cost price * 1.13 = selling price - - > cost price * 1.13 = $ 28 - - > cost price = $ 24.78 . answer : c ."

a ) 3.0 , b ) 3.36 , c ) 24.78 , d ) 25.0 , e ) 31.36

c

divide(multiply(28, const_100), add(const_100, 13))

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

gain

the average salary per head of the entire staff of an office including the officers and clerks is rs . 90 . the average salary of officers is rs . 500 and that of the clerks is rs . 84 . if the number of officers is 2 , find the number of officers in the office ?

final number = initial number + 18 % ( original number ) = 86 + 18 % ( 86 ) = 86 + 15 = 101 . answer e

a ) 105 , b ) 95 , c ) 80 , d ) 60 , e ) 101

e

multiply(86, add(const_1, divide(18, const_100)))

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

gain

if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 3720 , r will receive

let the man ' s rate upstream be x kmph and that downstream be y kmph . then , distance covered upstream in 8 hrs 48 min = distance covered downstream in 4 hrs . 44 * x / 5 = 4 * y y = 11 / 5 * x required ratio = ( y + x ) / 2 : ( y - x ) / 2 = 8 / 5 : 3 / 5 = 8 / 3 ans - b

a ) 8 / 5 , b ) 8 / 3 , c ) 3 / 5 , d ) 5 / 8 , e ) 5 / 3

b

divide(divide(add(divide(add(divide(48, const_60), 8), 4), const_1), const_2), divide(subtract(divide(add(divide(48, const_60), 8), 4), const_1), const_2))

divide(n1,const_60)|add(n0,#0)|divide(#1,n2)|add(#2,const_1)|subtract(#2,const_1)|divide(#3,const_2)|divide(#4,const_2)|divide(#5,#6)

physics

if x is equal to the sum of the integers from 40 to 50 , inclusive , and y is the number of even integers from 40 to 50 , inclusive , what is the value of x + y ?

"no . of toys = 100 / 1 = 100 answer : e"

a ) 40 , b ) 54 , c ) 45 , d ) 39 , e ) 100

e

divide(100, 1)

divide(n1,n0)|

physics

find the perimeter and area of the rectangle of length 15 cm and breadth 13 cm .

"20 % of 3000 gives 600 . so 600 attends chess and 40 % of 600 gives 240 so 240 enrolled for swimming answer : a"

a ) 240 , b ) 10 , c ) 100 , d ) 50 , e ) 20

a

divide(multiply(divide(multiply(20, 3000), const_100), 40), const_100)

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

gain

a train running at the speed of 60 km / hr crosses a pole in 6 seconds . find the length of the train .

"p = 280 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 280 * ( 1 + 10 / 100 ) = 280 * ( 11 / 10 ) = 308 answer is e"

a ) 100 , b ) 120 , c ) 200 , d ) 220 , e ) 308

e

add(280, divide(multiply(280, 10), const_100))

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

gain

on dividing 21 by a number , the quotient is 10 and the remainder is 1 . find the divisor .

# of boxes of cookies mary sold = x ann sold 5 times more = 5 x x + 5 x = 18 6 x = 18 x = 18 / 6 = 3 answer : a

a ) 3 , b ) 5 , c ) 6 , d ) 10 , e ) 18

a

divide(18, add(5, const_1))

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

general

kim finds a 4 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ?

8 x + 75 = 9 ( x + 7 ) x = 12 + 7 = 19 answer : b

a ) 12 , b ) 19 , c ) 26 , d ) 33 , e ) 40

b

add(subtract(75, multiply(7, 9)), 7)

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

general

a special municipal payroll tax charges not tax on a payroll less than $ 200,000 and only 0.2 % on a company ’ s payroll above $ 200,000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ?

"explanation : speed in still water = 5 kmph speed of the current = 1 kmph speed downstream = ( 5 + 1 ) = 6 kmph speed upstream = ( 5 - 1 ) = 4 kmph let the requited distance be x km total time taken = 1 hour = > x / 6 + x / 4 = 1 = > 2 x + 3 x = 12 = > 5 x = 12 = > x = 2.4 km . answer : option c"

a ) 3.2 km , b ) 3 km , c ) 2.4 km , d ) 3.6 km , e ) none of these

c

divide(multiply(subtract(5, 1), const_3), 5)

subtract(n0,n1)|multiply(#0,const_3)|divide(#1,n0)|

physics

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 correctly ?

rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 4 x / 5 x * 10 = 8 min ans : e

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

e

divide(multiply(4, 10), add(speed(10, 10), speed(multiply(2, 10), 5)))

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

physics

in a garden , there are 10 rows and 15 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is

"the bottom row has x bricks x + x - 1 + x - 2 + x - 3 = 134 4 x - 6 = 134 4 x = 128 x = 32 answer : c"

a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34

c

divide(subtract(subtract(subtract(subtract(134, const_1), const_2), const_3), const_4), 4)

subtract(n1,const_1)|subtract(#0,const_2)|subtract(#1,const_3)|subtract(#2,const_4)|divide(#3,n0)|

general

the price of stock increased by 8 % last year and decreased by 6 % this year . what is the net percentage change in the price of the stock ?

"total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 20 = 30 cost will be 30 * 3.1 = $ 93 ans : c"

a ) $ 1.60 , b ) $ 16.00 , c ) $ 93.00 , d ) $ 108.00 , e ) $ 196.00

c

multiply(divide(3.10, 20), surface_cube(10))

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

geometry

3 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire cost of the car , then the share of each of the remaining persons increased by :

"9 / 12 = 3 / 4 * 1000 = 750 550 - - - - - - - - - - - - - 200 1 / 4 - - - - - - - - 200 1 - - - - - - - - - ? = > rs . 800 answer : d"

a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 800 , e ) s . 120

d

multiply(divide(subtract(multiply(9, 1000), multiply(multiply(const_3, const_4), 550)), multiply(multiply(const_3, const_4), const_1)), const_4)

multiply(n0,n1)|multiply(const_3,const_4)|multiply(n2,#1)|multiply(#1,const_1)|subtract(#0,#2)|divide(#4,#3)|multiply(#5,const_4)|

general

1 , 3,5 , 7,9 , . . 50 find term of sequnce

start with the prime factorization : 33150 = 50 * 663 = ( 2 * 5 * 5 ) * 3 * 221 = ( 2 ) * ( 3 ) * ( 5 ^ 2 ) * ( 13 ) * ( 17 ) there are five distinct prime factors , { 2 , 3 , 5 , 13 , and 17 } answer : b .

a ) four , b ) five , c ) six , d ) seven , e ) eight

b

add(const_2, const_3)

add(const_2,const_3)

other

in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 40 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?

"in 12 days 12 * 0.06 = 0.72 ounces of water evaporated , which is 0.72 / 24 â ˆ — 100 = 3 of the original amount of water . answer : c ."

a ) 0.003 % , b ) 0.03 % , c ) 3 % , d ) 2 % , e ) 30 %

c

multiply(divide(multiply(0.06, 12), 24), const_100)

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

gain

the length of a rectangular floor is more than its breadth by 200 % . if rs . 450 is required to paint the floor at the rate of rs . 5 per sq m , then what would be the length of the floor ?

solution : let x be the number i chose , then x / 4 â ˆ ’ 18 = 7 x / 4 = 25 x = 100 answer b

a ) 600 , b ) 100 , c ) 800 , d ) 900 , e ) none

b

multiply(add(18, 7), 4)

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

general

what number has a 3 : 4 ratio to the number 400 ?

let ' a ' can be read hindu , let ' b ' can be read times , let ' c ' can be read deccan , from the given data : n ( aubuc ) = 76 , n ( a ) = 54 , n ( b ) = 43 , n ( c ) = 37 , n ( anbnc ) = 15 , n ( anc ) = 24 , n ( bnc ) = 27 , n ( anb ) = ? n ( aubuc ) = n ( a ) + n ( b ) + n ( c ) - n ( anb ) - n ( bnc ) - n ( anc ) + n ( anbnc ) = = > 76 = 54 + 43 + 37 - n ( anb ) - 24 - 27 + 15 = = > n ( anb ) = 54 + 43 + 37 + 15 - 24 - 27 - 76 = = > n ( anb ) = 149 - 127 = = > n ( anb ) = 22 answer : b

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

b

add(subtract(24, 15), subtract(27, 15))

subtract(n5,n4)|subtract(n6,n4)|add(#0,#1)

general

how many factors of 30 are odd numbers greater than 1 ?

"0.8 * ( 1.2 * 100 ) = $ 96 the answer is b ."

a ) $ 88 , b ) $ 96 , c ) $ 100 , d ) $ 106 , e ) $ 110

b

subtract(add(100, divide(multiply(100, 20), const_100)), divide(multiply(add(100, divide(multiply(100, 20), const_100)), 20), const_100))

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

general

if 8 a = 9 b and ab ≠ 0 , what is the ratio of a / 9 to b / 8 ?

"total score of the batsman in 20 matches = 800 . total score of the batsman in the next 30 matches = 600 . total score of the batsman in the 50 matches = 1400 . average score of the batsman = 1400 / 50 = 28 . answer : c"

a ) 31 , b ) 46 , c ) 28 , d ) 13 , e ) 12

c

divide(add(multiply(40, 20), multiply(20, 30)), add(20, 30))

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

general

in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 40 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?

"let x be the first integer in the set , then x + 54 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 54 ) = 55 x + 54 * 55 / 2 = 55 ( x + 27 ) then x + 27 = 101 x = 74 the largest integer in the set is 74 + 54 = 128 the answer is b ."

a ) 126 , b ) 128 , c ) 130 , d ) 132 , e ) 134

b

add(add(power(add(add(divide(subtract(subtract(55, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(55, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(55, const_10), const_2), const_4), const_2), power(add(divide(subtract(subtract(55, const_10), const_2), const_4), const_2), const_2)))

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

a train 110 m long is running with a speed of 30 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?

"a number of valid votes = 80 % of 5000 = 4000 . valid votes polled by other candidate = 45 % of 4000 = ( 45 / 100 x 4000 ) = 1800 ."

a ) 1800 , b ) 2700 , c ) 2900 , d ) 2200 , e ) 2300

a

multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 5000)

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

gain

if 5 a + 7 b = m , where a and b are positive integers , what is the largest possible value of m for which exactly one pair of integers ( a , b ) makes the equation true ?

"let x = ounces of 60 % salt solution to be added . 2 * 50 + . 6 x = . 5 ( 50 + x ) x = 150 answer e"

a ) 16.67 , b ) 30 , c ) 50 , d ) 60.33 , e ) 150

e

divide(subtract(multiply(divide(50, const_100), 50), multiply(divide(20, const_100), 50)), subtract(divide(50, const_100), divide(20, const_100)))

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

gain

the calendar of the year 2040 can be used again in the year ?

index for females = ( 20 - 8 ) / 20 = 3 / 5 = 0.6 index for males = ( 20 - 12 / 20 = 2 / 5 = 0.4 index for females exceeds males by 0.6 - 0.4 = 0.2 answer : c

a ) 0.05 , b ) 0.0625 , c ) 0.2 , d ) 0.25 , e ) 0.6

c

subtract(divide(subtract(20, 8), 20), divide(8, 20))

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

general

a train moves with a speed of 108 kmph . its speed in metres per second is :

let number of packs of four = f let number of packs of nine = n 4 f + 9 n = 97 now , we need to test for values of n . since sum 97 is odd and 4 f will always be even , n ca n ' t be even . now , we can test for values e = 2 , 4 and 6 4 * 4 + 9 * 9 = 16 + 81 = 97 answer d

a ) 3 , b ) 4 , c ) 8 , d ) 9 , e ) 13

d

divide(subtract(97, multiply(4, 4)), 9)

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

general

a man swims downstream 28 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?

"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 . = 120 % of rs . 1600 = 120 / 100 * 1600 = rs . 1920 . answer : d"

a ) 2000 , b ) 2778 , c ) 2299 , d ) 1920 , e ) 2771

d

multiply(divide(add(const_100, 20), 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

average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 860 . what was original rent of friend whose rent is increased ?

"the time spent on section b and section c is 27 minutes each . the ratio of c to a is 27 : 6 = 9 : 2 the answer is b ."

a ) 7 : 1 , b ) 9 : 2 , c ) 8 : 3 , d ) 5 : 2 , e ) 6 : 1

b

divide(3, const_4)

divide(n0,const_4)|

physics

how many 5 - digit numbers are there , if the two leftmost digits are even , the other digits are odd and the digit 2 can not appear more than once in the number .

"on dividing 531742 by 3 we get the remainder 1 , so 1 should be subtracted c"

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

c

subtract(531742, multiply(floor(divide(531742, 3)), 3))

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

general

a man can row 5 kmph in still water . when the river is running at 2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

10 men - working 2 hrs - cut 10 trees 1 men - working 1 hr - cuts = 10 / 10 * 2 thus 8 men - working 3 hrs - cut = 10 * 8 * 3 / 10 * 2 = 12 trees answer is a

a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 20

a

multiply(multiply(subtract(10, 2), divide(divide(10, 2), 10)), 3)

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

physics

a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ' s contribution in the capital

"let the mother ' s present age be x years then the person ' s present age = 2 x / 5 ( 3 x / 5 ) + 8 = 1 / 2 ( x + 8 ) 2 ( 3 x + 40 ) = 5 ( x + 8 ) x = 40 answer is e"

a ) a ) 25 , b ) b ) 44 , c ) c ) 32 , d ) d ) 45 , e ) e ) 40

e

divide(subtract(8, add(const_2, const_3)), subtract(divide(const_1, const_2), divide(const_2, add(const_2, const_3))))

add(const_2,const_3)|divide(const_1,const_2)|divide(const_2,#0)|subtract(n0,#0)|subtract(#1,#2)|divide(#3,#4)|

general

54671 - 10456 - 33466 = ?

"explanation : place value = local value face value = absolute value the place value of 3 in 5769354 is 3 x 100 = 300 the face value of 3 in 5769354 is nothing but 3 . = > 300 x 3 = 900 answer : option a"

a ) 900 , b ) 9000 , c ) 90 , d ) 9 , e ) 0.9

a

multiply(multiply(3, const_1000), 3)

multiply(n0,const_1000)|multiply(n0,#0)|

general

what annual installment will discharge a debt of $ 1092 due in 3 years at 12 % simple interest ?

"here x and y are integers . x ^ 2 = 2 y , xy = 32 . substitute ( x ^ 2 ) / 2 = y in xy = > x ^ 3 = 32 * 2 = > x ^ 3 = 64 . here x 3 is positive , x is also positive . x = 4 then y = 8 . x - y = - 4 so option d is correct"

a ) - 30 , b ) - 20 , c ) - 5 , d ) - 4 , e ) 20

d

subtract(power(multiply(32, 2), const_0_33), divide(32, power(multiply(32, 2), const_0_33)))

multiply(n1,n2)|power(#0,const_0_33)|divide(n2,#1)|subtract(#1,#2)|

general

two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 90 kmph . in how much time will the trains cross each other ?

"c $ 144 given that sp = $ 102 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 102 ) / 85 = 20 * 6 = $ 120 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 120 * 120 ) / 100 = $ 144"

a ) $ 165 , b ) $ 174 , c ) $ 144 , d ) $ 164 , e ) $ 183

c

add(divide(102, subtract(const_1, divide(15, const_100))), multiply(divide(102, subtract(const_1, divide(15, const_100))), divide(20, const_100)))

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

gain

anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 6 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?

"cp * ( 76 / 100 ) = 912 cp = 12 * 100 = > cp = 1200 answer : c"

a ) 226 , b ) 255 , c ) 1200 , d ) 2771 , e ) 332

c

divide(912, subtract(const_1, divide(24, const_100)))

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

gain

the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 35 % profit ?

first selling price = 110 % - - - - - > x rupees = sold at for rs . 60 / - = 120 % - - - - - > x + 60 rupees ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 10 % - - - - - - - - > 60 100 % - - - - - - - > rs . 600 / - option ' b '

a ) rs . 500 , b ) rs . 600 , c ) rs . 650 , d ) rs . 760 , e ) rs . 800

b

multiply(divide(60, subtract(20, 10)), const_100)

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

general

by selling an article at rs . 300 , a profit of 25 % is made . find its cost price ?

"speed = ( 10 / 20 * 60 ) km / hr = ( 30 * 5 / 18 ) m / sec = 8.333333 m / sec . length of the train = 8.333333 * 6 = 50 m . answer : a"

a ) 50 , b ) 80 , c ) 120 , d ) 100 , e ) 40

a

divide(10, subtract(divide(10, 20), 6))

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

physics

today jim is twice as old as fred , and sam is 4 years younger than fred . 4 years ago jim was 8 times as old as sam . how old is jim now ?

"x = √ 7 and y also = √ 7 applying the function ( √ 7 + √ 7 ) ^ 2 - ( √ 7 - √ 7 ) ^ 2 = ( 2 √ 7 ) ^ 2 - 0 = 4 x 7 = 28 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 7 and y = √ 7 you get the answer 28 . answer e"

a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 28

e

power(add(sqrt(7), sqrt(7)), 2)

sqrt(n2)|add(#0,#0)|power(#1,n0)|

general

a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 10 as remainder . find the no . is ?

man and days concept . . . 6 m * 80 d = m * 16 d solve it , total no of people required is 30 ; answer : c

a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50

c

divide(multiply(6, 80), 16)

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

physics

kathleen can paint a room in 2 hours , and anthony can paint an identical room in 7 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?

"the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is b ."

a ) 10 , b ) 10.5 , c ) 11 , d ) 11.5 , e ) 12

b

divide(subtract(multiply(10, 15), multiply(add(const_4, const_1), 9)), 10)

add(const_1,const_4)|multiply(n0,n1)|multiply(n2,#0)|subtract(#1,#2)|divide(#3,n0)|

general

a satellite is composed of 30 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 6 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?

"explanation : since 312 inch = 140 km so 1 inch = 140 / 312 km so 34 inch = ( 140 ã — 34 ) / 312 = 15.25 km answer : d"

a ) 14.83 , b ) 14.81 , c ) 14.8 , d ) 15.25 , e ) 14.12

d

divide(multiply(34, 140), 312)

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

physics

liz drove from point a to point b at 40 km / h . on her way back she drove at 50 km / h and therefore her way back lasted one hour less . what is the distance ( in km ) between a and b ?

"a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 40 % discount then the original price of it was x * 0.6 = $ 14 - - > x = $ 23,33 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 23,33 + 21 = $ 44,33 . answer : d ."

a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 44.33 , e ) $ 40.60

d

add(multiply(35, divide(40, const_100)), 35)

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

gain

how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 57 ?

"solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 8 / 100 x 12000 ) = rs . 960 . answer c"

a ) rs . 500 , b ) rs . 600 , c ) rs . 960 , d ) rs . 720 , e ) none

c

multiply(multiply(100, divide(add(add(multiply(const_10, const_1000), multiply(const_4, const_1000)), multiply(const_4, 100)), add(100, multiply(100, divide(20, 100))))), divide(8, 100))

divide(n3,n1)|divide(n2,n1)|multiply(const_10,const_1000)|multiply(const_1000,const_4)|multiply(n1,const_4)|add(#2,#3)|multiply(n1,#1)|add(#5,#4)|add(n1,#6)|divide(#7,#8)|multiply(n1,#9)|multiply(#0,#10)|

gain

a reduction of 10 % in the price of tea enables a dealer to purchase 25 kg more tea for rs . 22500 . what is the reduced price per kg of tea ?

principal = ( 100 * 1500 ) / ( 12 * 20 ) = rs . 625 answer : a

a ) 625 , b ) 700 , c ) 950 , d ) 825 , e ) 630

a

divide(divide(multiply(1500, const_100), 20), 12)

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

gain

a certain fruit stand sold apples for $ 0.70 each and guava for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.30 , what total number of apples and bananas did the customer purchase ?

time taken by lewis to reach tirupati = 160 / 80 = 2 hours in 2 hours , david travels 60 * 2 = 120 miles so distance at which they meet should be greater than 120 miles . only b satisfies . answer is b .

a ) 100 mlies , b ) 120 miles , c ) 90 miles , d ) 95 miles , e ) 110 miles

b

multiply(const_2, 60)

multiply(n1,const_2)

physics

find the value of ( 950 + 220 / 900 ) × 900

"the number needs to be divisible by 2 ^ 2 * 3 , 2 * 7 , and 2 * 3 * 7 . the smallest such perfect square is 2 ^ 2 * 3 ^ 2 * 7 ^ 2 = 1764 the answer is d ."

a ) 900 , b ) 1089 , c ) 1600 , d ) 1764 , e ) 2025

d

add(multiply(multiply(multiply(12, power(const_3, const_2)), 14), const_2), multiply(14, 42))

multiply(n1,n2)|power(const_3,const_2)|multiply(n0,#1)|multiply(n1,#2)|multiply(#3,const_2)|add(#4,#0)|

geometry

24 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?

"let the amount lent at 7 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 450 = > x = 5000 amount lent at 10 % = 1000 required ratio = 5000 : 1000 = 5 : 1 answer : a"

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

a

divide(divide(subtract(multiply(450, const_100), multiply(6000, 7)), subtract(10, 7)), divide(subtract(multiply(450, const_100), multiply(6000, 7)), subtract(10, 7)))

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

gain

3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 10 pumps work to empty the tank in 1 day ?

"x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.6 x ( 120 ) i . e . 160 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 160 = 62.5 i . e . y decreases from 100 to 62.5 i . e . decrease of 37.5 % answer : option d"

a ) 30 % , b ) 32 % , c ) 35 % , d ) 37.5 % , e ) 40 %

d

multiply(subtract(const_1, divide(const_100, add(const_100, 60))), const_100)

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

general

a store sells 2 kinds of jelly beans mixes ( a and b ) both made up of red and yellow beans . if b contains 20 % more red beans than a but 10 % fewer yellow beans . and jar a contains twice as many red beans as yellow by what percent is the number of beans in jar b larger than the number in jar a

if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 400 . so 1 / 4 of her savings is $ 400 . so her original savings are 4 times $ 400 = $ 1600 correct answer b

a ) $ 1500 , b ) $ 1600 , c ) $ 1700 , d ) $ 1800 , e ) $ 1900

b

divide(400, subtract(const_1, divide(3, 4)))

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

general

the cost price of a radio is rs . 1500 and it was sold for rs . 1230 , find the loss % ?

the total distance is 1 × 50 + 3 × 60 = 2301 × 50 + 3 × 60 = 230 . and the total time is 4 hours . hence , average speed = ( total distancetotal time ) = 2304 = 57.5 b

a ) 56 , b ) 57.5 , c ) 58.9 , d ) 61.4 , e ) 62

b

divide(add(multiply(50, 1), multiply(60, 3)), add(3, 1))

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

physics

in the faculty of reverse - engineering , 100 second year students study numeric methods , 300 second year students study automatic control of airborne vehicles and 200 second year students study them both . how many students are there in the faculty if the second year students are approximately 40 % of the total ?

"explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 15 kmph x 1 hr = 15 km total southward prasanna ' s distance = 45 kmph x 1 hr = 45 km total distance between prasanna and laxmi is = 15 + 45 = 60 km . answer : e"

a ) 11 , b ) 50 , c ) 28 , d ) 27 , e ) 60

e

add(15, 45)

add(n0,n1)|

physics

let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 16 , what is the maximum value of y for which f ( x , y ) = 0 ?

in 84 minutes , car x travels 49 miles . car y gains 7 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is d .

a ) 140 , b ) 175 , c ) 210 , d ) 245 , e ) 270

d

multiply(35, divide(multiply(divide(84, const_60), 35), subtract(42, 35)))

divide(n1,const_60)|subtract(n2,n0)|multiply(n0,#0)|divide(#2,#1)|multiply(n0,#3)

physics

the maximum number of students among them 848 pens and 630 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?

solution c ( 100 ) = 600 * 100 + 5500 = 125500 $ answer a

a ) 65500 $ , b ) 125800 $ , c ) 125900 $ , d ) 6500 $ , e ) 122500 $

a

add(multiply(100, 600), 5500)

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

general

the average of first five multiples of 6 is

the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 14 numbers . answer : c .

['a ) 12', 'b ) 13', 'c ) 14', 'd ) 15', 'e ) 16']

c

add(10, const_4)

add(n0,const_4)

geometry

how many seconds will a 200 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?

"m = 11 s = 1.2 ds = 12.2 us = 9.8 x / 12.2 + x / 9.8 = 1 x = 5.43 d = 5.43 * 2 = 10.87 answer : e"

a ) 6.24 km , b ) 6 km , c ) 5.76 km , d ) 5.66 km , e ) 10.87 km

e

multiply(divide(multiply(add(11, 1.2), subtract(11, 1.2)), add(add(11, 1.2), subtract(11, 1.2))), const_2)

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

physics

if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 284 pounds . what is jake ’ s present weight , in pounds ?

"h . c . f = ( product of the numbers ) / ( their l . c . m ) = 38880 / 720 = 54 . answer : d"

a ) 50 , b ) 30 , c ) 125 , d ) 54 , e ) none of these

d

divide(38880, 720)

divide(n1,n0)|

physics

how many cuboids of length 5 m , width 3 m and height 2 m can be farmed from a cuboid of 18 m length , 15 m width and 2 m height .

"a + b + c = 400 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 400 - - - - - - - - - - - - - - - - c = 150 answer : a"

a ) a ) 150 , b ) b ) 140 , c ) c ) 130 , d ) d ) 120 , e ) e ) 110

a

subtract(add(200, 350), 400)

add(n1,n2)|subtract(#0,n0)|

general

a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 10 sq . feet , how many feet of fencing will be required ?

explanation : let the total sale be rs . x . then , 2.5 % . of x = 12.50 < = > ( 25 / 100 * 1 / 100 * x ) = 125 / 10 < = > x = 500 . answer : b ) 500

a ) 333 , b ) 500 , c ) 887 , d ) 299 , e ) 132

b

divide(12.5, divide(2.5, const_100))

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

gain

if 5 ^ 5 × 5 ^ x = ( 125 ) ^ 4 , then what is the value of x ?

an empty wooden vessel weighs 20 % of its total weight when filled with paint : vessel = 0.2 ( vessel + paint ) ; 20 v = v + p ( so the weight of completely filled vessel is 10 v ) p = 19 v ( so the weight of the paint when the vessels is completely filled is 19 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 20 v ; p ' = 9 v ( so the weight of the paint when the vessels is partially filled is 9 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 9 v / 19 v = 9 / 19 . answer : d .

a ) 3 / 5 , b ) 5 / 9 , c ) 1 / 24 , d ) 9 / 19 , e ) 2 / 5

d

divide(subtract(divide(20, const_2), const_1), subtract(20, const_1))

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

gain

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

"900 - - - - 90 100 - - - - ? = > 10 % answer : e"

a ) 39 % , b ) 20 % , c ) 23 % , d ) 74 % , e ) 10 %

e

multiply(divide(subtract(990, 900), 900), const_100)

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

gain

what is the compound interest on rs . 8500 at 7.5 % p . a . compounded half - yearly for 2 1 / 2 years .

"( 0.0066 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.006 ) = 0.0060 * 360 / 4 * ( 0.1 ) ( 0.006 ) = 0.066 * 90 / 1 * 0.006 = 66 * 90 / 6 = 11 * 90 = 990 answer : a"

a ) 990 , b ) 99.0 , c ) 9.9 , d ) 0.99 , e ) 0.099

a

divide(multiply(0.0066, 3.6), multiply(multiply(0.04, 0.1), 0.006))

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

general

the current in a river is 5 mph . a boat can travel 20 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?

"0.09 * 0.05 = 0.0045 = 0.45 % the answer is b ."

a ) 0.15 % , b ) 0.45 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %

b

multiply(9, divide(5, const_100))

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

gain

alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 3,200 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ?

"prime numbers between 0 and 30 - 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 sum , c = 129 c / 3 = 43 answer e"

a ) 155 , b ) 129 , c ) 61 , d ) 47 , e ) 43

e

add(divide(3, const_10), power(const_2, add(const_2, const_4)))

add(const_2,const_4)|divide(n2,const_10)|power(const_2,#0)|add(#1,#2)|

general

the price of stock increased by 8 % last year and decreased by 6 % this year . what is the net percentage change in the price of the stock ?

required difference = [ 3 ½ % of rs . 9600 ] – [ 3 1 / 3 % of rs . 9600 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 9600 = 1 / 6 % of rs . 9600 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 9600 ] = rs . 16 . answer is e .

a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 16

e

divide(multiply(subtract(add(divide(1, 2), 3), add(divide(1, 3), 3)), 9600), const_100)

divide(n1,n2)|divide(n1,n0)|add(n0,#0)|add(n0,#1)|subtract(#2,#3)|multiply(n6,#4)|divide(#5,const_100)

general

60 boys can complete a work in 24 days . how many men need to complete twice the work in 20 days

for an income of rs . 8 , investment = rs . 100 . for an income of rs . 6 , investment = rs . 100 x 6 = rs . 75 . 8 market value of rs . 100 stock = rs . 75 . answer : b

a ) 33 , b ) 75 , c ) 44 , d ) 27 , e ) 91

b

multiply(divide(const_100, 8), 6)

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

gain

what is the probability for a family with 3 children to have a girl and two boys ( assuming the probability of having a boy or a girl is equal ) ?

"let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 16 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 16 solve for x x = $ 28.44 correct answer b"

a ) $ 18.44 , b ) $ 28.44 , c ) $ 48.44 , d ) $ 58.44 , e ) $ 38.44

b

divide(multiply(multiply(const_100, const_100), 16), subtract(multiply(subtract(const_100, 25), const_100), multiply(subtract(const_100, 25), 25)))

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

gain

a line that passes through ( – 1 , – 4 ) and ( 2 , k ) has a slope = k . what is the value of k ?

"note : majority ( 20 % ) = difference in votes polled to win ( 60 % ) & defeated candidates ( 40 % ) 20 % = 60 % - 40 % 20 % - - - - - > 280 ( 20 × 14 = 280 ) 100 % - - - - - > 1400 ( 100 × 14 = 1400 ) a )"

a ) 1400 , b ) 1600 , c ) 1800 , d ) 2000 , e ) 2100

a

divide(multiply(const_100, 280), subtract(60, subtract(const_100, 60)))

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

gain

if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 15 - m ) then m = ?

"work done by 5 women in 1 day = 1 / 16 work done by 1 woman in 1 day = 1 / ( 16 × 5 ) work done by 16 men in 1 day = 1 / 8 work done by 1 man in 1 day = 1 / ( 8 × 16 ) ratio of the capacity of a man and woman = 1 / ( 8 × 16 ) : 1 / ( 16 × 5 ) = 1 / 8 : 1 / 5 = 1 / 8 : 1 / 5 = 5 : 8 option e"

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

e

divide(divide(const_1, multiply(add(16, const_2), const_10)), divide(const_1, multiply(16, const_10)))

add(n0,const_2)|multiply(n0,const_10)|divide(const_1,#1)|multiply(#0,const_10)|divide(const_1,#3)|divide(#4,#2)|

physics

the difference of 2 digit number & the number obtained by interchanging the digits is 36 . what is the sum and the number if the ratio between the digits of the number is 1 : 2 ?

given h = 60 cm and r = 5 / 2 cm total surface area = 2 π rh + 2 & pir ( power 2 ) = 2 π r ( h + r ) = [ 2 × 22 / 7 × 5 / 2 × ( 60 + 5 / 2 ) ] cm ( power 2 ) = [ 44 / 7 × 5 / 2 × ( ( 120 + 5 ) / 2 ) ] cm ( power 2 ) = 22 / 7 × 5 × 125 / 2 cm ( power 2 ) = ( 55 × 125 ) / 7 cm ( power 2 ) = 6875 / 7 cm ( power 2 ) = 982.14 cm ( power 2 ) answer is c .

['a ) 918.14', 'b ) 981.41', 'c ) 982.14', 'd ) 928.41', 'e ) none of them']

c

surface_cylinder(divide(5, const_2), 60)

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

geometry

two pipes can fill a tank in 20 minutes and 12 minutes . an outlet pipe can empty the tank in 10 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?

"suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 7 7 / x = 1 / 7 x = 49 hours answer is d"

a ) 25 hr , b ) 35 hr , c ) 40 hr , d ) 49 hr , e ) 50 hr

d

multiply(add(add(multiply(const_2, const_2), const_2), const_1), 7)

multiply(const_2,const_2)|add(#0,const_2)|add(#1,const_1)|multiply(n1,#2)|

physics

two employees x and y are paid a total of rs . 660 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?

"let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 27 3 x = 27 = > x = 9 = > smaller number = 5 x = 45 . answer : c"

a ) 25 , b ) 66 , c ) 45 , d ) 88 , e ) 44

c

divide(multiply(27, 5), const_4)

multiply(n0,n2)|divide(#0,const_4)|

other

how many seconds does sandy take to cover a distance of 600 meters , if sandy runs at a speed of 18 km / hr ?

amount earned using her cell phone = 70 * 22 = 1540 earned for remaining surveys = 30 * 20 = 600 total earning = 2140 answer : a

a ) 2140 , b ) 1140 , c ) 550 , d ) 650 , e ) 750

a

add(multiply(20, 100), multiply(70, multiply(20, divide(10, const_100))))

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

gain

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 ?

"0.1 x = 0.08 ( 2000 - x ) + 38 0.18 x = 198 x = 1100 then the amount invested at 8 % is $ 2000 - $ 1100 = $ 900 the answer is c ."

a ) $ 700 , b ) $ 800 , c ) $ 900 , d ) $ 1100 , e ) $ 1200

c

subtract(multiply(multiply(const_100, 10), const_2), divide(add(multiply(multiply(10, 8), const_2), 38), add(divide(10, const_100), divide(8, const_100))))

divide(n0,const_100)|divide(n1,const_100)|multiply(n0,const_100)|multiply(n0,n1)|add(#0,#1)|multiply(#2,const_2)|multiply(#3,const_2)|add(n4,#6)|divide(#7,#4)|subtract(#5,#8)|

general

the true discount on a bill due 9 months hence at 16 % per annum is rs . 171 . the amount of the bill is

"in 4 miles , initial 1 / 5 mile charge is $ 2 rest of the distance = 4 - ( 1 / 5 ) = 19 / 5 rest of the distance charge = 19 ( 0.4 ) = $ 7.6 ( as the charge is 0.4 for every 1 / 5 mile ) = > total charge for 4 miles = 2 + 7.6 = 9.6 answer is d"

a ) $ 4.60 , b ) $ 9.80 , c ) $ 19.60 , d ) $ 9.60 , e ) $ 29.60

d

add(2.00, multiply(subtract(divide(2.00, divide(1, 5)), 1), 0.40))

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

general

the radius of a wheel is 12.6 cm . what is the distance covered by the wheel in making 200 resolutions ?

"the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 42 / 3 = 14 kmph . answer : c"

a ) 16 kmph , b ) 18 kmph , c ) 14 kmph , d ) 79 kmph , e ) 27 kmph

c

subtract(42, divide(multiply(42, const_2), const_3))

multiply(n0,const_2)|divide(#0,const_3)|subtract(n0,#1)|

physics

12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 12 hours a day , the number of men required ?

"sp = 300 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 300 * [ 100 / ( 100 + 25 ) ] = 300 * [ 100 / 125 ] = rs . 240 answer : c"

a ) s . 486 , b ) s . 455 , c ) s . 240 , d ) s . 480 , e ) s . 489

c

divide(multiply(300, const_100), add(const_100, 25))

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

gain

the lengths of the diagonals of a rhombus are 20 and 48 meters . find the perimeter of the rhombus ?

"explanation : ( 25000 × ( 1 + 12100 ) 3 ) = > 25000 × 2825 × 2825 × 2825 = > 35123.20 so compound interest will be 35123.20 - 25000 = rs 10123.20 answer : a"

a ) rs 10123.20 , b ) rs 10123.30 , c ) rs 10123.40 , d ) rs 10123.50 , e ) none of these

a

subtract(multiply(multiply(multiply(const_4, const_100), const_100), power(add(const_1, divide(12, const_100)), 3)), multiply(multiply(const_4, const_100), const_100))

divide(n2,const_100)|multiply(const_100,const_4)|add(#0,const_1)|multiply(#1,const_100)|power(#2,n1)|multiply(#3,#4)|subtract(#5,#3)|

gain

one pump drains one - half of a pond in 1 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?

number of runs scored more to increase the ratio by 1 is 26 - 14 = 12 to raise the average by one ( from 14 to 15 ) , he scored 12 more than the existing average . therefore , to raise the average by five ( from 14 to 19 ) , he should score 12 x 5 = 60 more than the existing average . thus he should score 14 + 60 = 74 . answer d

a ) 12 , b ) 18 , c ) 25 , d ) 74 , e ) 88

d

subtract(multiply(19, add(subtract(26, 15), const_1)), multiply(14, subtract(26, 15)))

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

general

how many of the positive divisors of 240 are also multiples of 4 not including 240 ?

"explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 30 + 1 / 30 ] = 10 [ 1 + 1 / 30 ] = 2 / 3 a complete remaining work in 2 / 3 * 30 = 20 total work = 10 + 20 = 30 days answer : option a"

a ) 30 days , b ) 35 days , c ) 40 days , d ) 45 days , e ) 50 days

a

divide(subtract(10, add(divide(10, 30), divide(10, 30))), divide(10, 30))

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

physics

pipe a can fill a tank in 9 hours . due to a leak at the bottom , it takes 12 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?

there are 520 players , only 1 person wins , 519 players lose . in order to lose , you must have lost a game . 519 games . ans - b

a ) 511 , b ) 519 , c ) 256 , d ) 255 , e ) 1023

b

add(add(add(add(add(add(add(divide(divide(divide(520, const_2), const_2), const_2), add(divide(520, const_2), divide(divide(520, const_2), const_2))), divide(divide(divide(divide(520, const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2))

divide(n0,const_2)|divide(#0,const_2)|add(#0,#1)|divide(#1,const_2)|add(#2,#3)|divide(#3,const_2)|add(#4,#5)|divide(#5,const_2)|add(#6,#7)|divide(#7,const_2)|add(#8,#9)|divide(#9,const_2)|add(#10,#11)|divide(#11,const_2)|add(#12,#13)|divide(#13,const_2)|add(#14,#15)

general

there are 6 people in the elevator . their average weight is 150 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .

( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22 or , [ 7 w + 6 + 3 ( 9 w + 8 ) ] / 6 = 22 or , 7 w + 6 + 27 w + 24 = 132 or , 34 w + 30 = 132 or , 34 w = 132 - 30 or , 34 w = 102 or , w = 102 / 34 therefore , w = 3 answer : c

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

c

divide(subtract(multiply(multiply(2, 6), 22), add(multiply(8, 6), multiply(2, 6))), add(multiply(9, 6), multiply(7, const_2)))

multiply(n1,n5)|multiply(n1,n4)|multiply(n1,n3)|multiply(n0,const_2)|add(#1,#0)|add(#2,#3)|multiply(n6,#0)|subtract(#6,#4)|divide(#7,#5)

general

a certain country is divided into 6 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 18 the total number of progressives in the entire country , what fraction of the country is traditionalist ?

"answer = b = 2 f ( x ) = 3 x – 5 2 * [ f ( x ) ] – 7 = f ( 3 x – 6 ) 2 ( 3 x - 5 ) - 7 = 3 ( 3 x - 6 ) - 5 6 x - 17 = 9 x - 23 x = 2"

a ) 0 , b ) 2 , c ) 6 , d ) 7 , e ) 13

b

divide(subtract(add(multiply(2, 5), 7), add(multiply(3, 3), 5)), subtract(multiply(2, 3), multiply(3, const_1)))

multiply(n1,n2)|multiply(n4,n0)|multiply(n0,n2)|multiply(n0,const_1)|add(n3,#0)|add(n1,#1)|subtract(#2,#3)|subtract(#4,#5)|divide(#7,#6)|

general

if $ 1088 are divided between worker a and worker b in the ratio 5 : 11 , what is the share that worker b will get ?

"sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 750 + 750 ) m = 1500 m . required time = ( 1500 x 6 / 125 ) sec = 72 sec . answer d"

a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 72 sec , e ) none

d

multiply(multiply(750, inverse(multiply(add(45, 30), const_0_2778))), const_2)

add(n1,n2)|multiply(#0,const_0_2778)|inverse(#1)|multiply(n0,#2)|multiply(#3,const_2)|

physics

what is the tens digit of 36 ^ 5 ?

let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 4800 12 x ^ 2 = 4800 x ^ 2 = 400 x = 20 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 80 the answer is c .

['a ) 1 : 72', 'b ) 1 : 76', 'c ) 1 : 80', 'd ) 1 : 84', 'e ) 1 : 88']

c

divide(divide(sqrt(multiply(const_3, 4800)), const_2), 4800)

multiply(n2,const_3)|sqrt(#0)|divide(#1,const_2)|divide(#2,n2)

geometry

a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a .

"x - - - - - - - 7 ( x + 10 ) - - - - 6 x * 7 = ( x + 10 ) 6 x = 60 \ answer : c"

a ) 22 , b ) 20 , c ) 60 , d ) 71 , e ) 11

c

divide(multiply(multiply(3, const_2), 10), subtract(7, multiply(3, const_2)))

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

physics

two pipes a and b can fill a tank in 36 hours and 45 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?

x can have at most 3 prime factors , namely the prime factors 2 and 3 , plus one other . if x had more than this number of prime factors , then ( 6 ) ( x ^ 2 ) would have more than 3 prime factors . the answer is c .

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

c

multiply(3, const_1)

multiply(n2,const_1)

general