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mathqa_shuffle_question_test

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in a garden , there are 12 rows and 14 columns of mango trees . the distance between 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

"lcm = 90 , ratio = 30 : 45 = 2 : 3 no of days = 90 / ( 2 + 3 ) = 90 / 5 = 18 days answer : e"

a ) 15 days , b ) 16 days , c ) 19 days , d ) 17 days , e ) 18 days

e

divide(const_1, add(divide(const_1, 30), divide(const_1, 45)))

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

physics

when 1 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?

"let the numbers be 3 x and 7 x their h . c . f . = 3 so the numbers are 3 * 12 , 7 * 12 = 36,84 l . c . m . = 252 answer is c"

a ) 20 , b ) 24 , c ) 252 , d ) 136 , e ) 160

c

sqrt(divide(12, add(power(7, 3), add(power(2, 3), power(3, 3)))))

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

other

a cycle is bought for rs . 750 and sold for rs . 1080 , find the gain percent ?

"if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 × 90 + 2 × 805 = 4305 = 86.3 × 90 + 2 × 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b"

a ) 70 , b ) 80 , c ) 85 , d ) 90 , e ) 95

b

multiply(multiply(const_2, const_4), const_10)

multiply(const_2,const_4)|multiply(#0,const_10)|

general

reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 300 as interest at the end of the loan period , what was the rate of interest ?

"explanation : b ' s 5 days work = 1 / 10 ∗ 5 = 1 / 2 remaining work = 1 − 1 / 2 = 1 / 2 a can finish work = 20 ∗ 1 / 2 = 10 days option a"

a ) 10 days , b ) 6 days , c ) 7.5 days , d ) 8.5 days , e ) 9 days

a

divide(const_1, add(divide(const_1, 20), divide(const_1, 10)))

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

physics

a towel , when bleached , lost 30 % of its length and 20 % of its breadth . what is the percentage decrease in area ?

solution - rolling dices is an independent event . the combinations to get 6 are ( 1,5 ) , ( 5,1 ) , ( 2,4 ) , ( 4,2 ) , ( 3,3 ) and total combinations of both dices is 25 . the probability of getting 6 in first attempt is 5 / 25 = 1 / 5 . probability of getting 6 again in second attempt = ( 1 / 5 ) * ( 1 / 5 ) = 1 / 25 . ans b

a ) 1 / 144 , b ) 1 / 25 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3

b

multiply(divide(5, power(5, const_2)), divide(5, power(5, const_2)))

power(n2,const_2)|divide(n2,#0)|multiply(#1,#1)

probability

we had $ 1400 left after spending 30 % of the money that we took for shopping . how much money did we start with ?

"explanation : average = total runs / no . of innings = 34 so , total = average x no . of innings = 34 x 10 = 340 . now increase in avg = 4 runs . so , new avg = 34 + 4 = 38 runs total runs = new avg x new no . of innings = 38 x 11 = 418 runs made in the 11 th inning = 418 - 340 = 78 answer : a"

a ) 78 , b ) 79 , c ) 85 , d ) 87 , e ) 89

a

subtract(multiply(add(10, const_1), add(4, 34)), multiply(10, 34))

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

general

rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 3000 . then his monthly salary is

"explanation : speed of the truck = distance / time = 288 / 8 = 36 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 36 + 18 ) = 54 kmph distance travelled by car = 288 + 90 = 378 km time taken by car = distance / speed = 378 / 54 = 7 hours . answer – c"

a ) 6 hours , b ) 5 hours , c ) 7 hours , d ) 8 hours , e ) none

c

divide(add(288, 90), add(divide(288, 8), 18))

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

physics

the hcf and lcm of two numbers m and n are respectively 8 and 200 . if m + n = 84 , then 1 / m + 1 / n is equal to

a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 6 / 25 * 75 = 18 answer : b

a ) 22 , b ) 18 , c ) 99 , d ) 77 , e ) 24

b

multiply(divide(75, add(add(multiply(divide(2, 3), divide(2, 5)), divide(2, 5)), const_1)), divide(2, 5))

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

general

a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 3 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?

"65 % answered the first question correctly and 20 % answered neither correctly . then 15 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 15 % = 35 % . the answer is c ."

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

c

subtract(add(add(65, 50), 20), const_100)

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

other

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

"( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 73000 / 129000 = 73 / 129 is a little above 1 / 2 . thus , our answer is just a little above 35 . answer : d"

a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 %

d

multiply(divide(add(multiply(divide(30, const_100), 56000), multiply(divide(40, const_100), 73000)), add(73000, 56000)), const_100)

add(n2,n3)|divide(n0,const_100)|divide(n1,const_100)|multiply(n2,#1)|multiply(n3,#2)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)|

gain

if 2 ^ k + 2 ^ k = ( 2 ^ 9 ) ^ ( 2 ^ 9 ) - 2 ^ k , then k = ?

"a 1 = 120 / 3 = 40 a 2 = a 1 - 6 = 34 sum of second list = 34 * 3 = 102 therefore the number = 102 - 80 = 22 answer : d"

a ) 15 , b ) 25 , c ) 35 , d ) 22 , e ) 55

d

subtract(add(add(20, 40), 60), add(add(multiply(6, const_3), 10), 70))

add(n0,n1)|multiply(n3,const_3)|add(n2,#0)|add(n4,#1)|add(n5,#3)|subtract(#2,#4)|

general

sum of 36 odd numbers is ?

the question actually asks the highest power of 10 which divides 150 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 150 factorial will have 37 as - 150 / 5 = 30 30 / 5 = 6 6 / 5 = 1 so answer will be ( e ) 37

a ) 38 , b ) 47 , c ) 32 , d ) 36 , e ) 37

e

add(divide(divide(150, add(const_4, const_1)), add(const_4, const_1)), divide(150, add(const_4, const_1)))

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

general

sales price is $ 60 , gross profit is 140 % of cost , what is the value of gross profit ?

"the total height was 20 cm too much . the average height should be reduced by 20 cm / 20 = 1 cm the answer is a ."

a ) 174 cm , b ) 173 cm , c ) 172 cm , d ) 171 cm , e ) 170 cm

a

divide(subtract(multiply(20, 175), subtract(151, 131)), 20)

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

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 ?

"number of workers = 10 * ( 85 - 10 ) / 10 = 75 answer is a"

a ) 75 , b ) 30 , c ) 28 , d ) 24 , e ) 32

a

divide(multiply(subtract(85, 10), 10), subtract(85, subtract(85, 10)))

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

physics

45 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?

"we can start with the known quantity and then go on to find the others . shiny igneous ricks are 40 . these are ( 4 / 5 ) of total igneous rocks . ( 4 / 5 ) * total igneous rocks = 40 total igneous rocks = 40 * ( 5 / 4 ) = 50 total sedimentary rocks = 2 * total igneous rocks = 2 * 50 = 100 total number of rocks = 50 + 100 = 150 answer ( b )"

a ) 30 , b ) 150 , c ) 60 , d ) 90 , e ) 135

b

divide(multiply(divide(multiply(multiply(4, 5), 40), 4), 5), 4)

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

general

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

"the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 48 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 38.4 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 38.4 miles / gallon * 10 gallons = 384 miles . answer b ."

a ) 320 , b ) 384 , c ) 400 , d ) 408.3 , e ) 440

b

multiply(multiply(subtract(const_1, divide(20, const_100)), 48), 10)

divide(n2,const_100)|subtract(const_1,#0)|multiply(n0,#1)|multiply(n4,#2)|

gain

how many cubes of 8 cm edge can be cut out of a cube of 16 cm edge

"∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 24000 ⁄ 12 = 2000 answer a"

a ) 2000 , b ) 8076 , c ) 9691.2 , d ) 4845.6 , e ) none of these

a

multiply(divide(divide(24000, divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100)), multiply(const_3, const_4)), divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100))

multiply(const_3,const_4)|subtract(const_100,n0)|multiply(n1,#1)|divide(#2,const_100)|divide(#3,const_100)|divide(n2,#4)|divide(#5,#0)|multiply(#6,#4)|

general

if n divided by 3 has a remainder of 2 , what is the remainder when 2 times n is divided by 3 ?

let the student who speaks tamil - x let the student who speaks telugu - y as ( xuy ) - ( xny ) = total 30 + 40 - ( xny ) = 50 = 20 c )

a ) a ) 8 , b ) b ) 10 , c ) c ) 20 , d ) d ) 30 , e ) e ) 32

c

subtract(add(40, 30), 50)

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

other

a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 7 % of bananas were rotten . find the percentage of fruits in good condition ?

if the two trains cover a total distance d , then train x travels ( 3 / 7 ) * d while train y travels ( 4 / 7 ) * d . if the trains travel 175 km to the meeting point , then train x travels ( 3 / 7 ) * 175 = 75 km . the answer is d .

a ) 66 , b ) 69 , c ) 72 , d ) 75 , e ) 78

d

multiply(divide(175, 4), divide(175, add(divide(175, 4), divide(175, 3))))

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

physics

given that 100.48 = x , 100.70 = y and xz = y 2 , then the value of z is close to :

solution let x be the first number . ley y be the second number x + y = 16 x - y = 4 solve the system of equations by elimination adding the left sides and the right sides gives : x + x + y + - y = 16 + 4 2 x = 20 x = 10 since x + y = 16 , 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 the numbers are 10 and 6 answer a

a ) 10 and 6 , b ) 10 and 5 , c ) 10 and 4 , d ) 10 and 3 , e ) 10 and 2

a

add(multiply(divide(add(16, 4), const_2), const_10), subtract(16, divide(add(16, 4), const_2)))

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

general

if the radius of a circle is decreased 50 % , what happens to the area ?

"6 x = 8 y = 10 z 3 x = 4 y = 5 z 3 ( 4 * 5 ) = 4 ( 3 * 5 ) = 5 ( 3 * 4 ) addition = 20 + 15 + 12 = 47 answer would be multiple of 47 which is 94 answer : d"

a ) 52 , b ) 58 , c ) 84 , d ) 94 , e ) 168

d

divide(multiply(multiply(8, 10), 6), const_4)

multiply(n1,n2)|multiply(n0,#0)|divide(#1,const_4)|

general

a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 480 less than the sum lent . what was the sum lent ?

"interest for 1 year = 320 / 4 = 80 interest on rs 2000 p / a = 80 interest rate = 80 / 2000 * 100 = 4 % answer : c"

a ) 4.5 % , b ) 4.25 % , c ) 4 % , d ) 4.3 % , e ) 4.1 %

c

divide(multiply(const_100, 320), multiply(2000, 4))

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

gain

in an it company , there are a total of 90 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ?

"sol . let the required numbers be 4 x and 5 x . then , their l . c . m . is 20 x . ∴ 20 x = 200 ⇔ x = 10 . hence , the first number is 40 . answer b"

a ) 60 , b ) 40 , c ) 20 , d ) 15 , e ) none

b

multiply(divide(200, multiply(4, 5)), 4)

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

other

( 3 x + 2 ) ( 2 x - 1 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?

"cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 170000 p = rs . [ ( 24 * 4 * 4 * 170000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 65280000 / 9600 ) = > p = rs . 6800 answer : d"

a ) rs . 9800 , b ) rs . 3800 , c ) rs . 9800 , d ) rs . 6800 , e ) rs . 6880

d

divide(multiply(multiply(multiply(24, 4), 4), 170000), multiply(multiply(multiply(10, 16), 6), 10))

multiply(n1,n3)|multiply(n0,n2)|multiply(n3,#0)|multiply(n4,#1)|multiply(n7,#2)|multiply(n0,#3)|divide(#4,#5)|

general

jacob is 12 years old . he is 3 times as old as his brother . how old will jacob be when he is twice as old ?

"s . i . for 1 year = rs . ( 854 - 835 ) = rs . 19 . s . i . for 3 years = rs . ( 19 x 3 ) = rs . 57 . principal = rs . ( 835 - 57 ) = rs . 778 . answer : c"

a ) 647 , b ) 698 , c ) 778 , d ) 847 , e ) 976

c

subtract(835, divide(multiply(subtract(854, 835), 3), 4))

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

gain

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

"here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e"

a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 81

e

divide(add(multiply(divide(subtract(multiply(81.1, const_10), const_2), const_10), divide(11, divide(const_2, const_10))), 11), divide(11, divide(const_2, const_10)))

divide(const_2,const_10)|multiply(n1,const_10)|divide(n0,#0)|subtract(#1,const_2)|divide(#3,const_10)|multiply(#4,#2)|add(n0,#5)|divide(#6,#2)|

general

in an election between the two candidates , the candidates who gets 60 % of votes polled is winned by 280 votes majority . what is the total number of votes polled ?

"let the actual distance traveled be x km . then , x / 8 = ( x + 14 ) / 10 2 x - 112 = > x = 56 km . answer : c"

a ) 50 , b ) 40 , c ) 56 , d ) 16 , e ) 20

c

multiply(8, divide(14, subtract(10, 8)))

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

general

a certain industrial loom weaves 0.13 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?

remainder in second case is , 32 . so , 3 d > = 33 . so , minimum value of d should 11 . if number = 28 . double of number = 56 and take d = 12 so 56 / 36 remainder = 20 . now 5 times of number = 140 . so 140 / 36 remainder = 32 . that is , 3 d = 36 satisfy the conditions . so d = 12 . answer : b

a ) 11 , b ) 12 , c ) 15 , d ) 14 , e ) 18

b

subtract(multiply(divide(32, 5), const_2), divide(const_1, const_4))

divide(n3,n2)|divide(const_1,const_4)|multiply(#0,const_2)|subtract(#2,#1)

general

if the price of gasoline increases by 25 % and a driver intends to spend only 20 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?

"ans 81 reverse of 18 answer : d"

a ) 80 , b ) 25 , c ) 36 , d ) 81 , e ) 56

d

multiply(18, divide(17, 71))

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

general

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 ?

tot no of votes = ( 1136 + 7636 + 11628 ) = 20400 req = > ( 11628 / 20400 * 100 ) = > 57 % answer c

a ) 40 % , b ) 45 % , c ) 57 % , d ) 58 % , e ) 60 %

c

multiply(divide(11628, add(add(1136, 7636), 11628)), const_100)

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

general

a , b and c have rs . 400 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?

"total number of students studying both are 500 + 300 - 300 = 500 ( subtracting the 300 since they were included in the both the other numbers already ) . so 50 % of total is 500 , so 100 % is 1000 answer is d"

a ) 1100 , b ) 1200 , c ) 1150 , d ) 1000 , e ) 1050

d

add(500, 300)

add(n0,n1)|

general

in covering a distance of 30 km , arun takes 22 hours more than anil . if arun doubles his speed , then he would take 1 hour less than anil . what is arun ' s speed ?

"1 / 8 + 1 / 10 - 1 / x = 1 / 10 x = 8 8 * 15 = 120 answer : e"

a ) 590 liters , b ) 160 liters , c ) 740 liters , d ) 560 liters , e ) 120 liters

e

multiply(multiply(inverse(subtract(add(add(divide(const_1, 8), divide(const_1, 10)), divide(const_1, 15)), divide(const_1, 10))), const_3), 10)

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

physics

a person saved $ 10 in buying an item on sale . if he spent $ 200 for the item , approximately how much percent he saved in the transaction ?

"let each installment be x [ x + ( x * 12 * 1 / 100 ) ] + [ x + ( x * 12 * 2 / 100 ) ] + x = 1092 28 x / 25 + 31 x / 25 + x = 1092 x = 325 answer is d"

a ) $ 210 , b ) $ 115 , c ) $ 295 , d ) $ 325 , e ) $ 415

d

multiply(multiply(const_100.0, divide(12, 1092)), 3)

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

gain

the principal that amounts to rs . 4903 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?

"yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 40 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 20 cents . fraction of spirit is 1 / 2 . 20 = k * ( 1 / 2 ) k = 40 cost per liter = 40 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 40 * ( 1 / 3 ) * 3 = 40 cents a . 40 cents"

a ) 40 , b ) 33 , c ) 50 , d ) 51 , e ) 52

a

multiply(multiply(40, divide(1, add(1, 2))), add(1, 2))

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

geometry

how many of the integers between 20 and 80 are even ?

"e 40 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 54 days . so , 27 women can do it in ( 20 * 54 ) / 27 = 40 days ."

a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days

e

inverse(add(divide(9, multiply(12, 54)), divide(12, multiply(20, 54))))

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

physics

cp of 3 buffaloes are $ 30,000 . by selling 1 at a loss of 15 % and other at a profit of 19 % , he foundthat sp of both buffaloes is the same . find the cp of each ?

a = { 3 , - 8 , y , 19 , - 6 } b = { k , - 3 , 0,16 , - 5,9 } y > 21 so l = median of q = 3 m = mode of set b z = ( 3 ) ^ m if z is a divisor of 26 , ( 3 ) ^ m = 1 because 26 does not have 3 as a factor = > m = 0 hence k = 0 , as m is mode and 0 will be the most frequently occuring number in set b . answer - c

a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2

c

log(3)

log(n0)

general

there are 24 students in a seventh grade class . they decided to plant birches and roses at the school ' s backyard . while each girl planted 3 roses , every three boys planted 1 birch . by the end of the day they planted 2424 plants . how many birches were planted ?

"g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 13 w 19 + 9 x = 13 ( x + 1 ) x = 3 / 2 ratio of gold with copper = 1 : 3 / 2 = 2 : 3 answer is b"

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

b

divide(subtract(13, 9), subtract(19, 13))

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

general

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

"remainder = 0.60 - - > 60 / 100 - - > can be written as ( 60 / 4 ) / ( 100 / 4 ) = 15 / 25 so remainders can be 15 , 30 , 45 , 60 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 15 + 30 + 45 + 60 + 75 + 90 = 315 answer : b"

a ) 560 , b ) 315 , c ) 672 , d ) 900 , e ) 1024

b

add(multiply(divide(const_3, const_2), const_100), add(multiply(add(const_2, const_3), 59.60), const_3))

add(const_2,const_3)|divide(const_3,const_2)|multiply(n0,#0)|multiply(#1,const_100)|add(#2,const_3)|add(#4,#3)|

general

abel can complete a work in 10 days , ben in 12 days and carla in 16 days . all of them began the work together , but abel had to leave after 2 days and ben 4 days before the completion of the work . how long did the work last ?

"explanation : suppose b invested rs . x for y months . then , a invested rs . 3 x for 2 y months . so , a : b = ( 3 x * 2 y ) : ( x * y ) = 6 xy : xy = 6 : 1 . b ' s profit : total profit = 1 : 7 . let the total profit be rs . x then , 1 / 7 = 4000 / x or x = 28000 . answer : b ) 28000"

a ) 23477 , b ) 28000 , c ) 28877 , d ) 1987 , e ) 1771

b

multiply(add(multiply(const_2, const_3), const_1), 4000)

multiply(const_2,const_3)|add(#0,const_1)|multiply(n0,#1)|

general

what will be the difference between simple and compound interest at 14 % per annum on a sum of rs . 1000 after 4 years ?

in 1 hr , the bus covers 100 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 100 - 40 ) km i . e 60 km at 100 km / hr . stoppage time = 60 / 100 hrs = 36 min answer : e

a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 36 min

e

subtract(multiply(const_1, const_60), multiply(divide(40, 100), const_60))

divide(n1,n0)|multiply(const_1,const_60)|multiply(#0,const_60)|subtract(#1,#2)

general

the h . c . f of two numbers is 11 and their l . c . m is 7700 . if one of the numbers is 275 , then the other is ?

avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 15 + 45 ) / ( ( 15 / 24 ) + ( 45 / 45 ) ) = 60 * 2 / 3 = 36.92 mph d

a ) 35.62 mph , b ) 25.45 mph , c ) 34.52 mph , d ) 36.92 mph , e ) 36.29 mph

d

divide(60, add(divide(45, subtract(60, 15)), divide(15, 24)))

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

physics

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

"0.04 x + 0.09 y = 325000 [ 1 ] 0.04 x = 0.80 * 325000 = 260000 [ 2 ] 260000 + 0.09 y = 325000 - - > 0.09 y = 65000 [ 3 ] 260000 / 12 = 21666.67 [ 4 ] 65000 / 12 = 5416.667 [ 5 ] adding [ 4,5 ] we get : 27083.33 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.354 , ans a"

a ) $ 1,354 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796

a

subtract(9, multiply(4, const_2))

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

general

a and b together can complete work in 10 days . a alone starts working and leaves it after working for 6 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?

"answer = e please refer diagram below 70 - 10 = 60"

a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 60

e

subtract(80, 10)

subtract(n0,n1)|

general

the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if x 20 = 190 , what is the value of x ?

"official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 114 , the smallest is 51 ) : 114 - 51 = 63 step 2 . divide by 3 : 63 / 3 = 21 step 3 . add 1 : 21 + 1 = 22 . so there are 22 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 114 , the smallest is 50 ) : 114 - 50 = 64 step 2 . divide by 2 : 64 / 2 = 32 step 3 . add 1 : 32 + 1 = 33 . so there are 33 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 22 multiples of 3 and the 33 multiples of 2 : 22 + 33 = 55 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 22 + 33 = 55 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 55 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 114 - 54 = 60 step 2 . divide by 6 : 60 / 6 = 10 step 3 . add 1 : 10 + 1 = 11 . so there are 11 multiples of 6 within the range : we counted 11 numbers twice . subtract the 11 multiples of 6 from the sum of the multiples of 2 and 3 : = 22 + 33 - 11 = 55 - 11 = 44 therefore , the final number of multiples of 2 , 3 or 6 is 44 . hence , this is the correct answer . ( b )"

a ) 34 , b ) 44 , c ) 45 , d ) 55 , e ) 72

b

subtract(add(floor(divide(subtract(114, 49), 3)), divide(subtract(114, 49), 2)), floor(divide(subtract(114, 49), multiply(2, 3))))

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

other

the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years q in which the population would be doubled assuming there is no emigration or immigration is

"another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 4 = 6 so we need 6 - 4 = 2 more machines . answer : a"

a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8

a

subtract(divide(multiply(12, add(const_4, const_1)), 8), add(const_4, const_1))

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

physics

what is the difference between the largest number and the least number written with the digits 6 , 3 , 2 , 5 ?

"here 8 articles selling price = 10 articles cost price so the difference = 10 - 8 = 2 % of profit = 2 * 100 / 8 = 25 % correct option is b"

a ) 10 % , b ) 25 % , c ) 20 % , d ) 30 % , e ) 50 %

b

multiply(divide(subtract(10, 8), 8), const_100)

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

gain

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 ?

"1 cut makes 2 pieces a second cut can make 4 pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces d"

a ) 10 , b ) 14 , c ) 15 , d ) 16 , e ) 17

d

multiply(5, const_3)

multiply(n0,const_3)|

geometry

a money lender lent rs . 1000 at 4 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .

ped = 3 / 5 = 12 / 20 sur = 1 / 4 = 4 / 20 gp = 1 - ( 12 / 20 + 4 / 20 ) = 1 - 16 / 20 = 4 / 20 hsur = ( 1 / 4 ) ( 4 / 20 ) = 1 / 20 if gp doubled = > ( 2 ) ( 4 ) = 8 ; then , total = 12 + 4 + 8 = 24 , and 1 is hsur = > proportion = 1 / 24 . answer : d

a ) 2 / 5 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 24 , e ) 1 / 25

d

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

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

general

the least number which when increased by 5 each divisible by each one of 24 , 32 , 36 and 54 is :

the intersection for two = 45 - 12 - 22 = 11 play both games . answer : c

a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13

c

subtract(45, add(12, 22))

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

other

if the given two numbers are respectively 7 % and 28 % of a third number , then what percentage is the first of the second ?

"total - neither = all air conditioning + all power steering - both or 75 - neither = 45 + 35 - 12 = 68 . = > neither = 7 , hence a . answer : a"

a ) 7 , b ) 8 , c ) 10 , d ) 15 , e ) 18

a

subtract(75, subtract(add(45, 35), 12))

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

other

a train 150 m long running at 72 kmph crosses a platform in 20 sec . what is the length of the platform ?

let the annual bonus be x . a corporation triples its annual bonus . so new bonus = 5 x . increase = 5 x - x = 4 x the increase is what percent of the employees ’ new bonus = ( 4 x / 5 x ) * 100 = 80 % hence c .

a ) 12 % , b ) 18 % , c ) 80 % , d ) 20 % , e ) 15 %

c

multiply(divide(subtract(5, const_1), 5), const_100)

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

general

in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 6000 , the number of valid votes that the other candidate got , was :

"explanation let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 x = 4 . age of the youngest child = x = 4 years . answer a"

a ) 4 years , b ) 8 years , c ) 10 years , d ) none of these , e ) can not be determined

a

subtract(subtract(divide(50, 5), 3), 3)

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

general

5 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?

total cost 940 940 * 25 / 100 = 235 so the cut in amount is 235 the less amount to be spend is 940 - 235 = 705 answer : a

a ) 705 , b ) 655 , c ) 656 , d ) 657 , e ) 658

a

multiply(divide(subtract(const_100, 25), const_100), 940)

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

general

two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 60 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?

"20 / 5 = 4 answer : c"

a ) 20 % , b ) 17 % , c ) 4.0 % , d ) 3.3 % , e ) 2.8 %

c

multiply(divide(divide(divide(const_100, const_3), 5), const_100), const_100)

divide(const_100,const_3)|divide(#0,n1)|divide(#1,const_100)|multiply(#2,const_100)|

general

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

"c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 20 . loss % = 30 / 50 * 100 = 60 % answer d"

a ) 45 % , b ) 23 % , c ) 20 % , d ) 60 % , e ) 56 %

d

subtract(50, 20)

subtract(n0,n1)|

gain

today is thursday . i came home from a trip 3 days before the day after last monday . how many days have i been home ?

"sol . therefore correct sum = ( 40 × 50 + 48 – 23 ) = 2023 . therefore correct mean = 2023 / 50 = 40.46 . answer a"

a ) 40.46 , b ) 36.1 , c ) 36.5 , d ) 39.1 , e ) none

a

divide(add(multiply(40, 50), subtract(subtract(50, const_2), 23)), 50)

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

general

a cat leaps 6 leaps for every 5 leaps of a dog , but 2 leaps of the dog are equal to 3 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?

each set has 12 even and 13 odd numbered questions leading to total 96 even and 104 odd questions . 96 + 3 / 4 â ˆ — 104 = 96 + 78 = 17496 + 3 / 4 â ˆ — 104 = 96 + 78 = 174 answer : a

a ) 174 , b ) 150 , c ) 180 , d ) 175 , e ) 190

a

add(divide(multiply(8, 25), const_2), multiply(divide(multiply(8, 25), const_2), divide(3, 4)))

divide(n4,n5)|multiply(n0,n1)|divide(#1,const_2)|multiply(#2,#0)|add(#2,#3)

general

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

"speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 30 ) m = 500 m . answer : a"

a ) 500 m , b ) 620 m , c ) 872 m , d ) 150 m , e ) 765 m

a

multiply(divide(multiply(60, const_1000), const_3600), 30)

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

physics

two trains start simultaneously from opposite ends of a 175 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 175 - km trip in 4 hours . train y , travelling at a constant rate , completes the 175 - km trip in 3 hours . how many kilometers had train x traveled when it met train y ?

"total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.6 = $ 306 answer a"

a ) $ 306 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550

a

multiply(divide(multiply(3.06, multiply(const_1000, const_1000)), multiply(multiply(20, 20), 15)), 0.60)

multiply(const_1000,const_1000)|multiply(n0,n0)|multiply(n4,#0)|multiply(n2,#1)|divide(#2,#3)|multiply(n3,#4)|

general

find the sum 3 / 10 + 5 / 100 + 8 / 1000 in decimal form ?

"2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 10 * 3 * 1 ) / 3 = 30 / 3 = 10 a"

a ) a ) 10 , b ) b ) 2 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4

a

divide(add(divide(subtract(multiply(7, 2), 5), subtract(multiply(2, 2), const_1)), subtract(7, multiply(2, divide(subtract(multiply(7, 2), 5), subtract(multiply(2, 2), const_1))))), 10)

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

general

the average of 5 consecutive odd numbers a , b , c , d and e is 33 . what percent of a is d ?

"let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 80 5 x = 50 x = 10 . age of the youngest child = x = 10 years . e )"

a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 10 years

e

subtract(subtract(divide(80, 5), 3), 3)

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

general

mary ' s income is 60 % more than tim ' s income and tim ' s income is 60 % less than juan ' s income . what % of juan ' s income is mary ' s income .

"2 = x * 40 / 100 x = 5 % ans ; c"

a ) 0.2 % , b ) 2 % , c ) 5 % , d ) 20 % , e ) 500 %

c

multiply(divide(2, 40), const_100)

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

gain

in a certain pond , 55 fish were caught , tagged , and returned to the pond . a few days later , 55 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 ` s the approximate number of fish in the pond ?

"221 + 43 = 264 / 17 = 9 ( remainder ) c"

a ) 3 , b ) 6 , c ) 9 , d ) 11 , e ) 15

c

divide(add(221, 43), 19)

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

general

each of the three people individually can complete a certain job in 3 , 5 , and 6 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?

"explanation : since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . cost of 1 kg tea of 1 st kind cost of 1 kg tea of 2 nd kind x - 153 / 22.50 = 1 = > x - 153 = 22.50 = > x = 175.50 . hence , price of the third variety = rs . 175.50 per kg . answer : c ) rs . 175.50"

a ) 175.59 , b ) 175.5 , c ) 175.57 , d ) 175.52 , e ) 175.11

c

divide(subtract(multiply(153, add(add(1, 1), 2)), add(126, 126)), 2)

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

other

what least number must be subtracted from 3832 so that the remaining number is divisible by 5 ?

"let the number of correct answers be x . number of incorrect answers = ( 80 â € “ x ) . 4 x â € “ 1 ( 80 â € “ x ) = 120 or 5 x = 200 or x = 40 . answer : e"

a ) 35 , b ) 46 , c ) 42 , d ) 30 , e ) 40

e

divide(add(120, 80), add(4, 1))

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

physics

the compound ratio of 5 : 6 , 3 : 2 and 6 : 5 ?

"required ratio = 2 / 3 * 6 / 11 * 11 / 4 = 2 / 1 = 1 : 1 answer is c"

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

c

multiply(divide(2, 11), multiply(divide(2, 3), divide(6, 3)))

divide(n0,n5)|divide(n2,n1)|multiply(#0,#1)|multiply(#0,#2)|

other

what is the unit digit in the product ( 3 ^ 65 x 6 ^ 59 x 7 ^ 71 ) ?

"( 555 + 445 ) * 2 * 110 + 10 = 220000 + 10 = 220010 a"

a ) 220010 , b ) 145778 , c ) 220110 , d ) 235467 , e ) 220001

a

add(multiply(multiply(add(555, 445), 2), subtract(555, 445)), 10)

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

general

what is the probability of drawing a queen from a deck of 52 cards ?

"23 + 29 = 52 but where as total number is 55 - 7 = 48 therefore answer is 52 - 48 = 4 hence answer is c"

a ) 3 , b ) 5 , c ) 4 , d ) 7 , e ) 8

c

subtract(add(add(23, 29), 7), 55)

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

other

a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 66 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?

"500 - - - - 20 500 - - - - 6 x - - - - - 3 x * 3 = 500 * 6 x = 1000 500 - - - - - - - 500 answer : a"

a ) 500 , b ) 1000 , c ) 1500 , d ) 3000 , e ) 2000

a

subtract(divide(subtract(multiply(500, 20), multiply(500, 14)), 3), 500)

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

physics

3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 12 pumps work to empty the tank in 1 day ?

"t = ( 660 + 165 ) / 54 * 18 / 5 t = 55 answer a"

a ) 55 sec , b ) 40 sec , c ) 45 sec , d ) 30 sec , e ) 35 sec

a

divide(add(165, 660), multiply(54, const_0_2778))

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

physics

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

"let abhay ' s speed be x km / hr . then , 54 / x - 54 / 2 x = 3 6 x = 54 x = 9 km / hr . answer : option e"

a ) 5 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7.5 kmph , e ) 9 kmph

e

divide(subtract(54, divide(54, 2)), add(1, 2))

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

physics

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 ?

area of circle is pi * r ^ 2 but in 10 minutes area covered is ( 10 / 60 ) * 360 = 60 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.6 ^ 2 ) * ( 60 / 360 ) = 16.41 cm ^ 2 answer : d

a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 16.41 , e ) 19.27

d

multiply(divide(add(multiply(const_2, const_10), const_2), add(const_3, const_4)), multiply(multiply(5.6, 5.6), divide(multiply(const_1, const_60), multiply(const_100, const_3_6))))

add(const_3,const_4)|multiply(const_10,const_2)|multiply(const_1,const_60)|multiply(const_100,const_3_6)|multiply(n0,n0)|add(#1,const_2)|divide(#2,#3)|divide(#5,#0)|multiply(#6,#4)|multiply(#7,#8)

physics

a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many cubes are painted on only 2 faces ?

suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e

a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 500

e

divide(subtract(1600, 600), const_2)

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

general

a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 35 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?

"speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 1000 + x ) / 60 = 65 / 3 x = 300 m . answer : c"

a ) 288 m , b ) 256 m , c ) 1000 m , d ) 278 m , e ) 287 m

c

divide(1000, multiply(subtract(78, 1), const_0_2778))

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

physics

if x / y = 5 / 3 , then ( x + y ) / ( x - y ) = ?

we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 181 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 181 m ) / ( w + m ) = 180 170 w + 181 m = 180 w + 180 m 1 m = 10 w m / w = 10 / 1 the ratio of men to women is 10 to 1 . e

a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 10 : 1

e

divide(subtract(180, 170), subtract(181, 180))

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

general

in a throw of dice what is the probability of ge æ « ng number greater than 4

"longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 18 = 2 * 9 so radius of the circle = 9 correct answer - b"

a ) 2.5 , b ) 9 , c ) 10 , d ) 15 , e ) 20

b

divide(18, const_2)

divide(n0,const_2)|

geometry

a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 28 adults have their meal , find the total number of children that can be catered with the remaining food .

area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 10 x 1.25 ) + 10 x 4 ] = 75 the answer is d .

a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85

d

add(add(multiply(10, 4), multiply(const_2, multiply(4, add(1, divide(25, const_100))))), multiply(const_2, multiply(10, add(1, divide(25, const_100)))))

divide(n3,const_100)|multiply(n0,n1)|add(n2,#0)|multiply(n1,#2)|multiply(n0,#2)|multiply(#3,const_2)|multiply(#4,const_2)|add(#1,#5)|add(#7,#6)

physics

the average age of a group of 10 students is 20 years . if 2 more students join the group , the average age increases by 1 year . the average age of the new students is

"total number of ways of choosing one student from each group is = 800 * 1000 number of cases in which a sibling pair will be got is = 60 thus the probability that the 2 students selected will be a sibling pair is = 20 / ( 800 * 1000 ) = 1 / 40,000 d"

a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 40,000 , e ) 1 / 15

d

divide(1, const_3)

divide(n3,const_3)|

probability

a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 40 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.5 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 6 hours ?

"50 % of ( x - y ) = 30 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 5 ( x - y ) = 3 ( x + y ) 2 x = 8 y x = 4 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 4 y ) x 100 ) = 25 % answer is e ."

a ) 2.5 % , b ) 10 % , c ) 5 % , d ) 15 % , e ) 25 %

e

multiply(divide(subtract(50, 30), add(50, 30)), const_100)

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

general

if 36 men can do a piece of work in 25 hours , in how mwny hours will 15 men do it ?

18 km / hr = 18000 m / 3600 s = 5 m / s time = 600 / 5 = 120 seconds the answer is b .

a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180

b

divide(600, multiply(18, const_0_2778))

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

physics

thirty percent of the members of a swim club have passed the lifesaving test . among the members who have not passed the test , 26 have taken the preparatory course and 65 have not taken the course . how many members are there in the swim club ?

"the length of wall painted by one boy in one day = 70 / 6 * 1 / 8 = 1.46 m no . of days required to paint 50 m cloth by 8 boys = 80 / 10 * 1 / 1.46 = 5.48 days . d"

a ) 9.48 days , b ) 3.48 days , c ) 7.48 days , d ) 5.48 days , e ) 6.48 days

d

divide(multiply(multiply(6, 8), 80), multiply(70, 10))

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

physics

a sum of money is distributed among a , b , c , d in the proportion of 1 : 3 : 4 : 2 . if c gets $ 500 more than d , what is the b ' s share ?

"( 555 + 445 ) * 2 * 110 + 60 = 220000 + 60 = 220060 e"

a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220060

e

add(multiply(multiply(add(555, 445), 2), subtract(555, 445)), 60)

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

general

on a certain transatlantic crossing , 40 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 20 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?

"if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 15 hrs it wil be 15 ft . bt since the height of the tree is 18 ft , so if the monkey hops up the tree in the next hr i . e 16 th hr then it reaches at the top of the tree . hence it takes 16 hrs for monkey to reach at the top answer : e"

a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs

e

subtract(divide(18, subtract(3, 2)), 2)

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

physics

a certain company reported that the revenue on sales increased 40 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?

"let us assume that the work is laying 40 bricks . jane = 5 bricks per day ashley = 1 brick per day together = 6 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 8 last 4 days jane works alone , no . of bricks = 20 remaining bricks = 40 - 28 = 12 so together , they would take 12 / 6 = 2 total no . of days = 8 + 4 + 2 = 14 answer is a"

a ) 14 days , b ) 15 days , c ) 16 days , d ) 18 days , e ) 20 days

a

add(add(divide(subtract(subtract(const_1, multiply(const_4, divide(const_1, 8))), multiply(add(const_4, const_4), divide(const_1, 40))), add(divide(const_1, 8), divide(const_1, 40))), add(const_4, const_4)), const_4)

add(const_4,const_4)|divide(const_1,n0)|divide(const_1,n1)|add(#1,#2)|multiply(#1,const_4)|multiply(#0,#2)|subtract(const_1,#4)|subtract(#6,#5)|divide(#7,#3)|add(#0,#8)|add(#9,const_4)|

physics

in a division , a student took 78 as divisor instead of 36 . his answer was 24 . the correct answer is -

"because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 and , thus , a probability of 1 / 8 that it will be divisible by 16 and , thus , a probability of 1 / 16 that it will be divisible by 32 1 * 1 / 16 = 1 / 16 answer : c"

a ) 2 / 7 , b ) 3 / 7 , c ) 1 / 16 , d ) 1 / 14 , e ) 1 / 12

c

divide(const_2, 32)

divide(const_2,n3)|

general

in what ratio should a variety of rice costing rs . 6.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?

we ' re asked how old jim is now . we ' re given three facts to work with : 1 ) today , jim is twice as old as fred 2 ) today , sam is 4 years younger than fred 3 ) four years ago , jim was 8 times as old as sam . let ' s test answer d : 20 if . . . . jim is currently 20 years old . . . . fred is 10 years old sam is 6 years old 4 years ago , jim was 16 and sam was 2 , so jim was 8 times sam ' s age . this is an exact match for what we were told , so this must be the answer . d

a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24

d

multiply(divide(subtract(multiply(8, 8), 4), subtract(8, const_2)), const_2)

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

general

oak street begins at pine street and runs directly east for 2 kilometers until it ends when it meets maple street . oak street is intersected every 400 meters by a perpendicular street , and each of those streets other than pine street and maple street is given a number beginning at 1 st street ( one block east of pine street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of maple street . what is the highest - numbered street that intersects oak street ?

e 15 sec speed of the bullet train relative to man = ( 30 + 6 ) kmph = 36 * 5 / 18 m / sec = 30 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 150 m at ( 30 / 3 ) m / sec = ( 150 * 3 / 30 ) sec = 15 sec

a ) 23 sec , b ) 15 sec , c ) 12 sec , d ) 11 sec , e ) 15 sec

e

divide(150, divide(multiply(add(30, 6), const_1000), const_3600))

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

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 ?

"- 20 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 20 - 19 sum of which is - 39 . hence option d . d"

a ) 0 , b ) - 2 , c ) - 25 , d ) - 39 , e ) - 51

d

add(add(negate(21), const_1), add(add(negate(21), const_1), const_1))

negate(n0)|add(#0,const_1)|add(#1,const_1)|add(#1,#2)|

general

in the seaside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?

"l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 150 ( 30 * 5 ) profit percentage = ( 150 - 100 ) / 100 * 100 = 50 % answer : b"

a ) 25 % , b ) 50 % , c ) 20 % , d ) 5 % , e ) none of these

b

subtract(multiply(30, 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

find the product of the place value and face value of 3 in 5769354

"is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 95 106 115 124 14 ways . . c"

a ) 7 , b ) 8 , c ) 14 , d ) 16 , e ) 20

c

subtract(subtract(24, 7), const_2)

subtract(n0,n2)|subtract(#0,const_2)|

general

selling an kite for rs . 30 , a shop keeper gains 40 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?

let x be the daily wage before the increase . 1.5 x = $ 30 x = $ 20 the answer is c .

a ) $ 15 , b ) $ 18 , c ) $ 20 , d ) $ 22 , e ) $ 25

c

divide(30, add(const_1, divide(50, const_100)))

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

physics

900 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?

"120 % * 13 / 24 * 360 = 1.2 * 13 * 25 = 390 the answer is b ."

a ) 320 , b ) 390 , c ) 440 , d ) 480 , e ) 510

b

divide(multiply(120, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100)

add(const_2,const_3)|add(const_3,const_4)|add(const_3,const_3)|multiply(const_3,const_4)|multiply(#0,const_2)|multiply(#3,const_100)|multiply(#1,#0)|multiply(#4,#5)|multiply(#6,#4)|add(#7,#8)|add(#9,#2)|multiply(n0,#10)|divide(#11,const_100)|

gain

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

"answer ∵ weight of 12 m long rod = 13.4 kg ∴ weight of 1 m long rod = 13.4 / 12 kg ∴ weight of 6 m long rod = 13.4 x 6 / 12 = 6.7 kg option : a"

a ) 6.7 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 18.0 kg , e ) none

a

divide(multiply(6, 13.4), 12)

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

physics

what is the range of all the roots of | x ^ 2 - 3 | = x ?

"according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 60 - 12 * 3 * 2 = 60 - 8 = 52 correct answer b"

a ) 42 , b ) 52 , c ) 62 , d ) 72 , e ) 82

b

subtract(60, multiply(multiply(12, 3), 2))

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

general

if the radius of a circle is decreased 50 % , what happens to the area ?

"let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 2 ) ( b + 2 ) = m - - - - ( 2 ) and ( l + 8 ) ( b + 8 ) = m + 108 - - - - - - - - - > ( l + 8 ) ( b + 8 ) - 108 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 8 ) ( b + 8 ) - 108 lb + 2 l + 2 b + 4 = lb + 8 l + 8 b + 64 - 108 simplify 6 l + 6 b = 48 - - - - - - > 2 ( l + b ) = 16 ( check eq ( 1 ) ) answer is c"

a ) 34 , b ) 36 , c ) 16 , d ) 40 , e ) 42

c

divide(subtract(108, subtract(power(multiply(4, const_2), const_2), power(multiply(1, const_2), const_2))), const_2)

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

geometry

a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts 6 hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?

a has 10 yellows 20 reds total = 30 so b has 1.2 x 20 = 24 reds 0.9 x 10 = 9 yellows total = 33 difference = 3 / 30 = 10 % answer : e

a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10

e

multiply(subtract(divide(add(add(const_100, 20), subtract(const_100, 10)), const_100), const_2), const_100)

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

general

there are 8 books on a shelf , of which 3 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?

we first write the prime factorization of each given number 24 = 2 × 2 × 2 × 3 = 23 * cubic * × 3 40 = 2 × 2 × 2 × 5 = 23 * cubic * × 5 60 = 2 × 2 × 3 × 5 = 22 * square * × 3 × 5 gfc = 22 * square * = 4 corect answer is d ) 4

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

d

gcd(gcd(24, 40), 60)

gcd(n0,n1)|gcd(n2,#0)

other

a chemist mixes one liter of pure water with x liters of a 50 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?

"let that divisor be x since remainder is 12 or 16 it means divisor is greater than 16 . now 242 - 12 = 230 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 16 = 682 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 230 + 682 ) + 12 + 16 = x ( k + l ) + 28 when we divide this number by x then remainder will be equal to remainder of ( 28 divided by x ) = 10 hence x = 28 - 10 = 18 hence b"

a ) 11 , b ) 18 , c ) 13 , d ) 23 , e ) none of these

b

subtract(add(12, 16), 10)

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

general

a train covers a distance of 10 km in 20 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?

"explanation : let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 80 gain % = 16 / 64 * 100 = 25 % . answer : option e"

a ) 37.5 % , b ) 48 % , c ) 50.5 % , d ) 52 % , e ) 25 %

e

multiply(subtract(divide(subtract(const_100, 20), 64), const_1), const_100)

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

gain

how many liters of water must be evaporated from 50 liters of a 6 - percent sugar solution to get a 10 - percent solution ?

"d 90 % - - - 22 150 % - - - ? 90 / 150 * 22 = 13"

a ) 12 , b ) 14 , c ) 45 , d ) 13 , e ) 65

d

inverse(add(divide(divide(const_100, subtract(const_100, 10)), 22), divide(multiply(divide(divide(const_100, subtract(const_100, 10)), 22), 50), const_100)))

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

gain