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mathqa_shuffle_question_test

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

"speed = 162 * ( 5 / 18 ) m / sec = 45 m / sec length of train ( distance ) = speed * time ( 45 ) * 9 = 405 meter answer : d"

a ) 150 meter , b ) 286 meter , c ) 186 meter , d ) 405 meter , e ) 265 meter

d

multiply(divide(multiply(162, const_1000), const_3600), 9)

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

physics

in a recent election , james received 0.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?

"let the maximum marks be x then , 30 % of x = 150 + 30 30 x / 100 = 180 30 x = 180 * 100 = 18000 x = 600 answer is b"

a ) 750 , b ) 600 , c ) 650 , d ) 550 , e ) 500

b

divide(add(150, 30), divide(30, const_100))

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

general

when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 5 , the remainder is 4 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 11 ?

"1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 5 = 7200 . answer : c"

a ) 5729 , b ) 5760 , c ) 7200 , d ) 2870 , e ) 2799

c

divide(multiply(5, multiply(8, const_60)), subtract(divide(multiply(8, const_60), multiply(6, const_60)), const_1))

multiply(n2,const_60)|multiply(n0,const_60)|divide(#0,#1)|multiply(n1,#0)|subtract(#2,const_1)|divide(#3,#4)|

physics

country x taxes each of its citizens an amount equal to 13 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?

"let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 560 . 6 ( 85 - g ) + 7 g = 560 . 510 - 6 g + 7 g = 560 . g = 560 - 510 = 50 . the answer is b ."

a ) a ) 36 , b ) b ) 50 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44

b

subtract(560, multiply(85, 6))

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

general

joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 36400 , how many months will it take joan to pay back her mortgage ?

"i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 72 and that c and l 1 = 0.10 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.1 x = 20 , therefore the grand total is 200 . now we know that l 2 is 200 - 72 = 128 . we also learn that c and no c are equally represented thus 100 each . therefore no c and no l 2 will be 100 - 52 = 48 . thus b is the correct answer choice"

a ) 46 , b ) 48 , c ) 56 , d ) 32 , e ) 58

b

divide(subtract(divide(20, divide(10, const_100)), 72), 2)

divide(n3,const_100)|divide(n6,#0)|subtract(#1,n4)|divide(#2,n1)|

general

there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 75 . how tall is the fourth person ?

"1498 - 1400 = 98 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 98 ) / ( 1400 ) = 7 % the answer is c ."

a ) 3 % , b ) 5 % , c ) 7 % , d ) 9 % , e ) 11 %

c

divide(multiply(subtract(1498, 1400), const_100), 1400)

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

gain

the simple interest on rs . 10 for 4 months at the rate of 3 paise per rupeeper month is

"m = 9 s = 3.1 ds = 12.1 us = 5.9 x / 12.1 + x / 5.9 = 1 x = 3.97 d = 3.97 * 2 = 7.94 answer : e"

a ) 2.21 , b ) 2.48 , c ) 9.24 , d ) 7.29 , e ) 7.94

e

multiply(divide(multiply(add(9, 3.1), subtract(9, 3.1)), add(add(9, 3.1), subtract(9, 3.1))), const_2)

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

physics

what is the angle between the minute and the hour hand of the clock which shows 12 : 24 ?

"n case of stock 1 , if he invest rs . 105 , he will get a dividend of rs . 12 ( assume face value = 100 ) in case of stock 2 , if he invest rs . 88 , he will get a dividend of rs . 8 ( assume face value = 100 ) ie , if he invest rs . ( 88 * 12 ) / 8 , he will get a dividend of rs . 12 required ratio = 105 : ( 88 × 12 ) / 8 = 105 : ( 11 × 12 ) = 35 : ( 11 × 4 ) = 35 : 44 answer : option d"

a ) 31 : 44 , b ) 31 : 27 , c ) 16 : 15 , d ) 35 : 44 , e ) 35 : 27

d

divide(multiply(105, const_2), multiply(88, const_3))

multiply(n1,const_2)|multiply(n3,const_3)|divide(#0,#1)|

other

little john had $ 8.50 . he spent $ 1.25 on sweets and gave to his two friends $ 1.20 and $ 2.20 . how much money was left ?

"let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 15 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 15 , d = 15 b - 15 c ; every 5 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 15 b - 15 c = 5 b + 5 c , - - > b = 2 c , - - > d = 15 b - 15 b / 2 = 15 b / 2 . interval = \ frac { d } { b } = \ frac { 15 / 2 b } { b } = 15 / 2 answer : e ( 15 / 2 minutes ) ."

a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 15 / 2 minutes

e

divide(subtract(15, divide(15, divide(add(5, 15), subtract(15, 5)))), const_1)

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

physics

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

explanation : number of questions attempted correctly = ( 70 % of 10 + 40 % of 30 + 60 % of 35 ) = 7 + 12 + 21 = 40 . questions to be answered correctly for 60 % = 60 % of total quotations = 60 % of 75 = 45 . he would have to answer 45 - 40 = 5 answer : a

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

a

subtract(divide(multiply(75, 60), const_100), add(add(divide(multiply(10, 70), const_100), divide(multiply(30, 40), const_100)), divide(multiply(35, 60), const_100)))

multiply(n0,n6)|multiply(n1,n4)|multiply(n2,n5)|multiply(n3,n6)|divide(#0,const_100)|divide(#1,const_100)|divide(#2,const_100)|divide(#3,const_100)|add(#5,#6)|add(#8,#7)|subtract(#4,#9)

general

a shopkeeper forced to sell at cost price , uses a 800 grams weight for a kilogram . what is his gain percent ?

"sqrt ( 7 x / 3 ) to be perfect square x has to 7 / 3 ans : b"

a ) 25 / 9 , b ) 7 / 3 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25

b

divide(7, 3)

divide(n0,n1)|

general

what is the tens digit of 36 ^ 5 ?

"240 = 2 ^ 4 * 3 * 5 = ( 4 ) * 2 ^ 2 * 3 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 2 , 1 , and 1 . there are ( 2 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 12 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 240 . the answer is d ."

a ) 6 , b ) 8 , c ) 9 , d ) 11 , e ) 12

d

divide(divide(divide(240, 4), const_2), const_3)

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

general

a parallelogram has a base that is four time the size of it ' s height . the total area of this parallelogram is 2,304 sq ft . what is the height of the parallelogram ?

connie has a 1 6 chance of winning 6 dollars her first turn . she has a 5 / 6 1 / 6 chance of winning 1 dollar her second turn . next , she has a 25 36 1 / 6 chance of winning 1 / 6 dollars her third turn . generalizing , connie ' s expected earnings form a geometric series with initial term 1 / 6 * 6 = 1 and common ratio 5 / 6 * 1 / 6 = 5 / 36 . hence , connie ' s expected earnings are 1 / 1 - 5 / 36 = 36 / 31 correct answer d

a ) 32 / 31 , b ) 33 / 31 , c ) 34 / 31 , d ) 36 / 31 , e ) 0 / 31

d

divide(const_1, subtract(const_1, divide(divide(subtract(6, 1), 6), 6)))

subtract(n0,n4)|divide(#0,n0)|divide(#1,n0)|subtract(const_1,#2)|divide(const_1,#3)

general

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

"0.06 * 0.05 = 0.003 = 0.3 % the answer is b ."

a ) 0.125 % , b ) 0.3 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %

b

multiply(6, divide(5, const_100))

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

gain

one half of a two digit number exceeds its one third by 4 . what is the sum of the digits of the number ?

"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 26 = > 2 x = 26 = > x = 13 c"

a ) 11 , b ) 12 , c ) 13 , d ) 16 , e ) 18

c

divide(26, const_2)

divide(n0,const_2)|

general

prints a page 40 pg per min . if the printed for 2 hours except 20 min . where there was an paper jam , how many page did it print

at 3 / 4 th of speed he is late by ' 2 hrs ' x - 3 / 4 ( x ) = 2 x = 8 so 8 - 2 = 6 hrs ( since 2 hrs late ) answer : c

a ) 5 hours , b ) 3 hours , c ) 6 hours , d ) 12 hours , e ) 15 hours

c

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

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

physics

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

because a + b = 1 , 2 a + 2 b = 2 ( a + b ) = 2 × 1 = 2 . correct answer d

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

d

subtract(add(add(2, 1), 2), add(2, 1))

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

general

a man is 22 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :

"let the sums be p . now , 45 % of p = 4016.25 or , p = 8925 answer a"

a ) 8925 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these

a

divide(multiply(const_100, 4016.25), multiply(9, 5))

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

gain

there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 15 , then find the smaller number ?

"there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 333 ) + 2 ( 555 ) = 2220 the answer is b ."

a ) 2210 , b ) 2220 , c ) 2230 , d ) 2240 , e ) 2250

b

multiply(add(add(multiply(add(add(5, 3), 2), const_100), multiply(add(add(const_4.0, 3), 2), const_10)), add(add(5, 3), 2)), 3)

add(n2,n3)|add(n1,#0)|multiply(#1,const_100)|multiply(#1,const_10)|add(#2,#3)|add(#4,#1)|multiply(#5,const_2)|

general

a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 798 find the share of a .

"let ' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 25 % are male i . e 25 / 100 * 20 = 5 geese ( males ) and now we know out of the total 20 geese , 5 are male , then 15 have to be female . now the ratio part , male geese ratios = 5 / 30 = 1 / 6 . - a female geese ratios = 15 / 70 = 3 / 14 - b cross multiply equations a and b and you get = 9 / 7 . ans e"

a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 9 / 7

e

divide(divide(divide(25, const_100), divide(30, const_100)), divide(divide(multiply(multiply(const_2, const_4), const_10), const_100), divide(30, const_100)))

divide(n1,const_100)|divide(n0,const_100)|multiply(const_2,const_4)|divide(#0,#1)|multiply(#2,const_10)|divide(#4,const_100)|divide(#5,#1)|divide(#3,#6)|

general

a circle graph shows how the budget of a certain company was spent : 61 percent for salaries , 10 percent for research and development , 6 percent for utilities , 5 percent for equipment , 3 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ?

"other number = ( 11 * 7700 ) / 275 = 308 . answer : c"

a ) 288 , b ) 277 , c ) 308 , d ) 988 , e ) 112

c

multiply(11, 275)

multiply(n0,n2)|

physics

how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?

"ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 7 = 21 the answer is b ."

a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27

b

add(add(11, divide(subtract(11, 5), 2)), 7)

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

physics

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

"between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 4 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 4 + 4 = 30 meter answer is e ."

a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30

e

add(add(multiply(subtract(12, const_1), 2), divide(10, 2)), divide(10, 2))

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

physics

the ratio of the two natural numbers is 5 : 6 . if a certain number is added to both the numbers , the ratio becomes 7 : 8 . if the larger number exceeds the smaller number by 10 , find the number added ?

"out of the 17 integers : 9 are odd and 8 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 9 odd numbers first 2 . 10 th number will be the first even number so we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 10 . ( d )"

a ) 19 , b ) 12 , c ) 11 , d ) 10 , e ) 3

d

add(divide(17, const_2), 1)

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

general

a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 108 . what was the number he chose ?

sum of last 4 matches = ( ( 10 × 45 ) – ( 6 × 48 ) = 162 average = 162 / 4 = 40.5 answer : d

a ) 43.25 , b ) 43 , c ) 38 , d ) 40.5 , e ) 36

d

divide(subtract(multiply(45, 10), multiply(6, 48)), 4)

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

general

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

"explanation : let the cost price = rs 100 then , marked price = rs 140 required gain = 8 % , so selling price = rs 108 discount = 140 - 108 = 32 discount % = ( 32 / 140 ) * 100 = 22.85 % option b"

a ) 23.85 % , b ) 22.85 % , c ) 21.85 % , d ) 20.85 % , e ) none of these

b

subtract(const_100, multiply(divide(add(8, const_100), add(40, const_100)), const_100))

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

gain

a bakery has 6 employees . it pays annual salaries of $ 19000 to each of 2 employees , $ 21000 to 1 employee , and $ 22000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?

"b 16.8 sec d = 60 + 80 = 140 m s = 60 * 5 / 18 = 50 / 3 t = 140 * 3 / 50 = 8.4 sec answer is b"

a ) 5.8 sec , b ) 8.4 sec , c ) 12.4 sec , d ) 6.8 sec , e ) 1.8 sec

b

divide(add(60, 80), multiply(60, const_0_2778))

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

physics

a palindrome is a number that reads the same forward and backward , such as 616 . how many even , 4 - digit numbers are palindromes ?

"the percent of the budget for transportation is 100 - ( 55 + 9 + 5 + 4 + 2 ) = 25 % 100 % of the circle is 360 degrees . then ( 25 % / 100 % ) * 360 = 90 degrees the answer is e ."

a ) 18 ° , b ) 36 ° , c ) 54 ° , d ) 72 ° , e ) 90 °

e

divide(multiply(const_360, subtract(const_100, add(add(add(add(55, 9), 5), 4), 2))), const_100)

add(n0,n1)|add(n2,#0)|add(n3,#1)|add(n4,#2)|subtract(const_100,#3)|multiply(#4,const_360)|divide(#5,const_100)|

geometry

what is the unit digit in 7105 ?

"96 / 7 = 13 . xx we are not concerned about the exact value of 96 / 7 as we just need the integers . since the values are small , we can write down the integers . the different integers between 5 and 96 / 7 would be 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12,13 total number of integers = 9 option b"

a ) 7 , b ) 9 , c ) 10 , d ) 12 , e ) 15

b

add(subtract(divide(96, 7), 5), const_1)

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

general

a work as fast as b . if b can complete a work in 20 days independently , the number of days in which a and b can together finish the work in ?

"( 256 ) ^ 2 - ( 144 ) ^ 2 = ( 256 + 144 ) ( 256 - 144 ) = 400 x 112 = 44800 answer is b"

a ) 761200 , b ) 44800 , c ) 761800 , d ) 761500 , e ) none of them

b

add(multiply(256, 256), multiply(144, 144))

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

general

a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long . over how much area of the field can it graze ?

"perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 20 ( p ^ 2 ) / 16 = 2 p + 20 p ^ 2 = 32 p + 320 p ^ 2 - 32 p - 320 = 0 p ^ 2 - 40 p + 8 p - 320 = 0 p ( p - 40 ) + 8 ( p + 40 ) = 0 ( p - 40 ) ( p + 8 ) = 0 p = 40 or - 8 discarding negative value , p = 40 answer is c"

a ) 28 , b ) 36 , c ) 40 , d ) 56 , e ) 64

c

subtract(subtract(add(const_10, multiply(20, 2)), const_0_25), const_0_25)

multiply(n0,n1)|add(#0,const_10)|subtract(#1,const_0_25)|subtract(#2,const_0_25)|

geometry

a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many e ways can the test be completed if every question is unanswered ?

first we need to figure out what numbers are exactly divisible by 7 , 12,10 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,10 ) = 42 * 10 = 420 the numbers which will leave remainder 4 will be { 420 + 4 , 420 x 2 + 4 , , . . . } the largest such number less than or equal to 1856 is 420 * 4 + 4 or 1684 to obtain this you need to subtract 172 . b

a ) 168 , b ) 172 , c ) 182 , d ) 140 , e ) 160

b

subtract(1856, add(4, multiply(gcd(1856, lcm(lcm(7, 12), 10)), lcm(lcm(7, 12), 10))))

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

general

a , b and c start a business each investing 20,000 . after 10 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 71400 was recorded . find the share of b .

"average = ( 5 + 10 + 15 ) / 3 = 10 answer is a"

a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 21

a

divide(add(add(add(3, const_1), add(add(3, const_1), const_2)), add(subtract(5, 3), subtract(5, const_2))), 3)

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

general

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

"explanation : increase in 10 years = ( 242500 - 134800 ) = 107700 increase % = ( 107700 / 134800 x 100 ) % = 79 % . required average = ( 79 / 10 ) % = 7.9 % . answer : option b"

a ) 4.37 % , b ) 7.9 % , c ) 6.8 % , d ) 8.75 % , e ) none

b

add(multiply(divide(subtract(divide(subtract(subtract(subtract(multiply(multiply(const_10, const_1000), const_10), const_1000), const_1000), multiply(add(2, const_3), const_100)), multiply(add(multiply(add(const_3, const_4), const_10), add(2, const_3)), const_1000)), 1), const_10), const_100), const_4)

add(n2,const_3)|add(const_3,const_4)|multiply(const_10,const_1000)|multiply(#2,const_10)|multiply(#0,const_100)|multiply(#1,const_10)|add(#0,#5)|subtract(#3,const_1000)|multiply(#6,const_1000)|subtract(#7,const_1000)|subtract(#9,#4)|divide(#10,#8)|subtract(#11,n0)|divide(#12,const_10)|multiply(#13,const_100)|add(#14,const_4)|

general

if xy = 4 , x / y = 16 , for positive numbers x and y , y = ?

"to solve this type of question , simply divide the volume of wall with the volume of brick to get the numbers of required bricks so lets solve this number of bricks = volume of wall / volume of 1 brick = 800 ∗ 600 ∗ 22.5 / 25 ∗ 11.25 ∗ 6 = 6400 answer : a"

a ) 6400 , b ) 3777 , c ) 2679 , d ) 2667 , e ) 1997

a

divide(multiply(multiply(multiply(8, const_100), multiply(6, const_100)), 22.5), 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

find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 15 cm and 5 cm ?

"65 % of 160 = x 0.65 * 160 = x 104 = x answer : c"

a ) 84 , b ) 94 , c ) 104 , d ) 114 , e ) 124

c

divide(multiply(65, 160), const_100)

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

gain

of the 150 employees at company x , 70 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?

"explanation : 80 + 25 = 105 / 15 = 7 ( remainder ) d"

a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 9

d

subtract(subtract(subtract(80, 25), const_4), const_2)

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

general

concentrated apples juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches . the tubes are packed into wooden boxes , each with dimensions of 11 inches by 10 inches by 31 inches . how many tubes of concentrated apples juice , at the most , can fit into 3 wooden boxes ?

"sp of 1 m of cloth = 9000 / 80 = rs . 112.5 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 112.5 - rs . 23.5 = rs . 89 . answer : b"

a ) 22 , b ) 89 , c ) 90 , d ) 78 , e ) 80

b

subtract(divide(9000, 80), 23.5)

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

physics

the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 12.5 percent , what was the annual interest rate last year ?

chicken - ch cows - c sheep - s ch + c = 6 s c > ch and c > s each cow has 4 legs and 1 head each chicken has 2 legs and 1 head so 5 c + 3 ch = 100 ( sum of legs and head ) there are 2 possible solutions to this equation c = 11 and ch = 9 or c = 14 and ch = 10 since from first equation where ch + c = 6 s the sum of ch and c should be divisbile by 6 . 20 is not so the only possible solution is c = 14 and ch = 10 . so s = 4 answer : d

a ) 5 , b ) 8 , c ) 10 , d ) 4 , e ) 17

d

subtract(6, const_2)

subtract(n0,const_2)

general

evaluate 35 % of 450 + 45 % of 350

"say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.75 = 45 democrats are expected to vote for candidate a ; 40 * 0.25 = 10 republicans are expected to vote for candidate a . thus total of 45 + 10 = 55 registered voters are expected to vote for candidate a , which is 55 % of the total number of registered voters . answer : d ."

a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %

d

add(multiply(60, divide(75, const_100)), multiply(subtract(const_100, 60), divide(25, const_100)))

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

gain

a policeman noticed a criminal from a distance of 200 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?

"let x be the distance to big rock . time = x / 3 + x / 7 = 1 x = 21 / 10 = 2.1 km the answer is c ."

a ) 1.5 , b ) 1.8 , c ) 2.1 , d ) 2.4 , e ) 2.7

c

multiply(divide(subtract(5, 2), add(add(5, 2), subtract(5, 2))), add(5, 2))

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

physics

one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field .

"24 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 24 = 1 / 100 * x = > x = 24000 answer : c"

a ) 29798 , b ) 27908 , c ) 24000 , d ) 25000 , e ) 27991

c

divide(divide(divide(multiply(multiply(multiply(24, const_100), multiply(2, const_100)), multiply(0.75, const_100)), 20), 10), 7.5)

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

physics

two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 23 seconds , what is the ratio of their speeds ?

"30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 65 + 26 = 91 members have not passed the test , thus 0.7 * total = 91 - - > total = 130 . answer : d ."

a ) 60 , b ) 80 , c ) 100 , d ) 130 , e ) 140

d

divide(add(26, 65), divide(subtract(const_100, 65), const_100))

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

gain

how many multiples of 3 are there between 5 and 59 , 5 and 59 inclusive ?

"12 x = 16 y = 28 z 3 x = 4 y = 7 z 3 ( 4 * 7 ) = 4 ( 3 * 7 ) = 7 ( 3 * 4 ) addition = 28 + 21 + 12 = 61 answer would be multiple of 61 which is 122 answer : c"

a ) 52 , b ) 58 , c ) 122 , d ) 84 , e ) 168

c

divide(multiply(multiply(16, 28), 12), const_4)

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

general

a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 60 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )

"first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 34000 - 30000 = 4000 so 10 more machines . . total = 110 machines imo b . ."

a ) 90 , b ) 110 , c ) 105 , d ) 115 , e ) 120

b

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

pat , kate , and mark charged a total of 126 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?

"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 28 = > 2 x = 28 = > x = 14 c"

a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18

c

divide(28, const_2)

divide(n0,const_2)|

general

what is 120 % of 13 / 24 of 600 ?

"explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 26 ) = rs . 208 . profit = 208 - 150 = 58 so , profit % = ( 58 / 150 ) * 100 = 39 % option b"

a ) 12 % , b ) 39 % , c ) 14 % , d ) 15 % , e ) 16 %

b

divide(multiply(subtract(multiply(26, add(5, 3)), add(multiply(5, 18), multiply(3, 20))), const_100), add(multiply(5, 18), multiply(3, 20)))

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

gain

a shopkeeper sold 8 articles at the cost price of 10 articles . then find the profit % or lost %

abel in the 2 days that he worked completed 1 / 5 of the job = 4 / 5 remains then if ben had to leave 4 days before the completion , this means that carla had to work alone for these 4 days in which she completed 1 / 4 of the job . now together , ben and carla completed the job in ( 1 / 12 + 1 / 15 ) ( t ) = 11 / 20 3 / 20 ( t ) = 11 / 20 - - - > t = 3 2 / 3 therefore , these 3 2 / 3 days worked plus the 4 days that carla had to work by herself add to 7 2 / 3 days answer : c

a ) 6 , b ) 7 , c ) 7 2 / 3 , d ) 9 , e ) 10

c

multiply(add(2, 4), 4)

add(n3,n4)|multiply(n4,#0)

physics

a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 50 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?

"total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 4 ) * 270 = 67 gallons total paint used = 157 gallons . option b"

a ) 18 , b ) 157 , c ) 175 , d ) 216 , e ) 250

b

add(multiply(divide(360, 4), 1), divide(subtract(360, multiply(divide(360, 4), 1)), 4))

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

physics

10 : 4 seconds : : ? : 6 minutes

"0 = 1 * 1 - 1 2 = 2 * 2 - 2 6 = 3 * 3 - 3 12 = 4 * 4 - 4 20 = 5 * 5 - 5 30 = 6 * 6 - 6 42 = 7 * 7 - 7 similarly 8 * 8 - 8 = 56 answer : e"

a ) 55 , b ) 85 , c ) 59 , d ) 63 , e ) 56

e

subtract(negate(20), multiply(subtract(6, 12), divide(subtract(6, 12), subtract(0,2, 6))))

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

general

in what time will a railway train 110 m long moving at the rate of 36 kmph pass a telegraph post on its way ?

"distance covered in 1 min = ( 66 * 1000 ) / 60 = 1100 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 1100 / 4.4 = 250 answer : e"

a ) 210 , b ) 220 , c ) 230 , d ) 240 , e ) 250

e

divide(divide(multiply(66, const_1000), const_60), multiply(multiply(divide(add(66, const_2), add(const_4, const_3)), const_2), divide(divide(140, const_100), const_2)))

add(n1,const_2)|add(const_3,const_4)|divide(n0,const_100)|multiply(n1,const_1000)|divide(#3,const_60)|divide(#2,const_2)|divide(#0,#1)|multiply(#6,const_2)|multiply(#5,#7)|divide(#4,#8)|

physics

marts income is 50 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income

"explanation : let the number of hens be x and the number of cows be y . then , x + y = 50 . . . . ( i ) and 2 x + 4 y = 160 x + 2 y = 80 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 30 the required answer = 20 . answer : d"

a ) 22 , b ) 23 , c ) 24 , d ) 20 , e ) 28

d

divide(subtract(multiply(50, const_4), 160), const_2)

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

general

solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 150 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?

"we ' re told that the number of women in a town is equal to 50 % of the number of men in that town . men = 10 women = 5 we ' re asked for the number of men , as a percentage of the number of women . m / w % = 10 / 5 = 200 % answer is c"

a ) 100 % , b ) 120 % , c ) 200 % , d ) 150 % , e ) 180 %

c

multiply(divide(const_100, 50), const_100)

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

gain

the average ( arithmetic mean ) of 4 positive integers is 50 . if the average of 2 of these integers is 40 , what is the greatest possible value that one of the other 2 integers can have ?

"650 = 10 * 65 1300 = 20 * 65 the even multiples are 65 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."

a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11

b

add(divide(subtract(1301, 649), multiply(65, const_2)), const_1)

multiply(n0,const_2)|subtract(n2,n1)|divide(#1,#0)|add(#2,const_1)|

general

on dividing a number by 357 , we get 38 as remainder . on dividing the same number by 17 , what will be the remainder ?

"explanation : relative speed = 70 + 90 = 160 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 160 hr = 1 / 80 hr = 3600 / 80 seconds = = 45 seconds answer : option b"

a ) 56 , b ) 45 , c ) 47 , d ) 26 , e ) 25

b

multiply(divide(add(1.10, 0.9), add(70, 90)), const_3600)

add(n2,n3)|add(n0,n1)|divide(#0,#1)|multiply(#2,const_3600)|

physics

a sum of money at simple interest amounts to $ 680 in 3 years and to $ 710 in 4 years . the sum is :

"0,08 r = x / 100 * 0.1 r answer a"

a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %

a

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

divide(n4,const_100)|divide(n3,const_100)|divide(n1,const_100)|subtract(const_1,#1)|multiply(#0,#3)|divide(#4,#2)|multiply(#5,const_100)|

gain

if 8 men or 12 women can do a piece of work in 35 days , in how many days can the same work be done by 6 men and 11 women ?

"one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 26 * 2 = 52 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one class ( 52 - 32 = 20 ) . thus we get a number of the available extra - classes for teachers , and all that we need is just to count how many teachers could take 2 more classes , which is 20 / 2 = 10 . so the greatest possible value of the # of teachers who had 3 classes is 10 . only answer c has this option ."

a ) 0 and 13 , b ) 0 and 14 , c ) 1 and 10 , d ) 1 and 9 , e ) 2 and 8

c

divide(subtract(multiply(26, 2), 32), 2)

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

general

n ^ ( n / 2 ) = 2 is true when n = 2 in the same way what is the value of n if n ^ ( n / 2 ) = 4 ?

"( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 5 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 5 hence x = 7 . answer is a"

a ) 7 , b ) 11 , c ) 13 , d ) 15 , e ) 17

a

add(5, 2)

add(n0,n5)|

general

tough and tricky questions : combinations . 8 contestants representing 4 different countries advance to the finals of a fencing championship . assuming all competitors have an equal chance of winning , how many possibilities are there with respect to how a first - place and second - place medal can be awarded ?

"1.8 hectares in ares 1 hectare = 100 ares therefore , 1.8 hectares = 1.8 × 100 ares = 180 ares . answer - c"

a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .

c

divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 1.8), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)))

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

physics

20 litres of mixture contains 40 % alcohol and the rest water . if 8 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?

explanation : number of students appeared from school ' p ' = 100 , say number of students qualified from school ' p ' = 70 and number of students appeared from school ' q ' = 130 number of students qualified from school ' q ' = 50 % more than those qualified from school ' p ' . = 70 + 35 = 105 % of students qualified to the number of students appeared from school b = 105 / 130 * 100 = 80.76 % answer : b

a ) 80.78 % , b ) 80.76 % , c ) 80.72 % , d ) 80.79 % , e ) 80.74 %

b

multiply(divide(multiply(divide(add(50, const_100), const_100), divide(70, const_100)), divide(add(30, const_100), const_100)), const_100)

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

general

the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 600 resolutions .

let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 75 ) = 300 x = 71 and the fourth person has a height of 71 + 10 = 81 inches the answer is e .

a ) 73 , b ) 75 , c ) 77 , d ) 79 , e ) 81

e

add(divide(subtract(multiply(75, 4), add(6, add(4, 6))), 4), add(4, 6))

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

general

the maximum number of students among them 1200 pens and 820 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?

sum of interior angles of a polygon = ( n - 2 ) × 180 ° where n = number of sides there will be n angles which are in a . p . therefore , since we need to find maximum value of n , put minimum value for a and d . i . e . , take a = 20 and d = 20 then sum of the angles = n / 2 [ 2 × 20 + ( n − 1 ) 20 ] therefore , 10 n ( n + 1 ) = ( n − 2 ) 180 n = 14.52 since number of sides must be a positive integer , maximum value of n = 14 answer : b

a ) 12 , b ) 14 , c ) 21 , d ) 25 , e ) cant determine

b

divide(add(sqrt(subtract(power(subtract(20, const_3), const_2), multiply(const_4, multiply(divide(add(multiply(const_10, multiply(const_4, const_2)), const_100), const_10), const_2)))), subtract(20, const_3)), const_2)

multiply(const_2,const_4)|subtract(n0,const_3)|multiply(#0,const_10)|power(#1,const_2)|add(#2,const_100)|divide(#4,const_10)|multiply(#5,const_2)|multiply(#6,const_4)|subtract(#3,#7)|sqrt(#8)|add(#9,#1)|divide(#10,const_2)

general

a certain barrel , which is a right circular cylinder , is filled to capacity with 60 gallons of oil . the first barrel is poured into a second barrel , also a right circular cylinder , which is empty . the second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel . if all of the oil in the first barrel is poured into the second barrel , how much empty capacity , in gallons , is left in the second barrel ?

"sum of the 9 numbers = 207 if each number is increased by 4 , the total increase = 4 * 9 = 36 the new sum = 207 + 36 = 243 the new average = 243 / 9 = 27 . answer : c"

a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29

c

multiply(23, 4)

multiply(n1,n2)|

general

in a certain parallelogram the degree measure of one angle exceeds that of the other by 20 what is the degree measure of the smaller angle ?

"shopkeeper sells 800 g instead of 1000 g . so , his gain = 1000 - 800 = 200 g . thus , % gain = 200 * 100 ) / 800 = 25 % . answer : option b"

a ) 10 % , b ) 25 % , c ) 11.11 % , d ) 12 % , e ) none of these

b

multiply(divide(add(multiply(const_2, const_100), divide(const_100, const_2)), 800), const_100)

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

gain

how many ounces of a 60 % salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50 % salt ?

"say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 54 . now , plug options for x . only b and e give an integer value for y . but only for b x > y as needed . answer : b ."

a ) 6 , b ) 10 , c ) 8 , d ) 9 , e ) 12

b

add(const_4, add(floor(divide(58, add(const_4, const_3))), const_1))

add(const_3,const_4)|divide(n0,#0)|floor(#1)|add(#2,const_1)|add(#3,const_4)|

general

the largest number of six digits

"four wheeler = 20 * 4 = 80 ( max ) 2 wheel = 1 so no of 4 wheeler = 20 answer : d"

a ) 11 , b ) 12 , c ) 13 , d ) 20 , e ) 25

d

divide(subtract(82, 2), 4)

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

general

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

"50 % of x = x / 2 ; 25 % of 2500 = 25 / 100 * 2500 = 625 given that , x / 2 = 625 - 25 = > x / 2 = 600 = > x = 1200 . answer : c"

a ) 1880 , b ) 2160 , c ) 1200 , d ) 8400 , e ) 1210

c

divide(subtract(multiply(2500, divide(25, const_100)), 25), divide(50, const_100))

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

general

a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 18 feet tall and 3 feet in circumference ?

"30 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 30 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 30 × 25 × 0.6 / 25 × 0.4 = 45 men answerc"

a ) 25 , b ) 30 , c ) 45 , d ) 20 , e ) none of these

c

divide(multiply(30, divide(subtract(const_100, 40), const_100)), divide(const_4, const_10))

divide(const_4,const_10)|subtract(const_100,n3)|divide(#1,const_100)|multiply(n1,#2)|divide(#3,#0)|

physics

if x + | x | + y = 4 and x + | y | - y = 6 what is x + y = ?

"pass percentage = 100 - ( 30 + 35 - 35 ) = 100 - 30 = 70 answer : d"

a ) 10 % , b ) 20 % , c ) 30 % , d ) 70 % , e ) 50 %

d

subtract(const_100, subtract(add(30, 35), 35))

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

general

if the average ( arithmetic mean ) of a and b is 120 , and the average of b and c is 150 , what is the value of a − c ?

let the cp = 100 profit = ( 320 / 100 ) × 100 = 320 sp = cp + profit = 100 + 320 = 420 if the cost increases by 25 % , new cp = ( 125 / 100 ) × 100 = 125 selling price is constant , hence new sp = 420 profit = sp – cp = 420 – 125 = 295 required percentage = ( 295 / 420 ) × 100 = 2950 / 42 = 1475 / 21 ≈ 70 answer : e

a ) 180 % , b ) 120 % , c ) 90 % , d ) 80 % , e ) 70 %

e

multiply(divide(subtract(add(320, const_100), add(25, const_100)), add(320, const_100)), const_100)

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

gain

there are 6 baskets numbered from 1 to 6 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?

total expenditure = 40 + 25 + 15 + 10 = 90 % saving = ( 100 - 90 ) = 10 % 10 / 100 × salary = 1200 , salary = 12000 rs . answer : a

a ) 12000 , b ) 6000 , c ) 8000 , d ) 10000 , e ) none of these

a

divide(multiply(1200, const_100), 10)

multiply(n4,const_100)|divide(#0,n3)

gain

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

"explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 7 ) + 6000 ( v - 7 ) < = > 2000 v = 42000 < = > v = 21 . answer : b"

a ) 76 , b ) 21 , c ) 26 , d ) 28 , e ) 11

b

add(7, divide(multiply(7, subtract(12000, 8000)), subtract(8000, 6000)))

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

general

a man has $ 480 in the denominations of one - dollar , 5 - dollar notes and 10 - dollar . the number of dollars of each denomination is equal . what is the total number of dollar that he has ?

"let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 108 x = 123 answer : a"

a ) 123 , b ) 267 , c ) 277 , d ) 267 , e ) 120

a

divide(add(108, 138), 2)

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

general

mary can do a piece of work in 12 days . rosy is 50 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?

"let the third number is x . then first number = ( 100 - 30 ) % of x = 70 % of x = 7 x / 10 second number is ( 63 x / 100 ) difference = 7 x / 10 - 63 x / 100 = 7 x / 10 so required percentage is , difference is what percent of first number ( 7 x / 100 * 10 / 7 x * 100 ) % = 10 % answer : b"

a ) 8 % , b ) 10 % , c ) 9 % , d ) 11 % , e ) 12 %

b

subtract(multiply(divide(subtract(37, 30), subtract(const_100, 30)), const_100), const_10)

subtract(n1,n0)|subtract(const_100,n0)|divide(#0,#1)|multiply(#2,const_100)|subtract(#3,const_10)|

gain

if the sides of a triangle are 52 cm , 48 cm and 20 cm , what is its area ?

"30 * 18 / 5 = 108 kmph answer : b"

a ) 122 , b ) 108 , c ) 110 , d ) 150 , e ) 100

b

multiply(divide(30, const_1000), const_3600)

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

physics

two employees x and y are paid a total of rs . 650 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?

"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 8 = > 2 x = 8 = > x = 4 b"

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

b

divide(8, const_2)

divide(n0,const_2)|

general

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

"for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 1500 = $ 2790 the total price is $ 4000 + $ 2850 + $ 2790 = $ 9640 the answer is e ."

a ) $ 8280 , b ) $ 8520 , c ) $ 8710 , d ) $ 8930 , e ) $ 9640

e

multiply(multiply(2, const_3), const_100)

multiply(n4,const_3)|multiply(#0,const_100)|

gain

the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if saran and david have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?

"log 8 x + log 8 ( 1 / 6 ) = 1 / 3 = > ( log x / log 8 ) + ( log 1 / 6 / log 8 ) = log ( 81 / 3 ) = log 2 = > log x = log 2 – log 1 / 6 = log ( 2 * 6 / 1 ) = log 12 answer : a"

a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26

a

multiply(power(8, divide(1, 3)), 6)

divide(n2,n5)|power(n0,#0)|multiply(n3,#1)|

general

what is the average of xx , 2 x 2 x , and 66 ?

"sol . let the numbers be x and y . then , ( x + y ) = 12 and x 2 + y 2 = 124 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 12 ) 2 - 124 = 144 - 124 = 20 xy = 10 . answer a"

a ) 10 , b ) 44 , c ) 80 , d ) 88 , e ) 90

a

divide(subtract(power(12, const_2), 124), const_2)

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

general

if the compound interest on a certain sum of money for 5 years at 10 % per annum be rs . 993 , what would be the simple interest ?

"c . p . = rs . 5 x and s . p . = rs . 8 x . then , gain = rs . 3 x required ratio = 3 x : 5 x = 3 : 5 d"

a ) 23 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 25

d

divide(subtract(8, 5), 5)

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

other

laura took out a charge account at the general store and agreed to pay 8 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?

"b 90 sum = ( n x n ) + n hence , 9 x 9 = 81 + 9 = 90"

a ) 80 , b ) 90 , c ) 30 , d ) 70 , e ) 60

b

multiply(add(9, const_1), 9)

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

physics

in a box of 9 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?

"line k passes through the origin and has slope 1 / 7 means that its equation is y = 1 / 7 * x . thus : ( x , 1 ) = ( 7 , 1 ) and ( 7 , y ) = ( 7,1 ) - - > x - y = 7 - 1 = 6 . answer : a"

a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 3

a

multiply(multiply(7, 7), divide(1, 7))

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

general

find the average of all numbers between 1 and 13 which are divisible by 2

"length = 15 cm , breadth = 13 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 15 + 13 ) cm = 2 × 28 cm = 56 cm we know that the area of rectangle = length × breadth = ( 15 × 13 ) cm 22 = 195 cm 2 answer : d"

a ) 71 cm 2 , b ) 121 cm 2 , c ) 141 cm 2 , d ) 195 cm 2 , e ) 221 cm 2

d

square_area(15)

square_area(n0)|

geometry

village a ’ s population is 300 greater than village b ' s population . if village b ’ s population were reduced by 600 people , then village a ’ s population would be 4 times as large as village b ' s population . what is village b ' s current population ?

"n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 400 - 50 = 350 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 350 = 150 . answer is b"

a ) 120 , b ) 150 , c ) 100 , d ) 180 , e ) 220

b

subtract(add(175, 325), subtract(400, 50))

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

other

car x began traveling at an average speed of 35 miles per hour . after 84 minutes , car y began traveling at an average speed of 42 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?

"sum of first 20 multiples of 12 are = ( 12 × 1 ) + ( 12 × 2 ) + ( 12 × 3 ) + . . . . . . + ( 12 × 19 ) + ( 12 × 20 ) . = 12 ( 1 + 2 + 3 + . . . . . + 20 ) use the formula : n ( n + 1 ) 2 ⇒ 12 × ( 20 × 21 ) 2 = 2520 . answer : a"

a ) 2520 , b ) 3878 , c ) 2778 , d ) 27 , e ) 911

a

add(divide(divide(20, divide(divide(divide(divide(divide(20, const_2), const_2), const_2), const_2), const_2)), const_2), add(const_1, sqrt(divide(divide(20, divide(divide(divide(divide(divide(20, const_2), const_2), const_2), const_2), const_2)), const_2))))

divide(n0,const_2)|divide(#0,const_2)|divide(#1,const_2)|divide(#2,const_2)|divide(#3,const_2)|divide(n0,#4)|divide(#5,const_2)|sqrt(#6)|add(#7,const_1)|add(#8,#6)|

general

the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 12.5 percent , what was the annual interest rate last year ?

total no . of handshakes = 49 + 48 + 47 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 1225 or , if there are n persons then no . of shakehands = nc 2 = 50 c 2 = 1225 answer : c

a ) 190 , b ) 200 , c ) 1225 , d ) 220 , e ) 230

c

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

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

general

two mechanics were working on your car . one can complete the given job in six hours , but the new guy takes 10 hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?

"since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 10 minutes the population increases by 10 x 4 = 40 people . answer . a ."

a ) 40 , b ) 100 , c ) 150 , d ) 240 , e ) 300

a

multiply(divide(const_60, 15), 10)

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

physics

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 ?

"let the retail price be = x selling price of z = 0.75 x selling price of x = 0.95 * 0.75 x = 0.71 x selling price of y = ( ( 0.75 x + 0.71 x ) / 2 ) * 0.70 = 0.73 x * 0.75 = 0.55 x 0.55 x = k * 0.71 x k = 0.55 / 0.71 = 55 / 71 answer : b"

a ) 21 / 34 , b ) 55 / 71 , c ) 25 / 34 , d ) 26 / 34 , e ) 27 / 34

b

multiply(divide(divide(multiply(divide(add(subtract(const_100, 25), multiply(subtract(const_100, 25), divide(subtract(const_100, 5), const_100))), const_2), subtract(const_100, 30)), const_100), multiply(subtract(const_100, 25), divide(subtract(const_100, 5), const_100))), const_10)

subtract(const_100,n1)|subtract(const_100,n0)|subtract(const_100,n2)|divide(#0,const_100)|multiply(#3,#1)|add(#4,#1)|divide(#5,const_2)|multiply(#6,#2)|divide(#7,const_100)|divide(#8,#4)|multiply(#9,const_10)|

general

find the smallest number of 6 digits exactly divisible by 25 , 3545 and 15 .

"p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 3 / 5 . 2 / 5 p ( a n b ) = 6 / 25 . a"

a ) 6 / 25 , b ) 3 / 25 , c ) 8 / 25 , d ) 2 / 13 , e ) 3 / 17

a

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

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

general

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

"on the first three flips , you must get heads . whats the probability of getting heads ? its 1 / 2 so for the first three flips , your probability is ( 1 / 2 ) ^ 3 = 1 / 8 now for the last two , you want to get tails only . whats the prob of getting tails ? well , its the same as prob of getting a heads , namely , 1 / 2 for the last two flips , your probability is ( 1 / 2 ) ^ 2 = 1 / 4 so your overall probability for the event in question is 1 / 8 * 1 / 4 = 1 / 32 answer : e"

a ) 3 / 5 , b ) 1 / 2 , c ) 1 / 5 , d ) 1 / 8 , e ) 1 / 32

e

power(divide(1, 2), 5)

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

probability

a number is doubled and 9 is added . if the resultant is trebled , it becomes 81 . what is that number ?

"x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] q = z - x = x + 9 - x = 9 ans : d"

a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10

d

add(add(5, const_2), const_2)

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

general

how many prime numbers are between 13 / 3 and 83 / 6 ?

originally let there be x men . less men , more days ( indirect ) : . ( x - 10 ) : x : : 100 : 110 or x - 10 / x = 100 / 110 or 11 x - 110 = 10 x or x = 110 so , originally there were 110 men . answer : d

a ) 75 , b ) 82 , c ) 100 , d ) 110 , e ) 120

d

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

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

physics

the largest 3 digit number exactly divisible by 88 is ?

d = 150 + 200 = 350 s = 54 * 5 / 18 = 15 mps t = 350 / 15 = 23.3 sec c ) 23.3 sec

a ) 17 sec , b ) 21 sec , c ) 23.3 sec , d ) 27.5 sec , e ) 29 sec

c

divide(add(200, 150), multiply(54, const_0_2778))

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

physics

the diameter of a circle is 4 / π . find the circumference of the circle .

"percentage error in calculated area = ( 6 + 6 + ( 6 ã — 6 ) / 100 ) % = 12.36 % answer : e"

a ) 14.05 % , b ) 14.02 % , c ) 14 % , d ) 13 % , e ) 12.36 %

e

divide(multiply(subtract(square_area(add(const_100, 6)), square_area(const_100)), const_100), square_area(const_100))

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

gain

on dividing 73 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?

distance is same s 1 t 1 = s 2 t 2 40 t = 50 ( t - 1 ) t = 5 distance = speed * time 40 * 5 = 200 answer : b

a ) 150 , b ) 200 , c ) 450 , d ) 500 , e ) 600

b

multiply(divide(50, subtract(50, 40)), 40)

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

physics

by how much is 50 % of 250 greater than 25 % of 400 .

"first , you must find the total weight of the mixture given that 80 % of it will be dough . 80 % * total = 36 = > ( 8 / 10 ) total = 36 = > total = 360 / 8 = > total = 45 oz , from there , you must find 10 % of the total 40 oz of the mixture . 20 % * total = > ( 2 / 10 ) ( 45 ) = 9 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 10 - 9 = 1 oz chocolate left over . answer : e"

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

e

multiply(divide(20, const_100), 20)

divide(n2,const_100)|multiply(n2,#0)|

gain

what is the total number of integers between 20 and 100 that are divisible by 9 ?

"a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 7 / 4 ) * 4 = 2 / 7 the answer is e ."

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

e

multiply(divide(subtract(const_100, 60), add(const_100, 75)), divide(5, 4))

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

general

tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 9 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?

ratio of 2 bedroom apartment : 1 bedroom apartment = 700 : 2100 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : a

a ) 25 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) 45 %

a

divide(multiply(700, const_100), add(add(multiply(const_2, const_1000), const_100), 700))

multiply(n0,const_100)|multiply(const_1000,const_2)|add(#1,const_100)|add(n0,#2)|divide(#0,#3)

general

in a 400 member association consisting of men and women , exactly 20 % of men and exactly 25 % women are homeowners . what is the least number of members who are homeowners ?

"actual miles / gallon is = 480 / 4 = 12 miles / gallon . current engine miles / gallon is 8 miles / gallon . additional 4 miles / gallon is required to match the actual mileage . answer : b"

a ) 2 , b ) 4 , c ) 12 , d ) 40 , e ) 160

b

subtract(divide(480, 40), 8)

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

physics

how many distinct prime numbers are factors of 33150 ?

"age of the teacher = ( 23 * 13 - 22 * 12 ) = 35 years . answer : c"

a ) 31 , b ) 36 , c ) 35 , d ) 53 , e ) 57

c

add(22, const_1)

add(n0,const_1)|

general