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mathqa_shuffle_question_test

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a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 16 days . in how many days b alone can do the work ?

"giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 31.1 ) / ( 100 â ˆ ’ 5 ) = 138 hence , required % profit = 138 â € “ 100 = 38 % answer a"

a ) 38 , b ) 27.675 , c ) 30 , d ) data inadequate , e ) none of these

a

subtract(divide(multiply(add(const_100, 31.1), const_100), subtract(const_100, 5)), const_100)

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

gain

john makes $ 60 a week from his job . he earns a raise andnow makes $ 80 a week . what is the % increase ?

"s . i . = ( 1000 * 14 * 4 ) / 100 = rs . 560 c . i . = [ 1000 * ( 1 + 14 / 100 ) 4 - 1000 ] = rs . 689 difference = ( 689 - 560 ) = rs . 129 answer : a"

a ) 129 , b ) 130 , c ) 124 , d ) 133 , e ) 145

a

subtract(subtract(multiply(1000, power(add(divide(14, const_100), const_1), 4)), 1000), multiply(multiply(1000, divide(14, const_100)), 4))

divide(n0,const_100)|add(#0,const_1)|multiply(n1,#0)|multiply(n2,#2)|power(#1,n2)|multiply(n1,#4)|subtract(#5,n1)|subtract(#6,#3)|

gain

a 250 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?

"the total number of stations = 30 from 30 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 3 ⁰ p ₂ ways . 30 p ₂ = 30 * 29 = 870 . answer : c"

a ) 156 , b ) 167 , c ) 870 , d ) 352 , e ) 380

c

multiply(add(28, const_1), add(add(28, const_1), const_1))

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

physics

find the product of the local value and absolute value of 2 in 564823

"p = 3888 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 3888 / ( 1 + 20 / 100 ) ^ 2 = 3888 / ( 6 / 5 ) ^ 2 = 2700 ( approximately ) answer is e"

a ) 2500 , b ) 2100 , c ) 3500 , d ) 3600 , e ) 2700

e

add(3888, divide(multiply(3888, 20), const_100))

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

gain

a certain farmer pays $ 70 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 605 feet ? ( 43,560 square feet = 1 acre )

"13 : 93 = 1 : 729 answer : e"

a ) 1 : 0 , b ) 1 : 8 , c ) 1 : 7 , d ) 1 : 2 , e ) 1 : 729

e

divide(power(const_2.0, 9), power(const_3.0, 9))

power(const_2.0,n1)|power(const_3.0,n1)|divide(#0,#1)|

other

find the smallest number in gp whose sum is 38 and product is 1728

"easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 1,0 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 s = - 49 . d is the answer ."

a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 51

d

add(add(negate(26), const_1), add(add(negate(26), const_1), const_1))

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

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 ?

"the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 36 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 360 / 10,000 = 36 / 1000 = 0.036 ft the answer is a ."

a ) 0.036 , b ) 0.36 , c ) 0.6 , d ) 6 , e ) 3.6

a

divide(volume_cylinder(6, 10), circle_area(100))

circle_area(n0)|volume_cylinder(n2,n3)|divide(#1,#0)|

geometry

when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 3 of the remaining balance , what will be the final balance in her bank account ?

"let x be the number of 35 ounce cans . therefore ( x + 20 ) is the number of 25 ounce cans . total volume is same , therefore 35 x = 25 ( x + 20 ) 10 x = 500 x = 50 therefore , number of 15 ounce cans = 50 + 20 = 70 ans - b"

a ) 60 , b ) 70 , c ) 80 , d ) 100 , e ) 120

b

add(25, 20)

add(n1,n2)|

general

if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 13 . what is the value of f ( 6 ) ?

"101 * n ^ 2 < = 10000 n ^ 2 < = 10000 / 101 which will be less than 100 since 10000 / 100 = 100 which is the square of 9 next closest value of n where n ^ 2 < = 100 is 9 ans c"

a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11

c

floor(sqrt(divide(10000, 101)))

divide(n2,n0)|sqrt(#0)|floor(#1)|

general

rahim bought 52 books for rs . 1200 from one shop and 32 books for rs . 480 from another . what is the average price he paid per book ?

"explanation : use formula for a work members ã — days = constant 10 ã — 4 = 5 ã — a a = 8 so answer is 8 days answer : d"

a ) 10 , b ) 4 , c ) 5 , d ) 8 , e ) 6

d

divide(const_1, multiply(divide(const_1, multiply(const_4.0, 10)), 4))

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

physics

p and q started a business investing rs . 48,000 and rs . 24,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?

"formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 80 / 100 ã — 80 / 100 x 80 / 100 = 4096 answer : b"

a ) 5100 , b ) 4096 , c ) 5200 , d ) 5400 , e ) 5500

b

subtract(subtract(8000, multiply(8000, divide(20, const_100))), multiply(subtract(8000, multiply(8000, divide(20, const_100))), divide(20, const_100)))

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

gain

the average of 6 no . ' s is 3.95 . the average of 2 of them is 4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?

"let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 140 % of rs . 1600 = 140 / 100 * 1600 = rs . 2240 . answer : e"

a ) 2000 , b ) 2778 , c ) 2299 , d ) 2778 , e ) 2240

e

multiply(divide(add(const_100, 40), const_100), divide(add(1920, 1280), const_2))

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

gain

if 3 ^ x = 2 , then 3 ^ ( 4 x + 3 ) =

"let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 360 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 360 x = ( 10 x 4 x 360 ) / ( 6 ) x = 2400 . answer : c"

a ) 648 , b ) 1800 , c ) 2400 , d ) 10800 , e ) 10900

c

multiply(multiply(divide(360, 6), 4), 10)

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

gain

mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8010 / - . find out the amount that he borrowed .

divide as ( 1 - 100 ) ( 100 - 200 ) . . . . ( 900 - 1000 ) total 192 answer : c

a ) 190 , b ) 191 , c ) 192 , d ) 193 , e ) 194

c

add(add(divide(1000, const_10), multiply(subtract(const_10, 1), const_10)), const_2)

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

general

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

"investment = rs . [ 20 x ( 50 - 5 ) ] = rs . 900 . face value = rs . ( 50 x 20 ) = rs . 1000 . dividend = rs . 27 x 1000 = rs . 135 . 2 100 interest obtained = 135 x 100 % = 15 % 900 view answer discuss in forum answer : c"

a ) 27 % , b ) 87 % , c ) 15 % , d ) 66 % , e ) 88 %

c

divide(multiply(multiply(20, 50), divide(13, const_100)), multiply(20, subtract(50, 5)))

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

gain

the average age of 36 students in a group is 13 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?

"? % of 360 = 108 or , ? = 108 × 100 / 360 = 30 answer a"

a ) 30 , b ) 36 , c ) 64 , d ) 72 , e ) none of these

a

divide(multiply(108, const_100), 360)

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

gain

a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is - .

"speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 300 + 150 = 450 m required time = 450 * 2 / 25 = 36 sec answer : option b"

a ) 40 , b ) 36 , c ) 41 , d ) 42 , e ) 34

b

divide(300, multiply(subtract(45, 150), const_0_2778))

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

physics

a box contains 8 pairs of shoes ( 16 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?

"10 ^ 29 is a 30 - digit number : 1 followed by 29 zeros . 10 ^ 29 - 41 is a 29 - digit number : 27 9 ' s and 59 at the end . the sum of the digits is 27 * 9 + 5 + 9 = 257 . the answer is a ."

a ) 257 , b ) 242 , c ) 231 , d ) 202 , e ) 187

a

multiply(add(divide(subtract(subtract(29, 10), const_2), const_2), 10), divide(add(subtract(29, 10), const_2), const_2))

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

general

a school has received 50 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?

"speed = ( 120 x ( 5 / 18 ) m / sec = ( 100 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 100 / 3 ) x 18 ) m = 600 m e"

a ) 560 , b ) 570 , c ) 580 , d ) 590 , e ) 600

e

multiply(divide(multiply(120, const_1000), const_3600), 18)

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

physics

how many figures are required to number the pages the pages of a book containing 223 pages ?

"s = ( 100 + 300 ) / 45 = 400 / 45 * 18 / 5 = 32 answer : a"

a ) 32 kmph , b ) 76 kmph , c ) 34 kmph , d ) 43 kmph , e ) 40 kmph

a

divide(divide(add(100, 300), const_1000), divide(45, const_3600))

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

physics

the lcm and hcf of two numbers are 8 and 48 respectively . if one of them is 24 , find the other ?

"for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 40 sell price = $ 400 + $ 40 thus , the sell price is $ 440 for each item . selling all 100 items gives the retailer . . . 100 ( $ 40 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 440 ) = $ 22 discount $ 418 = $ 400 + $ 18 now , the retailer makes a profit of just $ 18 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 18 ( x ) = $ 2,000 x = 2,000 / 18 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"

a ) 191 , b ) 213 , c ) 221 , d ) 223 , e ) 226

d

divide(multiply(100, 40), subtract(40, divide(multiply(add(divide(multiply(100, 40), 10), 40), 5), 100)))

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

gain

on dividing 123 by a number , the quotient is 7 and the remainder is 4 . find the divisor .

"age of the 15 th student = [ 15 * 14 - ( 14 * 5 + 16 * 9 ) ] = ( 210 - 214 ) = 4 years . answer : b"

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

b

subtract(multiply(15, 15), add(multiply(5, 14), multiply(9, 16)))

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

general

simplify : 0.3 * 0.3 + 0.3 * 0.3

"the bookman had 10 hardback ad 55 - 10 = 45 paperback copies ; 14 copies were sold , hence 55 - 14 = 41 copies were left . let # of paperback copies left be p then 10 p + 20 ( 41 - p ) = 460 - - > 10 p = 360 - - > p = 36 # of paperback copies sold is 45 - 36 = 9 answer : e"

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

e

divide(subtract(subtract(add(multiply(subtract(55, 10), 10), multiply(10, 20)), 460), multiply(gcd(55, 10), 20)), 10)

gcd(n0,n1)|multiply(n1,n2)|subtract(n0,n1)|multiply(n1,#2)|multiply(n2,#0)|add(#3,#1)|subtract(#5,n5)|subtract(#6,#4)|divide(#7,n1)|

general

a contractor undertakes to built a walls in 50 days . he employs 30 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?

"number of statues = all the paint ÷ amount used per statue = 1 / 2 ÷ 1 / 16 = 8 / 16 * 16 / 1 = 8 / 1 = 8 answer is a ."

a ) 8 , b ) 20 , c ) 28 , d ) 14 , e ) 19

a

divide(divide(1, 2), divide(1, 16))

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

general

john purchased some shirts and trousers for $ 1550 . he paid $ 250 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?

"let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.2 ( p * x ) y = ( 1.2 / 1.25 ) x = 0.96 x which is a reduction of 4 % . the answer is c ."

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

c

multiply(divide(subtract(add(25, const_100), add(20, const_100)), add(25, const_100)), const_100)

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

general

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

too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1000 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1000 - - > { not on display } = 1500 . according to ( i ) 2 / 3 * { total } = 1500 - - > { total } = 2250 . answer : b .

a ) 360 , b ) 2250 , c ) 540 , d ) 640 , e ) 720

b

divide(divide(1000, subtract(const_1, divide(1, 3))), subtract(const_1, divide(1, 3)))

divide(n0,n1)|subtract(const_1,#0)|divide(n6,#1)|divide(#2,#1)

general

a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 585.75 . how many boxes of plain cookies did she sell ?

"( 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 72000 / 132000 = 6 / 11 . 6 / 11 is a little above 6 / 12 = 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), 60000), multiply(divide(40, const_100), 72000)), add(72000, 60000)), 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

find the value of 201834 x 99999 = m ?

"area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 900 ã — 22 ) = rs . 19800 answer : option a"

a ) s . 19,800 , b ) s . 15,600 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 17,900

a

multiply(900, multiply(5.5, 4))

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

physics

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

"30 % of 1000 = 300 worked for 15 hours payment @ 5 / hr total payment = 300 * 15 * 5 = 22500 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 22500 + 100000 + 40000 + 15000 = 1775000 hence , answer is d"

a ) $ 180,000 , b ) $ 185,000 , c ) $ 190,000 , d ) $ 177,500 , e ) $ 205,000

d

multiply(add(divide(1, 15), 1), divide(multiply(1000, divide(add(add(multiply(add(multiply(divide(const_3, const_2), multiply(5, 15)), multiply(40, 5)), subtract(15, add(const_3, 5))), multiply(multiply(40, 5), 5)), multiply(multiply(5, 15), const_3)), 15)), 1000))

add(n1,const_3)|divide(n3,n6)|divide(const_3,const_2)|multiply(n1,n6)|multiply(n1,n2)|add(n3,#1)|multiply(#2,#3)|multiply(n1,#4)|multiply(#3,const_3)|subtract(n6,#0)|add(#6,#4)|multiply(#10,#9)|add(#11,#7)|add(#12,#8)|divide(#13,n6)|multiply(n0,#14)|divide(#15,n0)|multiply(#5,#16)|

general

half a number plus 7 is 11 . what is the number ?

let the annual bonus be x . a corporation double its annual bonus . so new bonus = 2 x . increase = 2 x - x = x the increase is what percent of the employees ’ new bonus = ( x / 2 x ) * 100 = 50 % hence a .

a ) 50 % , b ) 12 % , c ) 8 % , d ) 6 % , e ) 5 %

a

multiply(divide(subtract(const_2, const_1), const_2), 100)

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

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 ?

"( 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 b work in 1 days = [ a + b + c ] work in 1 days - work of ( a + c ) in 1 days = [ 1 / 10 - 1 / 12 ] = 1 / 60 b alone finish work in 60 days answer b"

a ) 50 , b ) 60 , c ) 45 , d ) 35 , e ) 48

b

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

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

"rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 16 = 76 * 5 / 18 t = 2500 / 9 * 18 / 380 = 13.15 sec . answer : d"

a ) 10.11 , b ) 8.11 , c ) 77.2 , d ) 13.15 , e ) 22.22

d

multiply(multiply(multiply(const_0_2778, subtract(60, 16)), 50), inverse(multiply(const_0_2778, add(60, 16))))

add(n0,n1)|subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(#1,const_0_2778)|inverse(#2)|multiply(n2,#3)|multiply(#4,#5)|

physics

two numbers are respectively 50 % and 20 % more than a third number . the percentage that is first of the second is ?

"explanation : 30 x = 50 y x : y = 30 : 50 = 3 : 5 answer : b"

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

b

divide(30, 50)

divide(n0,n1)|

general

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 :

"300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 34 = 86 sq m of the wallpaper overlaps in three layers . 86 sq m makes two extra layers hence the area over which it makes two extra layers is 43 sq m . answer ( a ) ."

a ) 43 square meters , b ) 36 square meters , c ) 42 square meters , d ) 83.3 square meters , e ) 120 square meters

a

divide(subtract(subtract(300, 180), 34), const_2)

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

geometry

a glass was filled with 24 ounces of water , and 0.06 ounce of the water evaporated each day during a 12 - day period . what percent of the original amount of water evaporated during this period ?

"the total number of ways to choose 6 managers is 9 c 6 = 84 we need to subtract the number of groups which include the two managers , which is 7 c 4 = 35 . 84 - 35 = 49 the answer is e ."

a ) 36 , b ) 40 , c ) 42 , d ) 45 , e ) 49

e

subtract(choose(9, 6), choose(subtract(9, 2), 2))

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

probability

find the length of the wire required to go 14 times round a square field containing 5625 m 2 .

"original price = 100 cp = 80 s = 80 * ( 140 / 100 ) = 112 100 - 112 = 12 % answer : c"

a ) 82 % , b ) 52 % , c ) 12 % , d ) 19 % , e ) 22 %

c

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

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

gain

the present population of a town is 280 . population increase rate is 10 % p . a . find the population of town after 1 years ?

explanation : unit digit in 3 ^ 4 = 1 unit digit in ( 3 ^ 4 ) 16 = 1 unit digit in 3 ^ 65 = unit digit in [ ( 3 ^ 4 ) 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 6 ^ 59 = 6 unit digit in 7 ^ 4 unit digit in ( 7 ^ 4 ) 17 is 1 . unit digit in 7 ^ 71 = unit digit in [ ( 7 ^ 4 ) 17 x 73 ] = ( 1 x 3 ) = 3 required digit = unit digit in ( 3 x 6 x 3 ) = 4 e

a ) 18 , b ) 12 , c ) 69 , d ) 32 , e ) 4

e

subtract(multiply(multiply(3, 6), 3), subtract(multiply(multiply(3, 6), 3), const_4))

multiply(n0,n2)|multiply(n0,#0)|subtract(#1,const_4)|subtract(#1,#2)

general

the sum of all the integers k such that – 21 < k < 24 is

"distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 6 + 5 / 9 = 6.55 answer b"

a ) 4.7 kmph , b ) 6.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph

b

add(divide(1, divide(add(const_60, 48), const_60)), 6)

add(n2,const_60)|divide(#0,const_60)|divide(n1,#1)|add(n0,#2)|

physics

the largest number of six digits

2 km / 400 m = 5 . however , the street at the 2 - km mark is not 5 th street ; it is maple street . therefore , the highest numbered street is 4 th street . the answer is a .

a ) 4 th , b ) 5 th , c ) 6 th , d ) 7 th , e ) 8 th

a

subtract(divide(multiply(2, const_1000), 400), const_1)

multiply(n0,const_1000)|divide(#0,n1)|subtract(#1,const_1)

physics

if two dice are thrown together , the probability of getting prime number on both dice is

"say there are 100 people in that group , then there would be 0.5 * 0.30 * 100 = 15 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 15 / 100 . answer : e"

a ) 0.16 , b ) 0.25 , c ) 0.45 , d ) 0.35 , e ) 0.15

e

multiply(divide(50, multiply(multiply(const_5, const_5), const_4)), divide(30, multiply(multiply(const_5, const_5), const_4)))

multiply(const_5,const_5)|multiply(#0,const_4)|divide(n0,#1)|divide(n1,#1)|multiply(#2,#3)|

gain

107 x 107 + 93 x 93 = ?

"1 / 2 * d ( 14 + 8 ) = 550 d = 50 answer : c"

a ) 76 , b ) 28 , c ) 50 , d ) 80 , e ) 25

c

divide(divide(divide(550, divide(add(14, 8), const_2)), 8), const_2)

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

physics

the ratio of spinsters to cats is 2 to 7 . if there are 40 more cats than spinsters , how many spinsters are there ?

"3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is c"

a ) 2 / 5 , b ) 7 / 5 , c ) 3 / 5 , d ) 8 / 15 , e ) 1 / 2

c

subtract(const_1, add(add(divide(4, multiply(add(const_2, 4), 4)), divide(const_2, multiply(add(const_2, 4), 4))), divide(const_1, multiply(add(const_2, 4), 4))))

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

physics

3 different containers contain 50 litres , 100 litres and 150 litres of mixture of milk and water respectively . what is the biggest measure can measure all the different quantities exactly ?

"let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 350 x = 50 4 x = 200 the answer is c ."

a ) $ 200 , b ) $ 225 , c ) $ 250 , d ) $ 275 , e ) $ 300

c

multiply(divide(350, add(add(divide(const_1, const_2), const_1), const_2)), const_2)

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

general

jane makes toy bears . when she works with an assistant , she makes 100 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?

"you could pick 40 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 45 . b"

a ) 10 , b ) 45 , c ) 55 , d ) 35 , e ) 65

b

add(subtract(80, 90), subtract(50, 35))

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

general

surface area of two spheres are in the ratio 1 : 4 what is the ratio of their volumes ?

"if arthur and david submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined no discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."

a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54

b

divide(subtract(multiply(const_2, multiply(80, 0.02)), multiply(multiply(160, divide(subtract(100, 25), 100)), 0.02)), const_2)

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

gain

how many words , with or without meaning , can be formed using all letters of the word good using each letter exactly once ?

"expanding we have 6 x ^ 2 - 15 x + 2 x - 5 6 x ^ 2 - 13 x - 5 taking coefficients , a = 6 , k = - 13 , n = - 5 therefore a - n + k = 6 - ( - 13 ) - 5 = 19 - 5 = 14 the answer is d ."

a ) 5 , b ) 8 , c ) 9 , d ) 14 , e ) 11

d

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

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

general

if 30 % of a class averages 95 % on a test , 50 % of the class averages 79 % on the test , and the remainder of the class averages 60 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .

let 1 man ' s 1 day ' s work = x and 1 women ' s 1 day ' s work = y . then , 6 x + 8 y = 1 and 26 x + 48 y = 1 . 10 2 solving these two equations , we get : x = 1 and y = 1 . 100 200 ( 15 men + 20 women ) ' s 1 day ' s work = 15 + 20 = 1 . 100 200 4 15 men and 20 women can do the work in 4 days . hence answer will be b

a ) 5 , b ) 4 , c ) 6 , d ) 7 , e ) 8

b

divide(multiply(add(divide(8, divide(subtract(multiply(48, 2), multiply(8, 10)), subtract(multiply(6, 10), multiply(26, 2)))), 6), 10), add(divide(20, divide(subtract(multiply(48, 2), multiply(8, 10)), subtract(multiply(6, 10), multiply(26, 2)))), 15))

multiply(n4,n5)|multiply(n1,n2)|multiply(n0,n2)|multiply(n3,n5)|subtract(#0,#1)|subtract(#2,#3)|divide(#4,#5)|divide(n1,#6)|divide(n7,#6)|add(n0,#7)|add(n6,#8)|multiply(n2,#9)|divide(#11,#10)

physics

when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 3 of the remaining balance , what will be the final balance in her bank account ?

"explanation : required number of students = h . c . f of 1345 and 775 = 5 . answer : d"

a ) 91 , b ) 10 , c ) 6 , d ) 5 , e ) none of these

d

gcd(1345, 775)

gcd(n0,n1)|

general

a rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size . which of the following could be a length of a side of the squares ?

"let c ' s share = rs . x then , b ' s share = rs . x / 4 ; a ' s share = rs . 2 / 3 * x / 4 = rs . x / 6 therefore x / 6 + x / 4 + x = 1360 17 x / 12 = 1360 x = 1360 * 12 / 17 = rs . 960 hence , b ' s share = rs . 960 / 4 = rs . 240 answer : c"

a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 300 , e ) rs . 500

c

subtract(subtract(multiply(divide(1360, const_10), const_2), const_12), const_12)

divide(n0,const_10)|multiply(#0,const_2)|subtract(#1,const_12)|subtract(#2,const_12)|

general

calculate the ratio between x and y if 90 % of x equal to 60 % of y ?

"( 18 × 15 × 12 ) / ( 5 × 3 × 2 ) = 108 answer is c ."

a ) 106 , b ) 109 , c ) 108 , d ) 101 , e ) 104

c

divide(multiply(multiply(18, 15), 2), multiply(multiply(5, 3), 2))

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

physics

if x ^ 2 + y ^ 2 = 20 and xy = 3 , then ( x − y ) ^ 2 =

"explanation : let the positive number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 x = √ 16 / 144 = 4 / 12 . answer : a"

a ) 4 / 12 , b ) 4 / 17 , c ) 4 / 15 , d ) 4 / 11 , e ) 4 / 03

a

sqrt(divide(multiply(16, const_3), multiply(216, const_2)))

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

general

a train 450 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :

"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 d"

a ) 1235 , b ) 1346 , c ) 1378 , d ) 1635 , e ) 1489

d

multiply(divide(subtract(1365, 15), subtract(6, const_1)), 6)

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

general

the sector of a circle has radius of 14 cm and central angle 135 o . find its perimeter ?

"7 + 11 + 13 = 31 / 3 = 10.3 answer : d"

a ) 12.6 , b ) 12.9 , c ) 22.3 , d ) 10.3 , e ) 12.7

d

add(5, const_1)

add(n0,const_1)|

general

a train is 435 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length

james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 10 = 991 answer : option d

a ) 901 , b ) 989 , c ) 990 , d ) 991 , e ) 1,001

d

subtract(add(const_1000, const_1000), multiply(add(const_1000, const_1000), 0.5))

add(const_1000,const_1000)|multiply(n0,#0)|subtract(#0,#1)

general

find the simple interest on $ 10000 at 7 % per annum for 12 months ?

explanation : treat 12 : 8 as 12 / 8 and x : 16 as x / 16 , treat : : as = so we get 12 / 8 = x / 16 = > 8 x = 192 = > x = 24 option b

a ) 18 , b ) 24 , c ) 28 , d ) 16 , e ) 20

b

divide(add(multiply(8, const_3.0), 8), 16)

multiply(const_3.0,n1)|add(n1,#0)|divide(#1,n2)|

general

55 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :

"on dividing 3832 by 5 , we get remainder = 2 . required number be subtracted = 2 answer : b"

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

b

subtract(3832, multiply(floor(divide(3832, 5)), 5))

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

general

alex and brian start a business with rs . 7000 each , and after 8 months , brian withdraws half of his capital . how should they share the profits at the end of the 18 months ?

"a 2 = 5625 = > a = 75 4 a = 300 300 * 14 = 4200 answer : c"

a ) 15840 , b ) 3388 , c ) 4200 , d ) 8766 , e ) 66711

c

multiply(square_perimeter(square_edge_by_area(5625)), 14)

square_edge_by_area(n1)|square_perimeter(#0)|multiply(n0,#1)|

physics

the number of students in each section of a school is 24 . after admitting new students , 3 new sections were started . now , the total number of sections is 16 and there are 21 students in each section . the number of new students admitted is :

"number of bricks = volume of the wall / volume of 1 brick = ( 100 x 200 x 20 ) / ( 25 x 11.25 x 6 ) = 237 . answer : option c"

a ) 5600 , b ) 6000 , c ) 237 , d ) 7200 , e ) 8600

c

divide(multiply(multiply(multiply(1, const_100), multiply(2, const_100)), 20), multiply(multiply(25, 11.25), 6))

multiply(n3,const_100)|multiply(n4,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(n2,#2)|multiply(n5,#3)|divide(#5,#4)|

physics

for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 21000 , my total savings for the two - year is

records last 90 min on each of 2 sides , = = > record last 90 * 2 = 180 min = 3 hours 16 full records - - > 16 * 3 = 48 hour broadcast given , 3 hours to translate 1 hour of broadcast let x be the time required to translate 48 hour broadcast ( 16 full records ) x = 48 * 3 = 144 hours answer : a

a ) 144 hours , b ) 124 hours , c ) 134 hours , d ) 154 hours , e ) 164 hours

a

multiply(multiply(divide(multiply(90, const_2), const_60), 16), 3)

multiply(n0,const_2)|divide(#0,const_60)|multiply(n2,#1)|multiply(n1,#2)

physics

there are 1000 students in a school and among them 10 % of them attends chess class . 10 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?

"45 * 12 : 54 * x = 2 : 1 x = 5 12 - 5 = 7 . answer : a"

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

a

subtract(multiply(const_4, const_3), divide(divide(multiply(45000, multiply(const_4, const_3)), 5400), 2))

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

other

10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 170000 , find the cost of a camel ?

"a ' s 1 hour work = 1 / 4 ; ( b + c ) ' s 1 hour work = 1 / 3 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 3 ) = 7 / 12 b ' s 1 hour work = ( 7 / 12 + 1 / 2 ) = 1 / 12 b alone will take 12 hours to do the work . answer : c"

a ) 15 hours , b ) 14 hours , c ) 12 hours , d ) 74 hours , e ) 79 hours

c

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

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

physics

a tank with a volume of 45 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 5 cubic inches / min and the 2 outlet pipes empty it out at the rates of 14 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )

"explanation : here distance d = 650 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 39 sec . answer : d"

a ) 48 , b ) 36 , c ) 26 , d ) 39 , e ) 18

d

divide(650, multiply(subtract(63, 3), const_0_2778))

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

physics

for all even integers n , h ( n ) is defined to be the sum of the even integers between 4 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?

d 6 days the day after last monday was tuesday . if i came home 3 days before that , i came home on saturday , sunday , monday , tuesday , wednesday , and thursday = 6 days .

a ) 1 day , b ) 2 days , c ) 7 days , d ) 6 days , e ) 10 days

d

add(add(3, const_1), const_2)

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

physics

the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 3 ?

"675 - - - - 425 100 - - - - ? = > = 63 % answer : c"

a ) 65 % , b ) 64 % , c ) 63 % , d ) 62 % , e ) 61 %

c

subtract(const_100, divide(multiply(1100, const_100), 675))

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

gain

if x / 4 years ago roger was 14 years old and x / 4 years from now he will be 4 x years old , how old will he be 3 x years from now ?

"sol . speed in still water = 1 / 2 ( 19 + 5 ) kmph = 12 kmph . answer d"

a ) 2 , b ) 4 , c ) 7 , d ) 12 , e ) 15

d

divide(add(19, 5), const_2)

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

physics

the perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters . what is the length of the yard if the area of the yard is 9 meters squared ?

"first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 46000 - 30000 = 16000 so 40 more machines . . total = 140 machines imo a . ."

a ) 140 , b ) 103 , c ) 105 , d ) 115 , e ) 120

a

add(100, divide(subtract(multiply(multiply(multiply(add(4, 3), multiply(3, const_2)), 100), multiply(add(4, const_1), const_2)), multiply(multiply(multiply(100, 100), divide(3, 100)), 100)), multiply(multiply(100, 100), divide(4, 100))))

add(n0,n2)|add(const_1,n2)|divide(n0,n1)|divide(n2,n1)|multiply(const_2,n0)|multiply(n1,n1)|multiply(#0,#4)|multiply(#1,const_2)|multiply(#2,#5)|multiply(#3,#5)|multiply(#6,n1)|multiply(n1,#8)|multiply(#10,#7)|subtract(#12,#11)|divide(#13,#9)|add(n1,#14)|

gain

a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 12 miles per gallon , and from town b to town c , the car averaged 14 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?

"d 4 9 x + x = 13 + 27 10 x = 40 = > x = 4"

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

d

divide(add(27, 4), add(6, 6))

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

general

a sprinter starts running on a circular path of radius r metres . her average speed ( in metres / minute ) is π r during the first 30 seconds , π r / 2 during next one minute , π r / 4 during next 2 minutes , π r / 8 during next 4 minutes , and so on . what is the ratio of the time taken for the nth round to that for the previous round ?

a profit of rs . 900 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 540 and 360 . difference in profit share = 540 - 360 = 180 answer : b

a ) s . 280 , b ) s . 180 , c ) s . 380 , d ) s . 50 , e ) s . 90

b

subtract(divide(divide(900, add(divide(1, 2), divide(1, 3))), 2), divide(divide(900, add(divide(1, 2), divide(1, 3))), 3))

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

general

the perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters . what is the length of the yard if the area of the yard is 9 meters squared ?

"explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 ⇒ 5 x = 25 ⇒ x = 5 . hence , b ' s age = 2 x = 10 years . answer : e"

a ) 7 , b ) 9 , c ) 8 , d ) 11 , e ) 10

e

divide(multiply(subtract(27, const_2), const_2), add(const_4, const_1))

add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)|

general

a train speeds past a pole in 10 seconds and a platform 50 m long in 20 seconds . its length is :

3 + 5 + 8 = 16 2880 / 16 = 180 so y ' s share = 3 * 180 = 540 answer : a

a ) 540 , b ) 520 , c ) 140 , d ) 560 , e ) 240

a

multiply(divide(2880, add(add(3, 5), 8)), 3)

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

general

at a wedding reception , 125 guests ate chicken and 75 guests ate beef . if exactly 100 guests ate only one of the two types of meat , how many guests ate both types of meat ?

"p - 3 = 3 ( k - 3 ) and so p = 3 k - 6 p + 9 = 2 ( k + 9 ) ( 3 k - 6 ) + 9 = 2 k + 18 k = 15 p = 39 p + k = 54 the answer is d ."

a ) 42 , b ) 46 , c ) 50 , d ) 54 , e ) 58

d

add(subtract(multiply(add(negate(subtract(9, multiply(9, const_2))), subtract(multiply(3, 3), 3)), 3), subtract(multiply(3, 3), 3)), add(negate(subtract(9, multiply(9, const_2))), subtract(multiply(3, 3), 3)))

multiply(n2,const_2)|multiply(n0,n1)|subtract(n2,#0)|subtract(#1,n0)|negate(#2)|add(#4,#3)|multiply(#5,n1)|subtract(#6,#3)|add(#5,#7)|

general

three pipes of same capacity can fill a tank in 8 hours . if there are only two pipes of same capacity , the tank can be filled in .

"speed = ( 54 x 5 / 18 ) = 15 m / sec . length of the train = ( speed x time ) . length of the train = 15 x 4 m = 60 m . answer : c"

a ) 90 , b ) 120 , c ) 60 , d ) 95 , e ) 75

c

multiply(divide(multiply(50, const_1000), const_3600), 4)

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

physics

find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 10 of money ?

speed upstream = 49 / 7 = 7 kmph speed down stream = 77 / 7 = 11 kmph speed of stream = ½ ( 11 - 7 ) = 2 kmph answer : c

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

c

divide(subtract(77, 49), multiply(7, const_2))

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

physics

if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?

is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 95 106 115 124 133 15 ways . . d

a ) 7 , b ) 8 , c ) 14 , d ) 15 , e ) 20

d

subtract(subtract(24, 7), const_2)

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

general

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

"let the numbers be 2 x and 5 x their h . c . f . = 6 so the numbers are 2 * 6 , 5 * 6 = 12,30 l . c . m . = 60 answer is e"

a ) 20 , b ) 24 , c ) 52 , d ) 36 , e ) 60

e

sqrt(divide(6, add(power(5, 2), add(power(2, 2), power(2, 2)))))

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

other

a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 55 percent .

"total work = 20 * 6 = 120 beaver hours 12 beaver * x = 120 beaver hours x = 120 / 12 = 10 answer : a"

a ) 10 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 8 .

a

divide(multiply(6, 20), 12)

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

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 10 minutes , then the area of the park ( in sq . m ) is :

"let x be the weight of the sister . then the student ' s weight is 2 x + 6 . x + ( 2 x + 6 ) = 126 3 x = 120 x = 40 kg then the student ' s weight is 86 kg . the answer is c ."

a ) 82 , b ) 84 , c ) 86 , d ) 88 , e ) 90

c

subtract(126, divide(subtract(126, 6), const_3))

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

other

the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 2.50 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?

"cost price = rs . 575 profit = 15 % of 575 = rs . 86.25 selling price = cost price + profit = 575 + 86.25 = 661.25 answer : d"

a ) 600 , b ) 277 , c ) 269 , d ) 661.25 , e ) 281

d

add(575, multiply(575, divide(15, const_100)))

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

gain

if 0.2 of a number is equal to 0.08 of another number , the ratio of the numbers is :

"break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many t hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."

a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8

a

add(inverse(subtract(divide(const_1, 12.5), divide(const_1, 30))), inverse(subtract(divide(const_1, 7.5), divide(const_1, 12))))

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

physics

what is the sum of natural numbers between 60 and 100

let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of a = 6 / 13 * 1638 = rs . 756 answer : c

a ) 656 , b ) 456 , c ) 756 , d ) 745 , e ) 720

c

multiply(divide(1638, add(add(2, 3), 4)), 4)

add(n2,n4)|add(n6,#0)|divide(n0,#1)|multiply(n6,#2)

general

at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 203 ?

"explanation : trick : number is divisible by 6 , if sum of all digits is divisible by 3 and 2 , so ( 2 + 5 + 5 + 1 + 1 + 1 + 2 + * ) = 17 + * should be divisible by , 17 + 1 will be divisible by 3 , but we ca n ' t take this number because 1 is not dividable by 2 ( 2 only dividable by those numbers who contain even number at last position ) so that least number is 4 . answer : option b"

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

b

subtract(6, subtract(6, 6))

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

general

you collect baseball cards . suppose you start out with 17 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?

"the units digit of 734 ^ 100 is 6 because 4 raised to the power of an even integer ends in 6 . the units digit of 347 ^ 83 is 3 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 83 is in the form 4 n + 3 , the units digit is 3 . then 6 + 3 = 9 . the answer is c ."

a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11

c

subtract(subtract(100, 83), divide(100, add(const_1, const_10)))

add(const_1,const_10)|subtract(n1,n3)|divide(n1,#0)|subtract(#1,#2)|

general

if x , y , and z are positive integers and 2 x = 3 y = 4 z , then the least possible value of x + y + z is

sol . let the bases of the two triangles be x and y and their heights be 3 h and 4 h respectively . then , ( ( 1 / 2 ) x xx 3 h ) / ( 1 / 2 ) x y x 4 h ) = 4 / 3  x / y = ( 4 / 3 x 4 / 3 ) = 16 / 9 required ratio = 16 : 9 . ans : c

['a ) 2 : 3', 'b ) 4 : 5', 'c ) 16 : 9', 'd ) 7 : 9', 'e ) 8 : 5']

c

multiply(divide(4, 3), inverse(divide(3, 4)))

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

geometry

20 men do a work in 20 days . how many men are needed to finish the work in 10 days ?

"explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 15 = rs . 190 cp on 40 metres = 190 x 40 = rs . 7600 profit earned on 40 metres cloth = rs . 8200 – rs . 7600 = rs . 600 . answer : option c"

a ) rs . 950 , b ) rs . 1500 , c ) rs . 600 , d ) rs . 1200 , e ) none of these

c

multiply(15, 40)

multiply(n0,n2)|

gain

the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 900 per sq . metre .

"total number of cards , n ( s ) = 52 total number of queen cards , n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 52 = 1 / 13 option b is answer"

a ) 4 / 13 , b ) 1 / 13 , c ) 4 , d ) 1 , e ) 2 / 13

b

divide(const_2, choose(add(const_3, const_3), const_3))

add(const_3,const_3)|choose(#0,const_3)|divide(const_2,#1)|

probability

20 people went to a hotel for combine dinner party 12 of them spent rs . 70 each on their dinner and rest spent 4 more than the average expenditure of all the 20 . what was the total money spent by them .

"explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 60 50 d = 20 rs = 60 – 50 = 10 t = 20 / 10 = 2 hours answer : option a"

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

a

subtract(divide(multiply(divide(const_1, const_2), 50), subtract(60, 50)), divide(const_1, const_2))

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

physics

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

"explanation : average weight of 18 boys = 50.25 total weight of 18 boys = 50.25 × 18 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 18 ) + ( 45.15 × 8 ) total boys = 18 + 8 = 26 average weight of all the boys = ( 50.25 × 18 ) + ( 45.15 × 8 ) / 26 = 48.68077 answer : option a"

a ) 48.68077 , b ) 42.25983 , c ) 50 , d ) 51.25388 , e ) 52.25

a

divide(add(multiply(18, 50.25), multiply(8, 45.15)), add(18, 8))

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

general

a car is purchased on hire - purchase . the cash price is $ 24 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ?

"the word good has exactly 4 letters which are all different . therefore the number of words that can be formed = number of permutations of 4 letters taken all at a time . = p ( 4 , 4 ) = 4 ! = 4 x 3 x 2 × 1 = 24 answer : e"

a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24

e

factorial(const_3)

factorial(const_3)|

general

p and q started a business investing rs . 48,000 and rs . 24,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?

"square ab + bc = 60 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 3600 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 40 ^ 2 = 1600 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 1600 + 2 * ab * bc = 3600 . 1600 + 2 * ab * bc = 3600 . ab * bc = 1000 . the area = 1 / 2 * ab * bc = 500 . answer : d ."

a ) 225 , b ) 450 , c ) 25 √ 2 , d ) 500 , e ) 200 √ 2

d

triangle_area_three_edges(40, multiply(const_3, const_10), multiply(const_4, const_10))

multiply(const_10,const_3)|multiply(const_10,const_4)|triangle_area_three_edges(n0,#0,#1)|

geometry

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 ?

answer : a ) 1 : 2

a ) 1 : 2 , b ) 1 : 0 , c ) 1 : 7 , d ) 1 : 5 , e ) 1 : 6

a

power(divide(const_1, sqrt(const_2)), const_2)

sqrt(const_2)|divide(const_1,#0)|power(#1,const_2)|

geometry

two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 25 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?

out of all the 5 options , only 4487 is not divisible by 3 . all others are divisible so answer = d ( no further calculation required ) addition of any two non - divisible numbers by 3 gives the resultant divisible by 3 19 is non - divisible by 3 ; we are adding a number to that so that the resultant becomes divisible by 3 applying the above rule , it means that the number which we are going to add should be non - divisible by 3 so comes the answer = 4487 answer : d

a ) 4461 , b ) 4473 , c ) 4479 , d ) 4487 , e ) 4491

d

add(multiply(multiply(multiply(4, 7), multiply(3, 19)), const_2), subtract(multiply(multiply(4, 7), multiply(3, 19)), multiply(const_2, const_100)))

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

general

3 years ago , the average age of a , b and c was 27 years and that of b and c 5 years ago was 20 years . a ’ s present age is :

one possible case is : girl - boy - boy the probability of this is 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 there are 3 c 2 = 3 such cases so we should multiply by 3 . p ( one girl and two boys ) = 3 / 8 the answer is d .

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

d

divide(subtract(const_1, multiply(power(divide(const_1, const_2), 3), const_2)), const_2)

divide(const_1,const_2)|power(#0,n0)|multiply(#1,const_2)|subtract(const_1,#2)|divide(#3,const_2)

general

how many of the positive factors of 24 are not factors of 27

"let x be the length of the size 8 shoe . then 0.3 x = 9 / 5 x = 90 / 15 = 6 inches the size 15 shoe has a length of 6 + 7 / 5 = 7.4 inches the answer is b ."

a ) 6.8 , b ) 7.4 , c ) 7.7 , d ) 8.2 , e ) 8.6

b

add(divide(multiply(divide(1, 5), subtract(17, 8)), divide(30, const_100)), multiply(subtract(15, 8), divide(1, 5)))

divide(n2,n3)|divide(n4,const_100)|subtract(n1,n0)|subtract(n5,n0)|multiply(#0,#2)|multiply(#0,#3)|divide(#4,#1)|add(#6,#5)|

general

a is twice as fast as b . if b alone can do a piece of work in 18 days , in what time can a and b together complete the work ?

"if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 5 hence answer should be d"

a ) 1 , b ) - 1 , c ) 3 , d ) 5 , e ) 13

d

multiply(5, const_2)

multiply(n1,const_2)|

general

the present population of a town is 280 . population increase rate is 10 % p . a . find the population of town after 1 years ?

"relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 240 ) / 9 = 500 / 9 = > x = 260 . answer : option a"

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

a

subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 240)

add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)|

physics

a envelop weight 8.2 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?

think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , one side and thehypothenuse use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the other side , 12 . correct answer a

['a ) 12', 'b ) 15', 'c ) 10', 'd ) 8', 'e ) 14']

a

sqrt(subtract(power(15, const_2), power(9, const_2)))

power(n2,const_2)|power(n1,const_2)|subtract(#0,#1)|sqrt(#2)

geometry

three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 34 square meters . what is the area that is covered with three layers of wallpaper ?

acid in 9 liters = 50 % of 9 = 4.5 liters suppose x liters of water be added . then 4.5 liters of acid in 9 + x liters of diluted solution 30 % of 9 + x = 4.5 27 + 3 x = 45 x = 6 liters answer is a

a ) 6 liters , b ) 8 liters , c ) 10 liters , d ) 12 liters , e ) 15 liters

a

subtract(divide(multiply(multiply(9, divide(50, const_100)), const_100), 30), 9)

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

gain

a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.3 m and its walls are 5 cm thick . the thickness of the bottom is :

"let c . p . = rs . x . then , s . p . = rs . ( 12 % of x ) = rs . 6 x / 5 new s . p . = 2 * 6 x / 5 = rs . 12 x / 5 profit = 12 x / 5 - x = rs . 7 x / 5 profit = 7 x / 5 * 1 / x * 100 = 140 % . \ answer : d"

a ) 327 , b ) 140 , c ) 277 , d ) 178 , e ) 112

d

add(multiply(subtract(multiply(add(const_1, divide(20, const_100)), const_2), const_1), const_100), const_100)

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

gain

there are 6 people in the elevator . their average weight is 170 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .

"20 x + 46 = 21 ( x – 5 ) x = 59 answer : e"

a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59

e

subtract(multiply(add(20, const_1), 5), 46)

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

general

if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is - .

a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 18 days whole work will be done by a in 18 * 4 / 3 = 24 days answer is b

a ) 10 , b ) 24 , c ) 60 , d ) 30 , e ) 20

b

divide(multiply(18, 40), subtract(40, 10))

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

physics