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mathqa_shuffle_question_test

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p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 15 days to complete the same work . then q alone can do it in

area of triangle is 1 / 2 * 12 * 8 = 48 side of square = x the entire triangle split into two right angled triangle and one square with dimensions as follows i ) square with side x ii ) right angled triangle with perpendicular sides x and 12 - x iii ) right angled triangle with perpendicular sides 8 - x and x sum of area of all three = 48 = x 2 + 1 / 2 * x * ( 12 - x ) + 1 / 2 * x * ( 8 - x ) = 48 = x = 4.8 cm answer : a

['a ) 4.8 cm', 'b ) 4.4 cm', 'c ) 4.9 cm', 'd ) 5.0 cm', 'e ) 5.2 cm']

a

divide(divide(multiply(12, 8), const_2), const_10)

multiply(n0,n1)|divide(#0,const_2)|divide(#1,const_10)

geometry

one pump drains one - half of a pond in 7 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 ?

"probability of first member an english teacher = 3 / 9 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 9 x 2 / 8 = 1 / 12 ( b )"

a ) 2 / 3 , b ) 1 / 12 , c ) 2 / 9 , d ) 1 / 2 , e ) 1 / 24

b

multiply(divide(3, add(add(3, 4), 2)), divide(2, subtract(add(add(3, 4), 2), const_1)))

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

probability

in town x , 64 percent of the population are employed , and 35 percent of the population are employed males . what percent of the employed people in town x are females ?

b runs 56 m in 7 sec . = > b runs 160 m in 7 / 56 * 160 = 20 seconds since a beats b by 7 seconds , a runs 160 m in ( 20 - 7 ) = 13 seconds hence , a ' s time over the course = 13 seconds answer : c

a ) 22 seconds , b ) 12 seconds , c ) 13 seconds , d ) 18 seconds , e ) 28 seconds

c

subtract(multiply(divide(7, 56), 160), 7)

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

physics

right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 7 ≤ x ≤ 1 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?

let . 002 / x = . 01 ; then x = . 002 / . 01 = . 2 / 1 = . 2 answer is a

a ) . 2 , b ) . 09 , c ) . 009 , d ) . 0009 , e ) none of them

a

divide(divide(2, const_1000), divide(1, const_100))

divide(n0,const_1000)|divide(n1,const_100)|divide(#0,#1)

general

there are 3 prizes to be distributed among 10 students . if no students gets more than one prize , then this can be done in ?

"filling rate - leak rate = net rate 1 / 7.5 - leak rate = 1 / 8 leak rate = 2 / 15 - 1 / 8 = 1 / 120 the answer is c ."

a ) 80 , b ) 100 , c ) 120 , d ) 140 , e ) 160

c

divide(1, subtract(divide(const_1, add(7, divide(1, 2))), divide(1, const_4)))

divide(n1,n2)|divide(n1,const_4)|add(const_3.0,#0)|divide(n1,#2)|subtract(#3,#1)|divide(n1,#4)|

physics

sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 324 per week . how much does she earn in dollars per hour ?

( 70 / 100 ) * 120 â € “ ( 35 / 100 ) * 200 84 - 70 = 14 answer : b

a ) 15 , b ) 14 , c ) 13 , d ) 16 , e ) 17

b

subtract(multiply(120, divide(70, const_100)), multiply(divide(35, const_100), 200))

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

gain

the probability that a man will be alive for 10 more yrs is 1 / 2 & the probability that his wife will alive for 10 more yrs is 1 / 3 . the probability that none of them will be alive for 10 more yrs , is

"2 ^ k + 2 ^ k = ( 2 ^ 9 ) ^ 2 ^ 9 - 2 ^ k 2 * ( 2 ^ k ) = 2 ^ ( 4 * 3 ^ 9 ) = 2 ^ ( 2 ^ 2 * 2 ^ 9 ) = 2 ^ ( 2 ^ 11 ) 2 ^ k + 1 = 2 ^ ( 2 ^ 11 ) so k + 1 = 2 ^ 11 so k = 2 ^ 11 - 1 answer is c"

a ) 11 / 3 , b ) 11 / 2 , c ) 2 ^ 11 - 1 , d ) 3 ^ 10 , e ) 3 ^ 11 - 1

c

subtract(power(2, add(9, const_2)), const_1)

add(n3,const_2)|power(n0,#0)|subtract(#1,const_1)|

general

a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked at 7 miles per hour for 2 hours . how many miles in total did she walk ?

"explanation : let b ' s age = x years . then , as age = ( x + 5 ) years . ( x + 5 + 10 ) = 2 ( x — 10 ) hence x = 35 . present age of b = 35 years answer : option a"

a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42

a

add(multiply(const_2, 10), add(5, 10))

add(n0,n3)|multiply(n0,const_2)|add(#0,#1)|

general

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 ?

"2 ^ 3 + 7 ^ 2 = 57 3 ^ 3 + 6 ^ 2 = 63 5 ^ 3 + 9 ^ 2 = 206 and 5 ^ 3 + 8 ^ 2 = 189 answer : e"

a ) 185 , b ) 186 , c ) 177 , d ) 168 , e ) 189

e

add(power(5, 3), power(8, 2))

power(n9,n3)|power(n10,n0)|add(#0,#1)|

general

if 150 ! / 10 ^ n is an integer , what is the largest possible value of n ?

"93 % - - - - 21 142 % - - - - ? 93 / 142 * 21 = 13.75 answer : e"

a ) 12.75 , b ) 11.75 , c ) 8.75 , d ) 15.75 , e ) 13.75

e

divide(multiply(subtract(const_100, 7), 21), add(const_100, 42))

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

gain

in school there are some bicycles and 4 wheeler wagons . one tuesday there are 190 wheels in the campus . how many bicycles are there ?

"5 ^ 6 - 1 = ( 5 ^ 3 - 1 ) ( 5 ^ 3 + 1 ) = 124 * 126 = 4 * 31 * 3 * 42 the answer is b ."

a ) 29 , b ) 31 , c ) 37 , d ) 41 , e ) 43

b

floor(divide(5, divide(6, const_2)))

divide(n1,const_2)|divide(n0,#0)|floor(#1)|

general

if x and y are integers such that x ^ 2 = 2 y and xy = 32 , then x – y = ?

"explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 140 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 140 - x ) = 8000 × 1000 = > ( 140 - x ) = 8000 × 1000 / 320 = 100 = > x = 40 cm = 4 dm . answer : b"

a ) 90 cm , b ) 4 dm , c ) 1 m , d ) 1.1 cm , e ) none of these

b

subtract(multiply(multiply(3.3, 2.6), 1.4), divide(8000, const_1000))

divide(n0,const_1000)|multiply(n1,n2)|multiply(n3,#1)|subtract(#2,#0)|

physics

if the sides of a triangle are 196 cm , 81 cm and 277 cm , what is its area ?

"c = 1 / 3 – 1 / 10 = 7 / 30 = > 4.3 days answer : b"

a ) 15.5 days , b ) 4.3 days , c ) 17.5 days , d ) 16.5 days , e ) 18.5 days

b

inverse(subtract(3, divide(3, 10)))

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

physics

in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.24 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]

"speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 15 / 60 ) = 4 kmhr speed in still water = 1 / 2 ( 2 + 4 ) = 3 kmhr time taken in stationary = 5 / 3 = 1 hrs 40 min answer : e"

a ) 40 minutes , b ) 1 hour , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 40 min

e

divide(5, divide(add(multiply(divide(1, 15), const_60), divide(2, 2)), const_2))

divide(n0,n0)|divide(n2,n3)|multiply(#1,const_60)|add(#0,#2)|divide(#3,const_2)|divide(n4,#4)|

physics

the workforce of company x is 60 % female . the company hired 20 additional male workers , and as a result , the percent of female workers dropped to 50 % . how many employees did the company have after hiring the additional male workers ?

"explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 16 x = 24 days answer : option d"

a ) 5 days , b ) 7 days , c ) 12 days , d ) 24 days , e ) 10 days

d

inverse(multiply(inverse(16), subtract(const_1, multiply(5, inverse(15)))))

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

physics

the sum of two numbers is 16 . the difference is 4 . what are the two numbers ? let x be the first number . ley y be the second number x + y = 16 x - y = 4

"1 / 10 + 1 / 40 = 0.125 days answer : b"

a ) 1.0875 days , b ) 0.125 days , c ) 0.0675 days , d ) 0.0875 days , e ) 0.0775 days

b

inverse(add(inverse(10), inverse(40)))

inverse(n0)|inverse(n1)|add(#0,#1)|inverse(#2)|

physics

how many seconds will a 650 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?

"speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 ∗ 2 / 25 = 40 seconds answer : d"

a ) 20 seconds , b ) 27 seconds , c ) 30 seconds , d ) 40 seconds , e ) 50 seconds

d

divide(add(360, 140), divide(multiply(45, const_1000), const_3600))

add(n0,n2)|multiply(n1,const_1000)|divide(#1,const_3600)|divide(#0,#2)|

physics

if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 10 m of the same rod ?

"a 2 - b 2 = 9 : given a 4 + b 4 - 2 a 2 b 2 = 92 : square both sides and expand . a * b = 4 : given a 2 b 2 = 42 : square both sides . a 4 + b 4 - 2 ( 16 ) = 81 : substitute a 4 + b 4 = 113 correct answer c"

a ) 32 , b ) 90 , c ) 113 , d ) 92 , e ) 81

c

add(power(9, 2), multiply(power(4, 2), 2))

power(n3,n0)|power(n2,n0)|multiply(#0,n0)|add(#2,#1)|

general

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

"ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 10 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 10 + 1 / 20 = 3 / 20 = > 20 / 3 = 6 2 / 3 a and b can finish the work in 6 2 / 3 days answer is e"

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

e

inverse(add(inverse(20), multiply(const_2, inverse(20))))

inverse(n0)|multiply(#0,const_2)|add(#0,#1)|inverse(#2)|

physics

a certain junior class has 1,000 students and a certain senior class has 800 students . among these students , there are 20 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?

"number of ways of selecting 2 fiction books = 9 c 2 number of ways of selecting 2 non fiction books = 6 c 2 9 c 2 * 6 c 2 = 36 * 15 = 540 answer : c"

a ) 90 , b ) 120 , c ) 540 , d ) 180 , e ) 200

c

divide(multiply(multiply(9, const_4), multiply(6, 9)), power(factorial(2), 2))

factorial(n2)|multiply(n0,const_4)|multiply(n0,n1)|multiply(#1,#2)|power(#0,n2)|divide(#3,#4)|

general

if 9 a - b = 10 b + 70 = - 12 b - 2 a , what is the value of 9 a - 11 b ?

"explanation : speed of the train relative to man = ( 62 - 8 ) kmph = ( 54 × 5 / 18 ) m / sec = 15 m / sec time taken by the train to cross the man = time taken by it to cover 120 m at 15 m / sec = 120 × 1 / 15 sec = 8 sec answer : option d"

a ) 5 sec , b ) 6 sec , c ) 7 sec , d ) 8 sec , e ) 9 sec

d

divide(120, multiply(add(62, 8), const_0_2778))

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

physics

how many boxes do we need if we have to carry 250 apples into boxes that each hold 25 apples ?

"concentration of salt in pure solution = 0 concentration of salt in salt solution = 50 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 50 - 15 ) / ( 15 - 0 ) = 7 / 3 1 / x = 7 / 3 x = 3 / 7 answer : e"

a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3 / 7

e

divide(15, subtract(50, 15))

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

gain

let c be defined as the sum of all prime numbers between 0 and 38 . what is c / 3

for the 15 minutes the motor - cyclist continues to overtake the cyclist , she is going at 30 miles per hour faster than the cyclist . once the motor - cyclist stops , the cyclist is going at 18 miles per hour while the motor - cyclist is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 30 / 18 * 15 or 25 minutes answer is ( a )

a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45

a

divide(multiply(subtract(divide(48, const_4), divide(18, const_4)), const_60), 18)

divide(n1,const_4)|divide(n0,const_4)|subtract(#0,#1)|multiply(#2,const_60)|divide(#3,n0)

physics

a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 420 less than the sum lent . what was the sum lent ?

"let the number be x . then , 3 ( 2 x + 9 ) = 81 2 x = 18 = > x = 9 answer : e"

a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 9

e

divide(subtract(81, multiply(const_3, 9)), multiply(const_3, const_2))

multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)|

general

a certain experimental mathematics program was tried out in 2 classes in each of 26 elementary schools and involved 32 teachers . each of the classes had 1 teacher and each of the teachers taught at least 1 , but not more than 3 , of the classes . if the number of teachers who taught 3 classes is n , then the least and greatest possible values of n , respectively , are

"explanation : 1 / 3 = . 33 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 6 = . 833 so biggest is 5 / 6 and smallest is 1 / 3 their difference is 5 / 6 - 1 / 3 = 3 / 6 = 1 / 2 option b"

a ) 2 / 5 , b ) 1 / 2 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these

b

subtract(divide(4, 5), divide(1, 3))

divide(n3,n5)|divide(n0,n1)|subtract(#0,#1)|

general

cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost q is what percent of the original cost ?

"every 2 seconds , 6 persons are added ( 9 - 3 ) . every second 3 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 3 = 259200 option e"

a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200

e

multiply(multiply(subtract(9, 3), const_3600), const_12)

subtract(n0,n1)|multiply(#0,const_3600)|multiply(#1,const_12)|

general

a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 2.00 , what total number of pens and pencils did the customer purchase ?

"solution given expression = 894.7 - ( 573.07 + 95.007 ) = 894.7 - 668.077 = 226.623 . answer a"

a ) 226.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these

a

subtract(894.7, divide(573.07, 95.007))

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

general

how many positive integers less than 50 have a reminder 5 when divided by 7 ?

"let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 1800 x = 30 the numbers are 3 * 30 , 4 * 30 , 5 * 30 hence required h . c . f . = 30 answer is b"

a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60

b

add(multiply(multiply(3, 5), const_100), multiply(4, 5))

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

other

evaluate : | 6 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?

"hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 65 = > v = 55 ( option d ) ."

a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70

d

multiply(subtract(const_100, 80), subtract(divide(const_100, 65), divide(80, 80)))

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

physics

in a group of 15 people , 8 read english , 7 read french while 3 of them read none of these two . how many of them read french and english both ?

"speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 35 minutes = 15 / 18 * 35 * 60 = 1750 m answer is b"

a ) 1250 m , b ) 1750 m , c ) 950 m , d ) 1000 m , e ) 1300 m

b

multiply(divide(multiply(15, const_1000), const_60), 35)

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

gain

a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 3,500 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?

diagonal 2 = 64 + b 2 or , 10 ( 2 ) = 64 + 6 ( 2 ) answer a

['a ) 6 cm', 'b ) 10 cm', 'c ) 8 cm', 'd ) data inadequate', 'e ) none of these']

a

subtract(sqrt(64), const_2)

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

geometry

what is the sum of all 3 digit integers formed using the digits 34 and 5 ( repetition is allowed )

"let the cost price = y the cost price of 60 articles = 60 y the selling price of x articles = 1.20 y * x 1.20 y * x = 60 y x = 60 / 1.2 = 50 the answer is d ."

a ) 42 , b ) 45 , c ) 48 , d ) 50 , e ) 54

d

divide(multiply(60, const_4), add(const_4, const_1))

add(const_1,const_4)|multiply(n0,const_4)|divide(#1,#0)|

gain

if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.50 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was

"increase in house value = $ 24,000 - $ 20,000 = $ 4000 so , tax increase = 10 % of $ 4000 = $ 400 answer : d"

a ) $ 32 , b ) $ 50 , c ) $ 320 , d ) $ 400 , e ) $ 500

d

divide(multiply(subtract(multiply(multiply(add(const_3, const_4), const_4), const_1000), multiply(multiply(add(const_4, const_1), const_4), const_1000)), 10), const_100)

add(const_3,const_4)|add(const_1,const_4)|multiply(#0,const_4)|multiply(#1,const_4)|multiply(#2,const_1000)|multiply(#3,const_1000)|subtract(#4,#5)|multiply(n0,#6)|divide(#7,const_100)|

general

find the value of ( 70 + 28 / 100 ) × 100

"let t be the total number of passengers . let x be the number of people with round trip tickets . 0.4 t had round trip tickets and took their cars . 0.8 x had round trip tickets and took their cars . 0.8 x = 0.4 t x = 0.5 t the answer is c ."

a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 80 %

c

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

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

gain

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

"salary grade of 5 is p ( 5 ) = 9.50 + 0.25 ( 5 – 1 ) = 9.50 + 0.25 * 4 ; salary grade of 3 is p ( 3 ) = 9.50 + 0.25 ( 3 – 1 ) = 9.50 + 0.25 * 2 ; p ( 5 ) - p ( 3 ) = 9.50 + 0.25 * 4 - 9.50 - 0.25 * 2 = 0.5 . answer : a ."

a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75

a

add(multiply(0.25, subtract(5, 1)), 0.25)

subtract(n1,n6)|multiply(n3,#0)|add(n3,#1)|

general

p has $ 63 more than what q and r together would have had if both b and c had 1 / 9 of what p has . how much does p have ?

30 , 870,000 = 2 ^ 4 * 5 ^ 4 * 3087 = 2 ^ 4 * 3 * 5 ^ 4 * 1029 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 343 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 7 ^ 3 the answer is c .

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

c

divide(multiply(3, const_1), const_1)

multiply(n2,const_1)|divide(#0,const_1)

general

the mass of 1 cubic meter of a substance is 200 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )

you can just write out the pattern and count : rgwbyrgwbyrgwby . . . but to save time a good test taker will just look for a pattern . min # is 3 , because w is the third one . then every 5 beads another white comes , so it must be 3 + 5 + 5 + 5 . . and so on . . . 3 + 5 = 8 3 + 5 + 5 = 13 3 + 5 + 5 + 5 = 18 3 + 5 + 5 + 5 + 5 = 23 so you see it ends in either 8 or 3 . pick an answer that ends in either 8 or 3 . only one answer does , b .

a ) 16 , b ) 28 , c ) 41 , d ) 54 , e ) 65

b

add(add(add(add(add(add(divide(88, 88), const_2), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3))

add(const_2,const_3)|divide(n0,n0)|add(#1,const_2)|add(#2,#0)|add(#3,#0)|add(#4,#0)|add(#5,#0)|add(#6,#0)

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 x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 16 ) = 0.8 x x = 1.2 ( 16 ) / 0.8 = 1.5 ( 16 ) = $ 24 the answer is e .

a ) $ 20 , b ) $ 21 , c ) $ 22 , d ) $ 23 , e ) $ 24

e

divide(add(multiply(divide(20, const_100), 16), 16), divide(subtract(const_100, 20), const_100))

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

gain

find the l . c . m of 15 , 18 , 28 and 30 .

"sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 3000 â ‡ ” 20 / 100 x = 3000 â ‡ ” x = 3000 ã — 5 = 15000 . answer a"

a ) rs . 15000 , b ) rs . 12000 , c ) rs . 9000 , d ) rs . 6000 , e ) rs . 3000

a

multiply(3000, add(const_4, const_1))

add(const_1,const_4)|multiply(n4,#0)|

gain

shahrukh starts from barabanki to fatehpur , 1 hour after ajay starts . shahrukh meets kajol 1.5 hours after shahrukh starts . if the speed of shahrukh is at least 20 km / h faster than the speed of kajol . what is the minimum speed of shahrukh to overtake ajay , before he meets kajol ?

"let initial price be 100 price in day 1 after 6 % discount = 94 price in day 2 after 6 % discount = 88.36 price in day 3 after 10 % discount = 79.52 so , price in day 3 as percentage of the sale price on day 1 will be = 79.52 / / 94 * 100 = > 84.6 % answer will definitely be ( b )"

a ) 82.3 % , b ) 84.6 % , c ) 85.6 % , d ) 89.6 % , e ) 79.2 %

b

add(multiply(divide(divide(10, const_100), subtract(1, divide(1, 6))), const_100), 2)

divide(n5,const_100)|divide(n1,n0)|subtract(n1,#1)|divide(#0,#2)|multiply(#3,const_100)|add(n2,#4)|

gain

mr . shah decided to walk down the escalator of a tube station . he found â that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stairs he would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins â to descend to the time he steps off the last step at the bottom , find out the height of the stair way in steps ?

"interest = 0.09 * 5000 = 0.065 * selling price - - > selling price = 0.09 * 5000 / 0.065 - - > selling price = ~ 6,923 answer : e ."

a ) 4063 , b ) 5325 , c ) 5351 , d ) 6000 , e ) 6923

e

divide(multiply(5000, divide(9, const_100)), divide(6.5, const_100))

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

gain

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

d = 40 * 60 + 1500 = 3900 m t = 3900 / 60 * 18 / 5 = 234 sec = 3.9 mins answer : d

a ) 6 , b ) 3 , c ) 4 , d ) 3.9 , e ) 3.6

d

add(divide(multiply(add(40, const_1), 60), const_1000), 1.5)

add(n0,const_1)|multiply(n1,#0)|divide(#1,const_1000)|add(n4,#2)

physics

how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?

80 : 7200 = 120 : x x = ( 7200 x 120 ) / 80 = 10800 . hence , s . p . = rs . 10,800 . answer : option c

a ) 10,400 , b ) 10,600 , c ) 10,800 , d ) 11,000 , e ) 11,200

c

floor(multiply(divide(divide(divide(multiply(divide(multiply(7200, const_100), subtract(const_100, 20)), add(const_100, 20)), const_100), const_100), 20), const_2))

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

gain

the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length q of a cube whose surface area is equal to 6 z ?

"given expression = ( 0.15 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + ( 0.15 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.15 - 0.1 ) = 0.05 answer is c ."

a ) 0.68 , b ) 0.08 , c ) 0.05 , d ) 0.06 , e ) none of them

c

divide(subtract(power(0.15, 3), power(0.1, 3)), add(add(power(0.15, 2), 0.015), power(0.1, 2)))

power(n0,n1)|power(n2,n1)|power(n0,n5)|power(n2,n5)|add(n6,#2)|subtract(#0,#1)|add(#4,#3)|divide(#5,#6)|

general

the sum of all the integers s such that - 26 < s < 24 is

first 2 shirts are sold for $ 38 and $ 42 = $ 80 . to get average price of $ 50 , total sale should be 7 * $ 50 = $ 350 so remaining 5 shirts to be sold for $ 350 - $ 80 = $ 270 answer should be 270 / 5 = $ 54.00 that is a

a ) $ 54.00 , b ) $ 57.00 , c ) $ 58.00 , d ) $ 60.50 , e ) $ 63.00

a

divide(subtract(multiply(7, 50), add(38, 42)), subtract(7, 2))

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

general

in triangle pqr , the angle q = 90 degree , pq = 5 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz

"distance = 500 meter time = 4 minutes = 4 x 60 seconds = 240 seconds speed = distance / time = 500 / 240 = 2.08 m / s = 2.08 ã — 18 / 5 km / hr = 7.5 km / hr answer : a"

a ) 7.5 , b ) 2.6 , c ) 3.9 , d ) 8.2 , e ) 2.7

a

divide(divide(500, const_1000), divide(multiply(4, const_60), const_3600))

divide(n0,const_1000)|multiply(n1,const_60)|divide(#1,const_3600)|divide(#0,#2)|

physics

the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 6 minutes , then the area of the park ( in sq . m ) is :

"10 / 100 p = 160 > > p = 160 * 100 / 10 = 1600 1600 - 160 = 1440 answer : e"

a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,440

e

subtract(multiply(160, divide(const_100, 10)), 160)

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

general

a student chose a number , multiplied it by 2 , then subtracted 180 from the result and got 104 . what was the number he chose ?

"2 ( l + 100 ) = 600 = > l = 200 m answer : c"

a ) 227 , b ) 247 , c ) 200 , d ) 277 , e ) 121

c

subtract(divide(600, const_2), 100)

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

physics

in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 10 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?

"the owner buys 100 kg but actually gets 150 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 150 - 90 ) / 90 * 100 = 50 % answer : d ."

a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 50 % , e ) ca n ' t be calculated

d

divide(multiply(subtract(add(const_100, 50), subtract(const_100, 10)), const_100), subtract(const_100, 10))

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

gain

the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length q of a cube whose surface area is equal to 6 z ?

solution : 3 ! + 15 + 9 = 30 explanation : 3 ! = 3 * 2 * 1 = 6 6 + 15 + 9 = 30 answer b

a ) 29 , b ) 30 , c ) 31 , d ) 32 , e ) 33

b

add(add(11, factorial(3)), 13)

factorial(n1)|add(n5,#0)|add(n6,#1)

general

the wages earned by robin is 40 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?

let x = length of pool at first meeting , combined distance = x at second meeting , combined distance = 3 x if andy swims 18.5 m of x , then he will swim 3 * 18.5 = 55.5 m of 3 x andy ' s total distance to second meeting = x + 10.5 m x + 10.5 = 55.5 m x = 45 m e

a ) 65 , b ) 60 , c ) 55 , d ) 50 , e ) 45

e

subtract(add(multiply(18.5, const_2), 18.5), 10.5)

multiply(n1,const_2)|add(n1,#0)|subtract(#1,n5)

physics

a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 40 % profit on the cost of the item ?

"if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 920.24 answer : d ."

a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24

d

add(multiply(add(multiply(divide(3, const_100), add(multiply(divide(2, const_100), power(const_100, 2)), power(const_100, 2))), add(multiply(divide(2, const_100), power(const_100, 2)), power(const_100, 2))), divide(4, const_100)), multiply(divide(3, const_100), add(multiply(divide(2, const_100), power(const_100, 2)), power(const_100, 2))))

divide(n1,const_100)|divide(n3,const_100)|divide(n5,const_100)|power(const_100,n1)|multiply(#0,#3)|add(#4,#3)|multiply(#5,#1)|add(#5,#6)|multiply(#7,#2)|add(#8,#6)|

gain

a certain university will select 1 of 8 candidates eligible to fill a position in the mathematics department and 2 of 12 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?

on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted answer : option a

a ) 725117481 , b ) 343564689 , c ) 454564690 , d ) 759900434 , e ) 656590009

a

subtract(subtract(subtract(multiply(multiply(multiply(427398, const_100), const_10), const_2), 427398), multiply(427398, const_100)), multiply(multiply(multiply(const_100, const_100), const_100), const_100))

multiply(n0,const_100)|multiply(const_100,const_100)|multiply(#0,const_10)|multiply(#1,const_100)|multiply(#2,const_2)|multiply(#3,const_100)|subtract(#4,n0)|subtract(#6,#0)|subtract(#7,#5)

general

weights of two friends ram and shyam are in the ratio 3 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?

"total work done by both machines in a minute = 30 + 20 = 50 copies total number of copies required = 2000 time = 2000 / 50 = 40 mins answer b"

a ) 20 minutes , b ) 40 minutes , c ) 45 minutes , d ) 50 minutes , e ) 55 minutes

b

divide(power(20, const_3), add(30, 20))

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

physics

a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?

"john spent and gave to his two friends a total of 1.25 + 1.20 + 2.20 = $ 4.65 money left 8.50 - 4.65 = $ 3.85 correct answer is c ) $ 3.85"

a ) $ 5.85 , b ) $ 6.85 , c ) $ 3.85 , d ) $ 2.85 , e ) $ 4.85

c

subtract(8.50, add(1.25, add(1.20, 1.20)))

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

general

if 12 men can reap 120 acres of land in 16 days , how many acres of land can 36 men reap in 32 days ?

"let abhay ' s speed be x km / hr . then , 48 / x - 48 / 2 x = 3 6 x = 48 x = 8 km / hr . answer : option e"

a ) 5 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7.5 kmph , e ) 8 kmph

e

divide(subtract(48, divide(48, 2)), add(1, 2))

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

physics

√ 4 percent of 4 √ 4 =

"explanation : l . c . m of 1250 = 2 x 5 x 5 x 5 x 5 2 , 5 number of different prime factors is 2 . answer : option b"

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

b

add(const_2, const_2)

add(const_2,const_2)|

other

if a man lost 4 % by selling oranges at the rate of 48 a rupee at how many a rupee must he sell them to gain 44 % ?

dist 1 st hr = 35 km speed of bus by 2 kmph 2 nd hr = 37 km 3 rd hr = 39 km tot = 35 + 37 + 39 + . . . . ( 12 terms ) 12 / 2 ( 2 * 35 + ( 12 - 1 ) 2 ] = 6 * 92 = 552 answer c

a ) 550 , b ) 500 , c ) 552 , d ) 560 , e ) 580

c

multiply(divide(12, 2), add(multiply(subtract(12, const_1), 2), multiply(2, 35)))

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

physics

joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 4 of the remaining paint . how many gallons of paint has joe used ?

"cost of 8 kg grapes = 90 × 8 = 720 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 720 + 495 = 1215 . b )"

a ) a ) 1055 , b ) b ) 1215 , c ) c ) 1065 , d ) d ) 1070 , e ) e ) 1080

b

add(multiply(8, 90), multiply(9, 55))

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

gain

the original price of a suit is $ 100 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?

"n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 16 . . . we get 15 / 2 [ 2 a + 14 d ] = 16 [ a + 7 d ] = 16 * 10 = 160 . . . answer is d . . ."

a ) 300 , b ) 120 , c ) 150 , d ) 160 , e ) 270

d

divide(multiply(20, 16), const_2)

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

general

in a school with 620 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is

"taking 2 red shoe the probablity is 3 c 2 from 10 shoes probablity of taking 2 red shoe is 3 c 2 / 10 c 2 = 1 / 15 answer : d"

a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 12 , d ) 1 / 15 , e ) 1 / 16

d

divide(choose(3, const_2), choose(add(3, 7), const_2))

add(n0,n1)|choose(n0,const_2)|choose(#0,const_2)|divide(#1,#2)|

probability

the equation of line a is y = 4 / 3 * x - 100 . what is the smallest possible distance in the xy - plane from the point with coordinates ( 0 , 0 ) to any point on line a ?

explanation : mary and her sister complete half work in 2.5 days = > they can complete whole work in 5 days answer : option d

a ) 6 , b ) 8 , c ) 2 , d ) 5 , e ) 4

d

add(divide(divide(const_1, 8), divide(const_1, 16)), const_3)

divide(const_1,n1)|divide(const_1,n0)|divide(#0,#1)|add(#2,const_3)

physics

if shreehari walks in the speed of 4.5 km / hr from his house , in what time will he reach his school which is 750 m long from his house ?

"d = ( d - r ) / q = ( 73 - 1 ) / 9 = 72 / 9 = 8 a )"

a ) a ) 8 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 18

a

floor(divide(73, 9))

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

general

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 ?

explanation : let the number of articles of types p , q and r be 3 a , 2 a and 3 a respectively . thus , we get , ( 200 x 3 a ) + ( 90 x 2 a ) + ( 60 x 3 a ) = 4800 960 a = 4800 a = 5 hence , the number of articles of type “ q ” = 2 x 5 = 10 answer b

a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16

b

multiply(divide(4800, add(add(multiply(3, 200), multiply(2, 90)), multiply(3, 60))), 2)

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

general

45 x ? = 25 % of 900

"producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 40 % of the final price - - > ( final price ) * 0.6 = $ 18 - - > ( final price ) = $ 30 . answer : b ."

a ) 18 , b ) 30 , c ) 22 , d ) 22.5 , e ) 27

b

multiply(multiply(15, divide(add(const_100, 40), const_100)), divide(add(const_100, 20), const_100))

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

gain

how many odd numbers between 10 and 1,000 are the squares of integers ?

987 = 3 x 7 x 47 so , the required number must be divisible by each one of 3 , 7 , 47 553681 - > ( sum of digits = 28 , not divisible by 3 ) 555181 - > ( sum of digits = 25 , not divisible by 3 ) 555681 is divisible by 3 , 7 , 47 answer c

a ) 553681 , b ) 555181 , c ) 555681 , d ) 556581 , e ) 556881

c

multiply(subtract(subtract(divide(559981, 987), const_4), const_0_33), 987)

divide(n1,n0)|subtract(#0,const_4)|subtract(#1,const_0_33)|multiply(n0,#2)

other

if 6 - 12 / x = 7 - 7 / x , then x =

solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 5 = 864 - 5 = 859 . answer b

a ) 427 , b ) 859 , c ) 869 , d ) 4320 , e ) none of these

b

subtract(lcm(lcm(lcm(24, 32), 36), 54), 5)

lcm(n1,n2)|lcm(n3,#0)|lcm(n4,#1)|subtract(#2,n0)

general

jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 7 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?

"compound interest : a = p ( 1 + r / n ) nt a = 10 , 217.85 c . i . > > 10 , 217.85 - 8500 > > rs . 1717.85 answer : b"

a ) 1409.85 , b ) 1717.85 , c ) 1427.85 , d ) 2717.85 , e ) 1817.85

b

multiply(8500, subtract(power(divide(add(divide(7.5, const_2), const_100), const_100), multiply(2, const_2)), const_1))

divide(n1,const_2)|multiply(n2,const_2)|add(#0,const_100)|divide(#2,const_100)|power(#3,#1)|subtract(#4,const_1)|multiply(n0,#5)|

gain

paul sells encyclopedias door - to - door . he earns $ 150 on every paycheck , regardless of how many sets he sells . in addition , he earns commission as follows : commission sales 10 % $ 0.00 - $ 10 , 000.00 5 % $ 10 , 000.01 - - - > he does not earn double commission . that is , if his sales are $ 12,000 , he earns 10 % on the first $ 10,000 and 5 % on the remaining $ 2,000 . his largest paycheck of the year was $ 1,320 . what were his sales for that pay period ?

"assume the revenue in 2000 to be 100 . then in 2003 it would be 140 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 140 ) / 140 = 40 / 140 = 2 / 7 = ~ 29 % . answer : e ."

a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 29 %

e

multiply(divide(subtract(add(const_1, divide(80, const_100)), add(const_1, divide(40, const_100))), add(const_1, divide(40, const_100))), const_100)

divide(n3,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|subtract(#2,#3)|divide(#4,#3)|multiply(#5,const_100)|

gain

the average age of 18 students of a class is 18 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 18 th student is

"let the numbers be 2 x and 3 x . then , their l . c . m = 6 x . so , 6 x = 48 or x = 8 . the numbers are 16 and 24 . hence , required sum = ( 16 + 24 ) = 40 . answer : c"

a ) 22 , b ) 67 , c ) 40 , d ) 88 , e ) 11

c

divide(multiply(2, 48), 3)

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

other

the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 10 and 11 . the larger of the two numbers is :

65 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 65 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 65 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 64 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 64 = r ^ 3 r = 4 a

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

a

power(subtract(65, const_1), divide(const_1, const_3))

divide(const_1,const_3)|subtract(n2,const_1)|power(#1,#0)

other

a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 30 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?

"as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 3 of 300 = 100 total amount in her account = 400 answer c"

a ) 300 , b ) 375 , c ) 400 , d ) 500 , e ) 575

c

multiply(subtract(divide(200, subtract(1, divide(const_3, 5))), 200), add(1, divide(1, 3)))

divide(n3,n4)|divide(const_3,n2)|add(n3,#0)|subtract(n3,#1)|divide(n0,#3)|subtract(#4,n0)|multiply(#2,#5)|

general

a number increased by 30 % gives 780 . the number is

total distance traveled = 1200 km . distance traveled by plane = 400 km . distance traveled by bus = x distance traveled by train = 2 x / 3 x + 2 x / 3 + 400 = 1200 5 x / 3 = 800 x = 480 km the answer is c .

a ) 400 , b ) 440 , c ) 480 , d ) 520 , e ) 560

c

divide(multiply(divide(multiply(1200, const_2), const_3), const_3), add(const_2, const_3))

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

physics

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 ?

"we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 40 are employed males , hence 24 % are employed females . ( employed females ) / ( total employed people ) = 24 / 64 = 38 % answer : a ."

a ) 38 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 52 %

a

multiply(divide(subtract(64, 40), 64), const_100)

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

gain

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

"sol . there are five prime numbers between 1 and 5 . they are 2 , 3 , 5 , 7 , 11 â ˆ ´ required average = [ 2 + 3 + 5 + 7 + 11 / 5 ] = 28 / 5 = 5.6 answer c"

a ) 30 , b ) 3.6 , c ) 5.6 , d ) 6.6 , e ) none

c

divide(add(add(add(1, const_1), add(add(1, const_1), const_2)), add(subtract(5, 1), subtract(5, const_2))), 1)

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

general

john and steve are speed walkers in a race . john is 10 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?

"125 % of 120 % of a = 237 125 / 100 * 120 / 100 * a = 237 a = 237 * 2 / 3 = 158 . answer c"

a ) 150 , b ) 120 , c ) 158 , d ) 160 , e ) 210

c

divide(237, multiply(add(const_1, divide(20, const_100)), add(const_1, divide(25, const_100))))

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

gain

kathleen can paint a room in 2 hours , and anthony can paint an identical room in 3 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?

"explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 756 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 756 : 756 / 42 = 18 hence , 42 * 16 = 756 is the last number divisible by 42 within 756 hence , total numbers divisible by 2 , 3 , 7 together are ( 18 â € “ 2 ) = 16 answer : d"

a ) 112 , b ) 77 , c ) 267 , d ) 16 , e ) 99

d

subtract(divide(756, multiply(multiply(2, 3), 7)), divide(100, multiply(multiply(2, 3), 7)))

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

general

what is the greatest possible length which can be used to measure exactly the lengths 10 m 50 cm , 14 m 55 cm and 50 cm ?

"explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 9 : 5 d 1 : d 2 = 9 : 5 where √ 3 cancelled both side answer : a"

a ) 9 : 5 , b ) 16 : 9 , c ) 4 : , d ) 3 : 4 , e ) 3 : 8

a

divide(9, 5)

divide(n0,n1)|

geometry

find the remainder of the division ( 2 ^ 14 ) / 7 .

( a + b ) work in 1 day = 1 / 20 , ( b + c ) work in 1 days = 1 / 15 . , ( c + a ) work in 1 days = 1 / 12 ( 1 ) adding = 2 [ a + b + c ] in 1 day work = [ 1 / 20 + 1 / 15 + 1 / 12 ] = 1 / 5 ( a + b + c ) work in 1 day = 1 / 10 so , all three together finish work in 10 days answer d

a ) 12 , b ) 15 , c ) 8 , d ) 10 , e ) 11

d

inverse(divide(add(inverse(12), add(inverse(20), inverse(15))), const_2))

inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|divide(#4,const_2)|inverse(#5)

physics

8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 6 men , 4 women and 10 children together complete the piece of work ?

d = 180 * 5 / 18 * 6 = 300 m answer : a

a ) 300 , b ) 125 , c ) 288 , d ) 266 , e ) 121

a

multiply(multiply(180, const_0_2778), 6)

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

physics

what least value must be given to * so that the number 451 * 603 is exactly divisible by 9 ?

"l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 180 ( 36 * 5 ) profit percentage = ( 180 - 100 ) / 100 * 100 = 80 % answer : a"

a ) 80 % , b ) 50 % , c ) 59 % , d ) 40 % , e ) 53 %

a

subtract(multiply(36, add(const_4, const_1)), multiply(25, const_4))

add(const_1,const_4)|multiply(n1,const_4)|multiply(n3,#0)|subtract(#2,#1)|

gain

the sum of ages of 5 children born at the intervals of 3 years each is 50 years . what is the age of the youngest child ?

lcm = 180 , ratio = 60 : 90 = 2 : 3 no of days = 180 / ( 2 + 3 ) = 180 / 5 = 36 days answer : a

a ) 36 days , b ) 32 days , c ) 19 days , d ) 17 days , e ) 18 days

a

divide(const_1, add(divide(const_1, 60), divide(const_1, 90)))

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

physics

a high school has 360 students 1 / 2 attend the arithmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 3 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .

"1536 ÷ 21 = 73 reminder - 3 3 + 18 = 21 hence 18 should be added to 1536 so that the sum will be divisible by 21 answer : c"

a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20

c

subtract(21, reminder(1536, 21))

reminder(n0,n1)|subtract(n1,#0)|

general

alex takes a loan of $ 8,000 to buy a used truck at the rate of 9 % simple interest . calculate the annual interest to be paid for the loan amount .

"i = ( 300 * 9 * 6 ) / 100 = 162 answer : c"

a ) 142 , b ) 152 , c ) 162 , d ) 172 , e ) 182

c

multiply(300, divide(9, const_100))

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

gain

a bus 75 m long is running with a speed of 21 km / hr . in what time will it pass a woman who is walking at 3 km / hr in the direction opposite to that in which the bus is going ?

distance = speed * time d 1 = s 1 t 1 d 2 = s 2 t 2 the distance from point a to point b is the same for each trip so , d 1 = d 2 and t 2 = t 1 - 5 thus , s 1 t 1 = s 2 t 2 60 t 1 = s 2 ( t 1 - 5 ) t 1 = 11 60 * 11 = 660 answer : c

a ) 600 . , b ) 630 . , c ) 660 . , d ) 690 . , e ) 720 .

c

multiply(60, divide(multiply(110, 5), subtract(110, 60)))

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

physics

if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 150 % of j ?

let n = 7 ( leaves a remainder of 7 when divided by 19 ) 18 n = 18 ( 7 ) = 126 , which leaves a remainder of 0 when divided by 9 . difference = 7 - 0 = 7 . answer a

a ) 7 , b ) 5 , c ) 0 , d ) 3 , e ) 9

a

subtract(7, reminder(18, 9))

reminder(n2,n3)|subtract(n1,#0)

general

the sum of 55 consecutive integers is 5555 . what is the greatest integer in the set ?

"75 % is 5 % - points below 80 % and 20 % - points above 55 % . so the ratio of solution p to solution q is 4 : 1 . mixture p is 4 / 5 = 80 % of the volume of mixture pq . the answer is d ."

a ) 40 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %

d

multiply(divide(subtract(divide(75, const_100), divide(55, const_100)), add(subtract(divide(75, const_100), divide(55, const_100)), subtract(divide(80, const_100), divide(75, const_100)))), const_100)

divide(n4,const_100)|divide(n3,const_100)|divide(n1,const_100)|subtract(#0,#1)|subtract(#2,#0)|add(#3,#4)|divide(#3,#5)|multiply(#6,const_100)|

gain

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 . 798 find the share of a .

"the required answer = ( 15 - 5 ) * 9 / 15 = 40 / 10 = 6 days answer is c"

a ) 2 days , b ) 4 days , c ) 6 days , d ) 7 days , e ) 10 days

c

add(multiply(15, 5), divide(15, 5))

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

physics

aaron will jog from home at 5 miles per hour and then walk back home by the same route at 10 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?

"clearly , the two will meet when they are 1000 m apart to be 20 + 15 = 35 km apart , they take 1 hour to be 1000 m apart , they take 35 * 1000 / 1000 = 35 min . answer is c"

a ) 50 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 20 min

c

add(20, 15)

add(n1,n2)|

general

4 liters of a 25 percent solution of alcohol in water are mixed with 3 liters of a 11 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?

weight of the teacher = ( 35.4 x 25 - 35 x 24 ) kg = 45 kg . answer : a

a ) 45 , b ) 46 , c ) 47 , d ) 48 , e ) 49

a

subtract(multiply(add(35, divide(400, const_1000)), add(24, const_1)), multiply(24, 35))

add(n0,const_1)|divide(n2,const_1000)|multiply(n0,n1)|add(n1,#1)|multiply(#3,#0)|subtract(#4,#2)

general

how many odd numbers between 10 and 1,000 are the squares of integers ?

"the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 24 oranges , so to get to 6 oranges , we should remove 24 - 6 = 18 oranges . answer a"

a ) 18 , b ) 6 , c ) 14 , d ) 17 , e ) 20

a

subtract(add(14, 24), divide(14, divide(70, const_100)))

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

general

a cubical tank is filled with water to a level of 3 feet . if the water in the tank occupies 75 cubic feet , to what fraction of its capacity is the tank filled with water ?

"juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 96 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 96 ) is 96 % of juan ' s income ( 100 ) . answer : c"

a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %

c

multiply(multiply(subtract(const_1, divide(40, const_100)), add(const_1, divide(60, const_100))), const_100)

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

general

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 22 per kg , then his gain percent is

given : the radius of a is 4 times as large as the diameter of b . = > r ( a ) = 4 * d ( b ) = 4 * 2 * r ( b ) = 8 r ( b ) . the radius are in ratio of 1 : 8 thus the area will be in the ratio of square of radius . 1 : 64 . hence d .

['a ) 1 : 8 .', 'b ) 1 : 2 .', 'c ) 1 : 24 .', 'd ) 1 : 64 .', 'e ) 1 : 6 .']

d

divide(power(const_1, const_2), power(multiply(const_2, const_4), const_2))

multiply(const_2,const_4)|power(const_1,const_2)|power(#0,const_2)|divide(#1,#2)

geometry

the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 170 runs and his average excluding these two innings is 58 runs , find his highest score .

"clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 192 / 32 = 6 m / s distance covered by b in 4 seconds = speed ã — time = 6 ã — 4 = 24 metre i . e . , a beat b by 24 metre answer is c"

a ) 38 metre , b ) 28 metre , c ) 24 metre , d ) 15 metre , e ) 28 metre

c

subtract(192, multiply(divide(192, 32), 28))

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

physics

running at the same constant rate , 6 identical machines can produce a total of 270 pens per minute . at this rate , how many pens could 10 such machines produce in 4 minutes ?

"let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1585.75 = > x = 791 e"

a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 791

e

divide(add(const_1000, 585.75), const_2)

add(n4,const_1000)|divide(#0,const_2)|

other

a man buys an article for $ 100 . and sells it for $ 125 . find the gain percent ?

"part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 30 + 1 / 20 + 1 / 10 ) = 11 / 20 part filled by b in 3 minutes = 3 / 20 required ratio = 3 / 20 * 20 / 11 = 3 / 11 answer : c"

a ) 1 / 11 , b ) 2 / 11 , c ) 3 / 11 , d ) 4 / 11 , e ) 5 / 11

c

multiply(divide(3, 10), divide(const_1, multiply(3, add(divide(const_1, 10), add(divide(const_1, 30), divide(const_1, 30))))))

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

physics

a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 5,500 meters of fabric ?

"the area a of the large cube is 5 * 5 * 6 = 150 square cm . the area of the 125 small cubes is 125 * 6 = 750 = 5 a , an increase of 400 % . the answer is d ."

a ) 100 % , b ) 200 % , c ) 300 % , d ) 400 % , e ) 500 %

d

multiply(const_100, divide(multiply(surface_cube(1), surface_cube(5)), surface_cube(5)))

surface_cube(n1)|surface_cube(n0)|multiply(#0,#1)|divide(#2,#1)|multiply(#3,const_100)|

geometry

a man invests some money partly in 9 % stock at 96 and partly in 12 % stock at 120 . to obtain equal dividends from both , he must invest the money in the ratio ?

"slope of 2 and a y - intercept of 2 y - coordinate is 550 y = 2 x + 2 548 = 2 x x = 274 answer : e . 274"

a ) 249 , b ) 498 , c ) 676 , d ) 823 , e ) 274

e

divide(subtract(550, 2), 2)

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

general

a is two years older than b who is twice as old as c . if the total ages of a , b and c be 27 . what is the age of b ?

"total work done by both machines in a minute = 30 + 15 = 45 copies total number of copies required = 900 time = 900 / 45 = 20 mins answer b"

a ) 15 minutes , b ) 20 minutes , c ) 25 minutes , d ) 30 minutes , e ) 35 minutes

b

divide(power(15, const_3), add(30, 15))

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

physics

a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 35 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?

"rate ( 1 ) = 1 / 6 rate ( 2 ) = 1 / 10 combined = 8 / 30 work done in 2 days = 8 / 15 work left = 7 / 15 rate * time = work left 1 / 8 * time = 7 / 15 time = 56 / 15 d"

a ) 7 / 4 , b ) 4 / 3 , c ) 15 / 4 , d ) 56 / 15 , e ) 17 / 5

d

max(divide(subtract(const_1, multiply(add(divide(const_1, add(const_4, const_2)), divide(const_1, 10)), const_2)), divide(const_1, 10)), const_3)

add(const_2,const_4)|divide(const_1,n0)|divide(const_1,#0)|add(#2,#1)|multiply(#3,const_2)|subtract(const_1,#4)|divide(#5,#1)|max(#6,const_3)|

physics