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mathqa_shuffle_question_test

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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 :

"explanation : dividend on 1 share = ( 20.5 * 50 ) / 100 = rs . 10.25 rs . 25 is income on an investment of rs . 100 rs . 10.25 is income on an investment of rs . ( 10.25 * 100 ) / 25 = rs . 41 answer : e"

a ) 25 , b ) 66 , c ) 18 , d ) 19 , e ) 41

e

divide(multiply(divide(multiply(20.5, 50), const_100), const_100), 25)

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

gain

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

a 59 - sided convex polygon has 59 vertices . if we examine a single vertex , we can see that we can connect it with 56 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 59 vertices can be connected with 56 vertices to create a diagonal then the total number of diagonals would be ( 59 ) ( 56 ) = 3304 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3304 by 2 to get 1652 . the answer is b .

a ) 1168 , b ) 1652 , c ) 2452 , d ) 3304 , e ) 4256

b

divide(factorial(59), multiply(factorial(subtract(59, const_2)), factorial(const_2)))

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

general

0.002 x 0.6 = ?

"let c . p . be $ 100 . then , s . p . = $ 133 let marked price be $ x . then , 95 / 100 x = 133 x = 13300 / 95 = $ 140 now , s . p . = $ 140 , c . p . = $ 100 profit % = 40 % . a"

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

a

multiply(const_100, divide(add(const_100, 33), subtract(const_100, 5)))

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

gain

jonathan can type a 30 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?

"swim in still water at = 5 speed of river = 3 us = 5 - 3 = 2 distance = 10 t = 10 / 2 = 5 answer : c"

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

c

divide(10, subtract(5, 3))

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

gain

a truck covers a distance of 376 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 14 km more than that travelled by the truck ?

"cost price = 900 profit = 30 % = 30 % of 900 = 270 selling price = cp + profit sp = 1170 a discount of 30 % to employees means 30 % off on 1170 so 30 % of 1170 = 351 ans a"

a ) 352 , b ) 356 , c ) 358 , d ) 362 , e ) 365

a

divide(add(divide(multiply(900, 30), const_100), 900), multiply(divide(900, const_100), const_2))

divide(n1,const_100)|multiply(n0,n1)|divide(#1,const_100)|multiply(#0,const_2)|add(n1,#2)|divide(#4,#3)|

gain

for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 5 of whom are females , by how much does the index for the females exceed the index for the males in the group ?

"let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 6360 [ 4 l - 40 ] = 6360 / 26.50 = 240 4 l = 280 l = 280 / 4 = 70 meters . answer : a"

a ) 70 , b ) 200 , c ) 300 , d ) 400 , e ) 140

a

subtract(divide(divide(6360, 26.50), const_2), multiply(const_2, 20))

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

physics

if the complement of a certain angle is 7 times the measure of that certain angle , then what is the measure of that certain angle ?

"the # of factors 240 has is 20 ; so out of 20 factors only four are multiples of 15 : 15 , 30 , 60 , 120 and 240 , itself ; so , the probability is 5 / 20 = 1 / 4 . answer : e ."

a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4

e

divide(divide(choose(15, const_1), 15), power(const_3, const_2))

choose(n1,const_1)|power(const_3,const_2)|divide(#0,n1)|divide(#2,#1)|

other

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

"let us first write the numbers in the form of prime factors : 15 = 3 * 5 22 = 2 * 11 24 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 1320 option d"

a ) 60 , b ) 120 , c ) 240 , d ) 1320 , e ) 1720

d

lcm(lcm(add(const_10, const_2), subtract(multiply(const_3, const_10), const_3)), 22)

add(const_10,const_2)|multiply(const_10,const_3)|subtract(#1,const_3)|lcm(#0,#2)|lcm(n1,#3)|

general

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

explanation : let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a ) 665

a ) 665 , b ) 376 , c ) 998 , d ) 1277 , e ) 1991

a

subtract(add(multiply(84, 8), 85), 92)

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

general

if p ( a ) = 0.4 , p ( b ) = 0.6 and p ( a ∪ b ) = 0.8 . what is the value of p ( a ∩ b ' ) = ?

"one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 3 , then 3 x = y , where x is the smaller integer . if adding 10 to the smaller integer makes the ratio 2 to 1 , then x + 10 = 2 y . substituting y = 3 x into the second equation yields x + 10 = 6 x . so , x = 2 ( smaller integer ) and , y = 3 x = 6 ( larger integer ) so a is the correct answer . another option is to test the answer choices . a ) the larger number is 6 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 2 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 2 ) , we get 12 . so , the new ratio is 12 to 6 which is the same as 2 to 1 . therefore choice a is correct . b ) the larger number is 9 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 3 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 3 ) , we get 13 so , the new ratio is 13 to 9 . no good . we want a resulting ratio of 2 to 1 eliminate b c ) the larger number is 10 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 3.33 ( which is not an integer ) since both numbers are integers , the larger number can not be 10 . eliminate c d ) the larger number is 12 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 4 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 4 ) , we get 14 so , the new ratio is 14 to 12 which is 7 to 6 . no good . we want a resulting ratio of 2 to 1 eliminate d e ) the larger number is 15 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 5 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 5 ) , we get 15 so , the new ratio is 15 to 15 . this is the same as the ratio of 1 to 1 eliminate e therefore a is the only correct choice ."

a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15

a

multiply(divide(multiply(1, 10), subtract(3, 1)), 3)

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

other

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 ?

"explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 20 / 5 = 4 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 4 = 44 secs . answer : c"

a ) 47 , b ) 76 , c ) 44 , d ) 66 , e ) 11

c

multiply(divide(20, subtract(6, const_1)), subtract(12, const_1))

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

physics

the cyclist going at a constant rate of 18 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 48 miles per hour . the motor - cyclist stops to wait for the cyclist 15 minutes after passing cyclist , while the cyclist continues to travel at constant rate , how many minutes must the motor - cyclist wait until the cyclist catches up ?

"money paid in cash = rs . 1000 balance payment = ( 30000 - 1000 ) = rs . 29000 answer : c"

a ) 22678 , b ) 26699 , c ) 29000 , d ) 19000 , e ) 26711

c

subtract(30000, 1000)

subtract(n0,n2)|

gain

if log 8 x + log 8 1 / 6 = 1 / 3 , then the value of x is :

"sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 55 ⇔ = [ 55 * 20 * 20 * 7 / 22 ] = 7000 cm = 70 m . answer d"

a ) 84 m , b ) 88 m , c ) 120 m , d ) 70 m , e ) none

d

divide(55, multiply(power(divide(1, const_2), const_2), const_pi))

divide(n1,const_2)|power(#0,const_2)|multiply(#1,const_pi)|divide(n0,#2)|

physics

a can do a piece of work in 8 days and b alone can do it in 12 days . how much time will both take to finish the work ?

"l = ( 48 - 16 ) m = 32 m , b = ( 34 - 16 ) m = 18 m , h = 8 m . volume of the box = ( 32 x 18 x 8 ) m 3 = 4608 m 3 . answer : option c"

a ) 4830 , b ) 5120 , c ) 4608 , d ) 7500 , e ) 8960

c

volume_rectangular_prism(subtract(48, multiply(8, const_2)), subtract(34, multiply(8, const_2)), 8)

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

geometry

a man walking at a constant rate of 12 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 24 miles per hour . the woman stops to wait for the man 10 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?

"let the length of the train be x meters . the speed of the train is x / 15 . then , x + 120 = 25 * ( x / 15 ) 10 x = 1800 x = 180 meters the answer is d ."

a ) 100 m , b ) 140 m , c ) 130 m , d ) 180 m , e ) 170 m

d

multiply(120, subtract(const_2, const_1))

subtract(const_2,const_1)|multiply(n1,#0)|

physics

a train running at a speed of 36 km / h passes an electric pole in 15 seconds . in how many seconds will the whole train pass a 370 - meter long platform ?

some multiple of 7 + some multiple of 5 should yield 63 . to get to a some multiple of 5 , we should ensure that a 3 or 8 ( 5 + 3 ) should be a multiple of 7 . 63 is a direct multiple of 7 , however in this case there wo n ' t be any guava . hence the next option is to look for a multiple of 7 that has 8 as the unit digit . 28 satisfies this hence no . of apples is 4 and no of bananas is 7 . c

a ) 12 , b ) 13 , c ) 11 , d ) 14 , e ) 5

c

add(divide(subtract(6.3, multiply(0.7, const_4)), 0.5), const_4)

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

other

7 m - 20 = 2 m , then m + 7 is equal to ?

"we know 25 % people study biology , therefore the no of people not studying = 100 - 25 = 75 % > therefore the people not studying biology out of a total 880 people are = 75 % of 880 > ( 75 / 100 ) * 880 = 660 people e"

a ) 500 , b ) 600 , c ) 620 , d ) 640 , e ) 660

e

multiply(divide(880, const_100), subtract(const_100, 25))

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

other

two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 4 carpenters build in 1 hours ?

"let the smaller number be x . then larger number = ( x + 1380 ) . x + 1380 = 6 x + 15 5 x = 1365 x = 273 large number = 273 + 1380 = 1653 e"

a ) 1245 , b ) 1345 , c ) 1455 , d ) 1577 , e ) 1653

e

multiply(divide(subtract(1380, 15), subtract(6, const_1)), 6)

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

general

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

"the total number of elementary events associated to the random experiments of throwing four dice simultaneously is : = 6 × 6 × 6 × 6 = 64 = 6 × 6 × 6 × 6 = 64 n ( s ) = 64 n ( s ) = 64 let xx be the event that all dice show the same face . x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } n ( x ) = 6 n ( x ) = 6 hence required probability , = n ( x ) n ( s ) = 664 = n ( x ) n ( s ) = 664 = 1 / 216 c"

a ) 2 / 113 , b ) 3 / 117 , c ) 1 / 216 , d ) 3 / 111 , e ) 4 / 121

c

multiply(divide(const_3, add(const_3, const_3)), divide(const_3, add(const_3, const_3)))

add(const_3,const_3)|divide(const_3,#0)|multiply(#1,#1)|

probability

a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 50 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?

official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 8 = 10 / 2 + 8 = 13 . the correct answer is d

a ) 5 , b ) 8 , c ) 10 , d ) 13 , e ) 17

d

add(sqrt(divide(100, 4)), 8)

divide(n6,n0)|sqrt(#0)|add(n4,#1)

general

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

"n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 88 , there are 44 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 44 + 12 ) / 88 = 66 / 88 = 33 / 44 ans is e"

a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 33 / 44

e

divide(add(divide(88, 2), divide(88, 8)), 88)

divide(n1,n3)|divide(n1,n4)|add(#0,#1)|divide(#2,n1)|

general

how many internal diagonals does a pentagon ( five sided polygon ) have ?

"its e . total juice rquired = 240 * 6 = 1440 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1440 / 48 = 30 . answer e"

a ) a ) 25 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 30

e

divide(divide(multiply(240, 6), 12), const_4)

multiply(n3,n4)|divide(#0,n2)|divide(#1,const_4)|

general

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

"∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 38400 ⁄ 12 = 3200 answer c"

a ) 4038 , b ) 8076 , c ) 3200 , d ) 4845.6 , e ) none of these

c

multiply(divide(divide(38400, 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

a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 40 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?

total cost of the items he purchased = rs . 50 given that out of this rs . 50 , 90 paise is given as tax = > total tax incurred = 90 paise = rs . 90 / 100 let the cost of the tax free items = x given that tax rate = 15 % ∴ ( 50 − 90 / 100 − x ) 15 / 100 = 90 / 100 ⇒ 15 ( 50 − 0.9 − x ) = 90 ⇒ ( 50 − 0.9 − x ) = 6 ⇒ x = 50 − 0.9 − 6 = 43.1 c

a ) a ) 19.7 , b ) b ) 20 , c ) c ) 43.1 , d ) d ) 21.5 , e ) e ) 22

c

subtract(subtract(50, divide(90, const_100)), divide(90, 15))

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

gain

a certain class of students is being divided into teams . the class can either be divided into 8 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?

"answer given expression = ( 7 + 7 + 7 ÷ 7 ) / ( 5 + 5 + 5 ÷ 5 ) = ( 14 + 1 ) / ( 10 + 1 ) = 15 / 11 option : c"

a ) 1 , b ) 1 / 5 , c ) 15 / 11 , d ) 3 / 11 , e ) none

c

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

add(n3,const_1)|subtract(n0,const_1)|multiply(n3,#0)|multiply(n0,#1)|divide(#2,const_2)|divide(#3,const_2)|subtract(#4,#5)|

general

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 6 ?

"explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 3410 * ( 6 / 31 ) = 110 * 6 = 660 . answer : option a"

a ) 660 , b ) 700 , c ) 800 , d ) 900 , e ) none of these

a

multiply(3410, divide(6, add(add(add(10, add(4, const_1)), 10), 6)))

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

general

a cycle is bought for rs . 900 and sold for rs . 990 , find the gain percent ?

let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 1 * 6 = 6 days to produce 1 w widgets . answer : b

a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12

b

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

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

general

the area of a triangle is with base 5.5 m and height 6 m ?

"let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 175 ⇒ 1.75 x = 175 ⇒ x = 100 coins answer d"

a ) 20 coins , b ) 30 coins , c ) 50 coins , d ) 100 coins , e ) none of these

d

divide(175, add(add(inverse(const_4), inverse(const_2)), const_1))

inverse(const_4)|inverse(const_2)|add(#0,#1)|add(#2,const_1)|divide(n2,#3)|

general

what is the remainder when 1250 * 1090 * 1045 * 1055 is divided by 18 ?

solution suppose y invested rs . y then , 5000 / y = 2 / 6 â € ¹ = â € º y = ( 5000 ã — 6 / 2 ) . â € ¹ = â € º y = 15000 . answer d

a ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 15,000 , e ) none

d

divide(multiply(5000, 6), 2)

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

gain

the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 3 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ?

"this implies 9 a - b = 10 b + 70 , 9 a - b = - 12 b - 2 a , 10 b + 70 = - 12 b - 2 a manipulating the second equation gives us 9 a - b = 10 b + 70 = = > 9 a - 11 b = 70 answer is b"

a ) - 4 , b ) 70 , c ) 0 , d ) 2 , e ) 4

b

multiply(negate(multiply(divide(70, 2), 2)), 9)

divide(n2,n4)|multiply(#0,n4)|negate(#1)|multiply(n5,#2)|

general

if the arithmetic mean of seventy 5 numbers is calculated , it is 35 . if each number is increased by 5 , then mean of new number is ?

answer : option e

a ) 100000 , b ) 222222 , c ) 333333 , d ) 888888 , e ) 999999

e

square_area(const_pi)

square_area(const_pi)|

general

43 : 34 : : 52 : ?

"s = 600 / 40 = 15 mps s = 3600 / 15 = 240 sec = 4 min . answer : a"

a ) 4 min , b ) 2 min , c ) 8 min , d ) 9 min , e ) 3 min

a

divide(divide(multiply(3, const_1000), speed(600, 40)), const_60)

multiply(n2,const_1000)|speed(n0,n1)|divide(#0,#1)|divide(#2,const_60)|

physics

the average height of 30 students in a class was calculated as 177 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm . what was the actual average height of the students in the class ?

if x is a positive integer , the lowest value would be x = 1 , because 0 is not included in the natural numbers . that ' s a technicality the gmat would not expect students to know . if x = 1 , then the expression equals - 14 . answer = ( b ) .

a ) - 15 , b ) - 14 , c ) - 13 , d ) - 12 , e ) - 11

b

subtract(subtract(const_1, const_1), 15)

subtract(const_1,const_1)|subtract(#0,n1)

general

set a consists of the integers from 4 to 16 , inclusive , while set b consists of the integers from 6 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?

john spent and gave to his two friends a total of 3.25 + 2.20 + 2.20 = $ 7.65 money left 16.10 - 7.65 = $ 8.45 answer : e

a ) $ 6.45 , b ) $ 8.35 , c ) $ 8.75 , d ) $ 8.85 , e ) $ 8.45

e

subtract(16.1, add(3.25, add(2.2, 2.2)))

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

general

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

"3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 10 pumps then 48 / 10 = 4.8 hrs . answer : a"

a ) 4.8 , b ) 3.6 , c ) 1.1 , d ) 1.2 , e ) 1.3

a

divide(multiply(multiply(3, 8), 2), 10)

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

physics

two numbers are less than a third number by 40 % and 47 % respectively . how much per cent is the second number less than the first ?

given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !

['a ) 6 / π', 'b ) 9 / π', 'c ) 6', 'd ) 9', 'e ) 12']

d

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

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

geometry

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 ?

"5354 x 51 = 5354 x ( 50 + 1 ) = 5354 x 50 + 5354 x 1 = 267700 + 5354 = 273054 a"

a ) 273054 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273258

a

multiply(divide(5354, 51), const_100)

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

general

if | x - 20 | = 40 what is the sum of all the values of x .

we write n ! = n * ( n - 1 ) ( n - 2 ! ) therefore n ! / ( n - 2 ) ! = n ( n - 1 ) * ( n - 2 ) ! / ( n - 2 ) ! = n ( n - 1 ) . - - > n ( n - 1 ) = 342 - - > n ^ 2 - n - 342 = 0 - - > n ^ 2 - 19 n + 18 n - 342 = 0 - - > n ( n - 19 ) + 18 ( n - 19 ) = 0 - - > ( n - 19 ) ( n + 18 ) = 0 therefore n - 19 = 0 ; n + 18 = 0 ; ( i . e ) n = 19 ; n = - 18 we want positive integer . so , n = 19 . answer : c

a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21

c

sqrt(add(342, divide(const_1, const_4)))

divide(const_1,const_4)|add(n1,#0)|sqrt(#1)

general

of the votes cast on a certain proposal , 62 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )

let amount of 10 $ be x . then amount of 5 $ be 2 x . now 5 * 2 x + 10 * x = 100 . thus x = 5 . answer : e

a ) 2 , b ) 6 , c ) 7 , d ) 8 , e ) 5

e

divide(divide(100, 10), const_2)

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

general

express 25 mps in kmph ?

"index for females = ( 20 - 5 ) / 20 = 3 / 4 = 0.75 index for males = ( 20 - 15 / 20 = 1 / 4 = 0.25 index for females exceeds males by 0.75 - 0.25 = 0.5 answer : c"

a ) 0.05 , b ) 0.0625 , c ) 0.5 , d ) 0.25 , e ) 0.6

c

subtract(divide(subtract(20, 5), 20), divide(5, 20))

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

general

calculate the largest 6 digit number which is exactly divisible by 99 ?

"the radius of tank a is 12 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 144 / ( 4 * pi ^ 2 ) = 360 / ( pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 12 * pi * 100 / ( 4 * pi ^ 2 ) = 300 / ( pi ) tank a / tank b = 360 / 300 = 12 / 10 = 120 % the answer is e ."

a ) 80 % , b ) 90 % , c ) 100 % , d ) 110 % , e ) 120 %

e

multiply(multiply(power(divide(12, 10), const_2), divide(10, 12)), const_100)

divide(n0,n2)|divide(n1,n3)|power(#1,const_2)|multiply(#0,#2)|multiply(#3,const_100)|

physics

kavi spends 50 % of his monthly salary on food and saves 80 % of the remaining amount . if his monthly salary is rs . 19000 , how much money does he save every month ?

sandra score can be like 1,4 , 9,16 , 25,36 eric score less then 1 - - > 0 eric score less then 4 = ( 1,1 ) , ( 1,2 ) ( 2,1 ) - - > 3 eric score less then 9 are ( 1,1 ) ( 1,2 ) ( 1,3 ) ( 1,4 ) ( 1,5 ) ( 1,6 ) ( 2,1 ) ( 2,2 ) ( 2,3 ) ( 2,4 ) ( 2,5 ) ( 2,6 ) ( 3,1 ) ( 3,2 ) ( 3,3 ) ( 3,4 ) ( 3,5 ) ( 4,1 ) ( 4,2 ) ( 4,3 ) ( 4,4 ) ( 5,1 ) ( 5,2 ) ( 5,3 ) ( 6,1 ) ( 6,2 ) - - > 26 eric score will always be less then 16 - - - > 36 eric score will always be less then 25 - - - > 36 eric score will always be less then 36 - - - > 36 total favorable outcomes = 3 + 26 + 36 + 36 + 36 = 137 total possible outcomes = 216 ( 36 * 6 ) probability = 137 / 216 answer : a

['a ) 137 / 216', 'b ) 137 / 218', 'c ) 137 / 217', 'd ) 136 / 216', 'e ) 138 / 216']

a

divide(add(add(add(add(const_3, subtract(power(multiply(2, const_3), const_2), const_10)), power(multiply(2, const_3), const_2)), power(multiply(2, const_3), const_2)), power(multiply(2, const_3), const_2)), multiply(power(multiply(2, const_3), const_2), multiply(2, const_3)))

multiply(n0,const_3)|power(#0,const_2)|multiply(#0,#1)|subtract(#1,const_10)|add(#3,const_3)|add(#4,#1)|add(#5,#1)|add(#6,#1)|divide(#7,#2)

geometry

find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm ?

worker b will get 9 / 14 = 64.29 % the answer is c .

a ) 62.27 % , b ) 63.28 % , c ) 64.29 % , d ) 65.31 % , e ) 66.32 %

c

divide(910, add(5, 9))

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

other

the smallest number when increased by ` ` 1 ` ` is exactly divisible by 2 , 8 , 24 , 36 is :

"per second = > 8 * 5280 ft / 60 * 60 = 11.73 ft 5 seconds = > 11.73 * 5 = 58.65 ft answer : e"

a ) 60 ft , b ) 52 ft , c ) 53 ft , d ) 55 ft , e ) 58.65 ft

e

multiply(5, divide(multiply(8, 5280), const_3600))

multiply(n0,n3)|divide(#0,const_3600)|multiply(n1,#1)|

physics

x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if x invested rs . 40000 , the amount invested by y is

"30 * t = 1 km = > t = 1 / 30 km / h v * ( t + 30 / 3600 ) = 1 v ( 1 / 30 + 30 / 3600 ) = 1 v ( 150 / 3600 ) = 1 v = 24 km / h the answer is e ."

a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24

e

divide(1, divide(add(multiply(const_3600, divide(1, 30)), 30), const_3600))

divide(n1,n3)|multiply(#0,const_3600)|add(n0,#1)|divide(#2,const_3600)|divide(n1,#3)|

physics

a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 48 now , the son age 5 years back was

say a 100 families existed in 1998 then the number of families owning a computer in 1998 - 30 number of families owning computer in 2002 = 30 * 120 / 100 = 36 number of families in 2002 = 108 the percentage = 36 / 108 * 100 = 33.33 % . option : d

a ) 50.12 % , b ) 52.66 % , c ) 56.33 % , d ) 33.33 % , e ) 74.12 %

d

multiply(const_100, divide(divide(multiply(add(20, const_100), 30), const_100), add(const_100, 8)))

add(n3,const_100)|add(n5,const_100)|multiply(n1,#0)|divide(#2,const_100)|divide(#3,#1)|multiply(#4,const_100)

general

car z travels 55 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?

26 steps 30 seconds and for 34 steps only 18 seconds left to reach botto . means he covered 8 steps ( i . e . 34 - 26 ) in 12 ( i . e 30 - 18 ) seconds the spped of the boy is 8 steps in 12 seconds after further simplyfy . . 2 steps in 3 seconds after 34 steps only 18 seconds , means 12 more steps are left total steps are 34 + 12 = 46 answer : e

a ) 43 , b ) 44 , c ) 45 , d ) 40 , e ) 46

e

add(add(multiply(const_3, const_10), 4), multiply(divide(subtract(add(multiply(const_3, const_10), 4), add(20, 6)), subtract(multiply(const_3, const_10), multiply(6, const_3))), multiply(6, const_3)))

add(n0,n1)|multiply(const_10,const_3)|multiply(n1,const_3)|add(n2,#1)|subtract(#1,#2)|subtract(#3,#0)|divide(#5,#4)|multiply(#6,#2)|add(#3,#7)

physics

tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 52 people bought tickets to the concert , what was the total revenue from ticket sales ?

"soln : - can be reduced to y / 10 + 3 y / 10 = 2 y / 5 = 40 % answer : a"

a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %

a

multiply(const_100, add(divide(2, 20), divide(3, 10)))

divide(n1,n2)|divide(n3,n4)|add(#0,#1)|multiply(#2,const_100)|

general

the circumferences of the fore and hind - wheels of a carriage are 2 2 / 5 and 3 3 / 7 meters respectively . a chalk mark is put on the point of contact of each wheel with the ground at any given moment . how far will the carriage have travelled so that their chalk marks may be again on the ground at the same time ?

let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 5 x / 6 ) ( 2 y / 3 ) = 5 xy / 9 the total number of boxes is xy + 5 xy / 9 = 14 xy / 9 the fraction loaded by the day crew is xy / ( 14 xy / 9 ) = 9 / 14 the answer is d .

a ) 6 / 11 , b ) 7 / 12 , c ) 8 / 13 , d ) 9 / 14 , e ) 11 / 15

d

divide(multiply(6, 3), add(multiply(6, 3), multiply(2, 5)))

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

physics

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

"e e = 90 * 5 / 18 * 6 = 150 m"

a ) 281 m , b ) 112 m , c ) 117 m , d ) 125 m , e ) 150 m

e

multiply(multiply(90, const_0_2778), 6)

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

physics

a and b are two circles . the radius of a is four times as large as the diameter of b . what is the ratio between the areas of the circles ?

explanation : l . c . m of 25650 = 2 x 3 x 3 x 3 x 5 x 5 x 19 3 , 2 , 5,19 number of different prime factors is 4 . answer : option a

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

a

add(const_2, const_2)

add(const_2,const_2)

other

a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 175 , how many coins of each type are there ?

"correct sum = ( 36 * 50 + 58 - 43 ) = 1815 . correct mean = 1815 / 50 = 36.3 answer : e"

a ) 36.7 , b ) 36.1 , c ) 36.5 , d ) 36.9 , e ) 36.3

e

divide(add(multiply(36, 50), subtract(subtract(50, const_2), 43)), 50)

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

general

when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.12 , what is the value of y ?

"44 + 28 + 10 = 82 % 100 – 82 = 18 % 450 * 18 / 100 = 81 answer : d"

a ) 72 , b ) 75 , c ) 80 , d ) 81 , e ) 90

d

divide(multiply(450, subtract(const_100, add(add(44, 28), 10))), const_100)

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

gain

jane and ashley take 8 days and 40 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an eight day leave from work . this led to jane ' s working for four extra days on her own to complete the project . how long did it take to finish the project ?

"oa is ' c ' . oe : take the remainder from each of 1250 / 32 , 1040 / 32 and so on . . 1250 / 32 gives remainder = 2 1040 / 32 gives remainder = 16 1057 / 32 gives remainder = 1 1145 / 32 gives remainder = 25 the net remainder is the product of above individual remainders . i . e = 2 * 16 * 1 * 25 break them into pairs 2 * 16 / 32 gives remainder 0 and 1 * 25 / 32 gives remainder 25 so 0 * 25 / 32 gives remainder 0 . answer : c"

a ) 3 , b ) 5 , c ) 0 , d ) 2 , e ) 9

c

reminder(multiply(1040, 1250), 1057)

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

general

a train 520 m long can cross an electric pole in 20 sec and then find the speed of the train ?

"let c . p . of each article be re . 1 . then , c . p . of 80 articles = rs . 80 ; s . p . of 80 articles = rs . 40 . loss % = 40 / 80 * 100 = 50 % answer : c"

a ) 30 % , b ) 35 % , c ) 50 % , d ) 55 % , e ) 40 %

c

subtract(80, 40)

subtract(n0,n1)|

gain

2 , 6 , 12 , 20 , 30 , 42 , 56 , ( . . . )

volume = ( 16 x 14 x 7 ) m ^ 3 = 1568 m ^ 3 . surface area = [ 2 ( 16 x 14 + 14 x 7 + 16 x 7 ) ] cm ^ 2 = ( 2 x 434 ) cm ^ 2 = 868 cm ^ 2 . answer is d

['a ) 878 cm ^ 2', 'b ) 858 cm ^ 2', 'c ) 838 cm ^ 2', 'd ) 868 cm ^ 2', 'e ) none of them']

d

multiply(add(multiply(16, 7), add(multiply(16, 14), multiply(14, 7))), const_2)

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

geometry

a man whose bowling average is 22.2 , takes 4 wickets for 36 runs and thereby decreases his average by 1.2 . the number of wickets , taken by him before his last match is :

"sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 24000 + 35000 ) = 66000 - 59000 = rs . 7000 b"

a ) s . 8000 , b ) s . 7000 , c ) s . 9900 , d ) s . 9990 , e ) s . 10000

b

add(subtract(42000, divide(multiply(24000, 5), 3)), subtract(divide(multiply(42000, 4), 7), 24000))

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

general

the surface of a cube is 294 sq cm . find its volume ?

{ total } = { retirees } + { bridge players } - { both } + { neither } x = 5 / 20 * x + x / 2 - 3 / 20 * x + 120 20 x = 5 x + 10 x - 3 x + 120 * 20 ( multiply by 20 ) 12 x = 120 * 20 x = 200 . answer : c

a ) 240 , b ) 300 , c ) 200 , d ) 400 , e ) 480

c

multiply(subtract(120, multiply(5, const_4)), const_2)

multiply(n1,const_4)|subtract(n2,#0)|multiply(#1,const_2)

general

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

"description : = > x + y = 8 , x - y = 6 adding these 2 x = 14 = > x = 7 , y = 1 . thus the number is 71 answer d"

a ) 85 , b ) 94 , c ) 83 , d ) 71 , e ) none

d

add(multiply(divide(add(8, 6), const_2), 8), subtract(8, divide(add(8, 6), const_2)))

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

general

a bullet train 150 m long is running with a speed of 30 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the bullet train is going ?

let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 80 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 80 + 20 ) / 2 = 50 . answer : d

a ) 40 , b ) 30 , c ) 25 , d ) 50 , e ) none of these .

d

divide(add(80, 20), const_2)

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

general

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

"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 44 / 2 = 55 cm 2 answer : b"

a ) 38 cm 2 , b ) 55 cm 2 , c ) 65 cm 2 , d ) 45 cm 2 , e ) 35 cm 2

b

triangle_area(2.5, 44)

triangle_area(n0,n1)|

geometry

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

"principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4903 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4076 . answer : b"

a ) s . 3096 , b ) s . 4076 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096

b

divide(4903, power(add(1, divide(add(6, divide(1, 4)), const_100)), 3))

divide(n3,n4)|add(n2,#0)|divide(#1,const_100)|add(#2,n3)|power(#3,n1)|divide(n0,#4)|

gain

solving a linear equation with several occurrences of the variable , solve for w . simplify answer as much as possible . ( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22

"number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 90 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 95 - 59 = 36 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 95 = 36 + 32 + 36 - x or x = 9 now , number of students taking only history will be h - x or 36 - 9 = 27 answer : - e"

a ) 9 , b ) 19 , c ) 23 , d ) 45 , e ) 27

e

subtract(36, subtract(add(36, 32), 59))

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

other

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 ?

"the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 80 = $ 1.00 cents on commodity y , which will take 10 years . the answer is b ."

a ) 2010 . , b ) 2011 . , c ) 2012 . , d ) 2013 . , e ) 2014 .

b

add(2001, divide(add(divide(80, const_100), subtract(4.40, 4.20)), subtract(divide(30, const_100), subtract(4.40, 4.20))))

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

general

the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 8 , is :

favorable case = the club is picked in the third draw or later unfavorable cases = the club is picked in either first draw , second draw or third draws probability = favorable outcomes / total out comes also probability = 1 - ( unfavorable outcomes / total out comes ) unfavorable case 1 : probability of club picked in first draw = 13 / 52 = 1 / 4 unfavorable case 2 : probability of club picked in second draw ( i . e . first draw is not club ) = ( 39 / 52 ) * ( 13 / 52 ) = ( 3 / 4 ) * ( 1 / 4 ) = 3 / 16 unfavorable case 3 : probability of club picked in third draw ( i . e . first and 2 nd draws are not clubs ) = ( 39 / 52 ) * ( 39 / 52 ) * ( 13 / 52 ) = ( 3 / 4 ) * ( 3 / 4 ) * ( 1 / 4 ) = 9 / 64 total unfavorable probability = ( 1 / 4 ) + ( 3 / 16 ) + ( 9 / 64 ) = ( 16 / 64 ) + ( 12 / 64 ) + ( 9 / 64 ) = 37 / 64 i . e . , favorable probability = 1 - ( 37 / 64 ) = 27 / 64 answer : option e

a ) 1 / 2 , b ) 3 / 4 , c ) 7 / 8 , d ) 27 / 32 , e ) 27 / 64

e

multiply(multiply(divide(subtract(52, 13), 52), divide(subtract(52, 13), 52)), divide(subtract(52, 13), 52))

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

probability

if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2160 less than the principal . what was the principal ?

"a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 80 = 25 answer : b"

a ) 15 , b ) 25 , c ) 35 , d ) 45 , e ) 55

b

subtract(add(add(20, 40), 60), add(add(multiply(5, const_3), 10), 70))

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

general

cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 51 after it went on sale for 15 % off , what is the difference between the original price and the final price ?

"assume the cost of the least sized ( 26 inch ) tv = x cost of 28 inches tv = x + 200 cost of 30 inches tv = x + 400 cost of 32 inches tv = x + 600 total cost = 4 x + 1200 = 3200 therefore x = 2000 / 4 = 500 price of 28 inch + 30 inch = 700 + 900 = 1600 option b"

a ) 850 , b ) 1,600 , c ) 1,700 , d ) 2,550 , e ) 3,400

b

divide(add(add(divide(subtract(add(200, const_3600), multiply(add(add(const_1, const_2), const_3), 200)), 4), 200), add(add(divide(subtract(add(200, const_3600), multiply(add(add(const_1, const_2), const_3), 200)), 4), 200), 200)), subtract(multiply(const_2, const_10), const_1))

add(n5,const_3600)|add(const_1,const_2)|multiply(const_10,const_2)|add(#1,const_3)|subtract(#2,const_1)|multiply(n5,#3)|subtract(#0,#5)|divide(#6,n0)|add(n5,#7)|add(n5,#8)|add(#8,#9)|divide(#10,#4)|

general

what is the units digit of 33 ^ 2 * 17 ^ 3 * 39 ^ 2 ?

use the elimination method to find the correct option . of all the options only 90 fits 28 % of 90 = 25.2 18 % of 90 = 16.2 25.2 - 16.2 = 7.2 required number is 90 . answer : e

a ) 50 , b ) 34 , c ) 55 , d ) 60 , e ) 90

e

add(divide(7.2, divide(subtract(28, 18), const_100)), 18)

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

gain

a and b can do a piece of work in 11 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?

prime factors of 60 are 2 ^ 2,3 ^ 1,5 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3,5 , ) = ( 1 + 1 ) ( 1 + 1 ) = 4 since we need odd divisors other than 1 = > 4 - 1 = 3 odd divisors d is the answer

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

d

divide(60, multiply(const_10, const_2))

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

other

the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 25 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?

d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , e = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d

a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %

d

subtract(const_100, divide(subtract(const_100, 68), const_2))

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

general

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

p = q + 1150 . p = 4 ( q - 200 ) . 4 ( q - 200 ) = q + 1150 . 3 q = 1950 . q = 650 . the answer is c .

a ) 600 , b ) 625 , c ) 650 , d ) 675 , e ) 700

c

divide(add(1150, multiply(200, 4)), const_3)

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

general

1 / 0.05 is equal to

"explanation : we can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak , as work done for 1 hour without leak = 1 / 3 work done with leak = 3 1 / 2 = 7 / 2 work done with leak in 1 hr = 2 / 7 work done by leak in 1 hr = 1 / 3 = 2 / 7 = 1 / 21 so tank will be empty by the leak in 21 hours . answer is d"

a ) 10 hours , b ) 13 hours , c ) 17 hours , d ) 21 hours , e ) 25 hours

d

divide(3, const_1)

divide(n1,const_1)|

physics

in one hour , a boat goes 11 km / hr along the stream and 5 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :

"now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 35 % profit . this means the clocks ' selling price was c ( 1.35 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , the store buys it for 15 % the price at which the collector bought it . thus , you get = 1.35 * 0.15 * c = 0.2025 c furthermore , the store sells the clock for the second time for 65 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.65 = 1.65 * 0.2025 c finally given that c - 0.2025 c = 105 - - - - > c = 131.66 $ thus , the cost of the clock the second time around = 1.65 * 0.2025 c = 1.65 * 0.2025 * 131.66 = 43.99 $ . hence e is the correct answer ."

a ) $ 75.44 , b ) $ 88.23 , c ) $ 64.77 , d ) $ 54.32 , e ) $ 43.99

e

divide(multiply(105, divide(multiply(add(105, 65), divide(add(105, 35), const_2)), 105)), subtract(divide(add(105, 35), const_2), 35))

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

general

the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 8 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?

"present age of total members = 6 x 26 = 156 10 yrs back their ages were = 6 x 10 = 60 ages at the birth of youngest member = 156 - 60 = 96 therefore , avg age at the birth of youngest member = 96 / 6 = 16 . answer : c"

a ) 15 , b ) 18 , c ) 16 , d ) 12 , e ) 19

c

subtract(divide(subtract(multiply(6, 26), 10), const_4), 10)

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

general

what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 450 ?

say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job e in 44 hours . answer : c .

a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above .

c

divide(const_1, divide(add(divide(const_1, 4), divide(const_1, 11)), 15))

divide(const_1,n2)|divide(const_1,n5)|add(#0,#1)|divide(#2,n0)|divide(const_1,#3)

physics

ele , the circus elephant , is currently 3 times older than lyn , the circus lion . in 15 years from now , lyn the circus lion will be exactly half as old as ele , the circus elephant . how old is ele today ?

"1 = 5,2 = 4,3 = 253,4 = 2,6 = 15 , then 15 = ? 15 = 6 check the fifth eqn . answer : e"

a ) 1 , b ) 255 , c ) 345 , d ) 445 , e ) 6

e

divide(subtract(subtract(15, multiply(multiply(add(const_4, const_2), add(const_4, const_2)), const_10)), 1), const_2)

add(const_2,const_4)|multiply(#0,#0)|multiply(#1,const_10)|subtract(n5,#2)|subtract(#3,n0)|divide(#4,const_2)|

general

the length and breadth of a rectangular courtyard is 75 m and 32 m . find the cost of leveling it at the rate of $ 3 per m 2 . also , find the distance covered by a boy to take 4 rounds of the courtyard .

"the pattern is 1 × 2 , 2 × 3 , 3 × 4 , 4 × 5 , 5 × 6 , 6 × 7 , 7 × 8 . hence , next number is 8 × 9 = 72 answer is c"

a ) 62 , b ) 74 , c ) 72 , d ) 81 , e ) 58

c

subtract(negate(20), multiply(subtract(6, 12), divide(subtract(6, 12), subtract(2, 6))))

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

general

the food in a camp lasts for 40 men for 20 days . if 10 more men join , how many days will the food last ?

"16 * 16 = 256 sq m the answer is d ."

a ) 225 sq m , b ) 286 sq m , c ) 298 sq m , d ) 256 sq m , e ) 231 sq m

d

divide(square_area(16), const_2)

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

geometry

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

"30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 50,000 i . e . rs . 25,000 answer : c"

a ) rs . 27,000 , b ) rs . 24,000 , c ) rs . 25,000 , d ) rs . 36,000 , e ) none of these

c

multiply(add(multiply(multiply(multiply(const_4, 2), multiply(add(2, const_3), 2)), const_100), multiply(multiply(add(2, const_3), const_100), const_100)), divide(divide(multiply(add(2, const_3), 2), 2), multiply(const_4, const_3)))

add(n1,const_3)|multiply(n1,const_4)|multiply(const_3,const_4)|multiply(#0,n1)|multiply(#0,const_100)|divide(#3,n1)|multiply(#1,#3)|multiply(#4,const_100)|divide(#5,#2)|multiply(#6,const_100)|add(#9,#7)|multiply(#10,#8)|

gain

what percent of 5.2 kg is 16 gms ?

"solution ( place value of 7 ) - ( place value of 3 ) = ( 7000 - 30 ) = 6970 . answer d"

a ) 4 , b ) 5 , c ) 45 , d ) 6970 , e ) none

d

subtract(multiply(const_10, 7), 7)

multiply(n0,const_10)|subtract(#0,n0)|

general

a 1 k . m . long wire is held by n poles . if one pole is removed , the length of the gap becomes 12 / 3 m . what is the number of poles initially ?

"the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 160 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 160 . so 1 part corresponds to 160 / 8 = 20 and so 5 parts correspond to 5 * 10 = 100 . a"

a ) 100 , b ) 36 , c ) 45 , d ) 72 , e ) 117

a

subtract(divide(160, subtract(const_1, divide(5, 13))), 160)

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

other

one night a certain hotel rented 4 / 5 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?

"1 hour he walk 4 km he walk 40 km in = 40 / 4 * 1 = 10 hours answer is b"

a ) 5 hrs , b ) 10 hrs , c ) 15 hrs , d ) 20 hrs , e ) 30 hrs

b

divide(40, 4)

divide(n2,n0)|

physics

how many positive integers less than 400 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ?

if ramesh attempts ' x ' questions correct and ' y ' questions wrong , then x + y = 108 - - - ( i ) & x - ( 1 / 3 ) y = 0 - - - ( ii ) on solving x = 27 , y = 81 answer : d

a ) 78 , b ) 79 , c ) 80 , d ) 81 , e ) 82

d

subtract(108, divide(multiply(divide(1, 3), 108), add(const_1, divide(1, 3))))

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

general

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 .

"c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be x = 60 . c"

a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90

c

divide(const_180, const_3)

divide(const_180,const_3)|

geometry

there are 5 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .

"cp * ( 85 / 100 ) = 915 cp = 10.76 * 100 = > cp = 1076 answer : c"

a ) 915 , b ) 1000 , c ) 1076 , d ) 1067 , e ) 1760

c

divide(915, subtract(const_1, divide(15, const_100)))

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

gain

two 100 multiples of 7 are chosen at random , and 300 multiples of 8 are chosen at random . approximately what percentage of the 500 selected numbers are odd ?

"dan can complete 1 / 15 of the job per hour . in 12 hours , dan completes 12 ( 1 / 15 ) = 4 / 5 of the job . annie can complete 1 / 10 of the job per hour . to complete the job , annie will take 1 / 5 / 1 / 10 = 2 hours . the answer is a ."

a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10

a

multiply(subtract(const_1, divide(12, 15)), 10)

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

physics

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

here all percentage when summed we need to get 100 % . as per data 17 + 24 + 15 + 29 + 8 = 93 % . so remaining 7 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 7 % will be 26 degrees . . imo option c .

a ) 8 ° , b ) 10 ° , c ) 26 ° , d ) 36 ° , e ) 52 °

c

divide(multiply(subtract(const_100, add(add(add(add(17, 24), 15), 29), 8)), divide(const_3600, const_10)), const_100)

add(n0,n1)|divide(const_3600,const_10)|add(n2,#0)|add(n3,#2)|add(n4,#3)|subtract(const_100,#4)|multiply(#1,#5)|divide(#6,const_100)

gain

in a certain quiz that consists of 10 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 300 points , how many points is the third question worth ?

"a = 1600 ( 21 / 20 ) 3 = 2522 answer : c"

a ) 3388 , b ) 2778 , c ) 2522 , d ) 2988 , e ) 2771

c

subtract(multiply(1600, multiply(add(const_1, divide(const_0_25, const_4)), add(const_1, divide(const_0_25, const_4)))), 1600)

divide(const_0_25,const_4)|add(#0,const_1)|multiply(#1,#1)|multiply(n0,#2)|subtract(#3,n0)|

gain

two spherical balls lie on the ground touching . if one of the balls has a radius of 8 cm , and the point of contact is 12 cm above the ground , what is the radius of the other ball ( in centimeters ) ?

"explanation : 20 cp = 25 sp cost price cp = 25 selling price sp = 20 formula = ( sp - cp ) / cp * 100 = ( 20 - 25 ) / 25 * 100 = 20 % loss answer : option a"

a ) 20 % loss , b ) 30 % loss , c ) 40 % gain , d ) 40 % loss , e ) 50 % loss

a

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

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

gain

solve the equation for x : 21 ( x + y ) + 5 = 21 ( - x + y ) + 47

"since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 830 = 24 interest earned for 3 years = 24 * 3 = 72 amount invested = 830 - 72 = 758 answer : d"

a ) 670 , b ) 664 , c ) 698 , d ) 758 , e ) 700

d

subtract(830, multiply(divide(subtract(854, 830), subtract(divide(4, const_100), divide(3, const_100))), divide(3, const_100)))

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

gain

the sum q of prime numbers that are greater than 60 but less than 70 is

let the amount be x . from the question , x × 14 × 6 / 1200 − x × 8 × 8 / 1200 = 250 ∴ x = 15000 answer a

a ) 15000 , b ) 25000 , c ) 7500 , d ) 14500 , e ) none of these

a

divide(250, subtract(multiply(divide(14, const_12), divide(6, const_100)), multiply(divide(8, const_12), divide(8, const_100))))

divide(n0,const_12)|divide(n1,const_100)|divide(n3,const_12)|divide(n3,const_100)|multiply(#0,#1)|multiply(#2,#3)|subtract(#4,#5)|divide(n2,#6)

general

from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 13 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?

"there is no certain way to solve 2 unknown with 1 equation . the best way is to look at the question and retrospect the most efficient way . in this question , a and b are only positive integers . so that is a big relief . now , we can start with putting a = 1,2 , . . and so on till the time we are confident about one of the options . so , we start with a = 1 , we get b as - ve . out a = 2 , we get b as 6 . yes ( now ( a , b ) = ( 2,6 ) . we can directly see that ( a , b ) = ( 6,2 ) will also satisfy . so we have 2 possible solutions ) a = 3 , we get b as 3 . yes ( now we have 3 possible solutions ) a = 4 , we get b as fraction . out a = 5 , we get b again as some fraction . out a = 6 already taken . we have a , b options left . c , d , e are out . a is 6 . to have 6 as the answer , we will need one more pair like 2,6 and one more solution where a = b . when a = b , we have only 1 solution = 5 . so , one more solution , where a = b is not possible . so , answer will be e ."

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

e

divide(34, 57)

divide(n2,n3)|

general

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

"120 amounts to 240 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 240 120 + 120 * ( r / 100 ) * ( 3 ) = 240 = > r = 100 / 3 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) = 450 answer is e ."

a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 340 , e ) $ 450

e

add(150, divide(multiply(multiply(150, 6), divide(divide(multiply(subtract(240, 120), 120), 120), 3)), 120))

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

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 ?

"total manufacturing cost = 10500 + 1000 * 30 = 40500 total selling cost = 1000 * 60 = 60000 profit = 60000 - 40500 = 19500 answer : a"

a ) $ 19500 , b ) $ 15500 , c ) $ 29500 , d ) $ 39500 , e ) $ 1500

a

multiply(subtract(60, multiply(30, const_2)), 1000)

multiply(n1,const_2)|subtract(n2,#0)|multiply(n3,#1)|

gain

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

we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 6 x : 5 x : 2 x we are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 9 x + 6 x + 5 x = 40 20 x = 40 x = 2 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 5 ) ( 2 ) = 10 pounds of apples = ( 9 ) ( 2 ) = 18 thus we know that there are 18 – 10 = 8 more pounds of apples than grapes . answer is c .

a ) 15 , b ) 12 , c ) 8 , d ) 6 , e ) 4

c

subtract(multiply(9, const_2), multiply(5, const_2))

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

general

a 240 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .

"explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1500 * 100 / 120 * 100 / 125 = 1000 answer : option a"

a ) a ) 1000 , b ) b ) 1100 , c ) c ) 1200 , d ) d ) 1300 , e ) e ) 1400

a

divide(1500, multiply(add(const_1, divide(20, const_100)), add(const_1, divide(25, const_100))))

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

gain

the angle between the minute hand and the hour hand of a clock when the time is 4.20 , is

"one case is : 1 / 4 * 1 / 4 * 3 / 4 * 3 / 4 = 9 / 256 the total number of possible cases is 4 c 2 = 6 p ( event a occurs exactly twice ) = 6 * ( 9 / 256 ) = 27 / 128 the answer is b ."

a ) 14 / 65 , b ) 27 / 128 , c ) 33 / 140 , d ) 37 / 165 , e ) 41 / 187

b

subtract(1, divide(const_2, 4))

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

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 5000 , the number of valid votes that the other candidate got , was :

"64 / 5000 = 64 / ( 5 * 10 ^ 3 ) = ( 64 / 5 ) * 10 ^ - 3 = 12.8 * 10 ^ - 3 = . 0128 thousandths digit = 2 answer a"

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

a

floor(multiply(const_100, divide(64, 5000)))

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

general

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

"solution average = ( 10 + 15 + 20 + 25 + 30 / 5 ) = 100 / 5 = 20 . answer b"

a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 32

b

divide(add(add(6, const_4), subtract(34, const_4)), const_2)

add(n0,const_4)|subtract(n1,const_4)|add(#0,#1)|divide(#2,const_2)|

general

if 20 men can build a wall 66 metres long in 10 days , what length of a similar can be built by 86 men in 8 days ?

"a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 24 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 8 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 16 eggs = 16 / 12 * 24 = 32 cents . answer : c ."

a ) 0.32 , b ) 0.44 , c ) 32 , d ) 44 , e ) 55

c

multiply(divide(divide(8, divide(const_1, const_2)), const_12), multiply(0.24, 100))

divide(const_1,const_2)|multiply(n1,n2)|divide(n0,#0)|divide(#2,const_12)|multiply(#3,#1)|

general