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mathqa_shuffle_question_test

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how many diagonals does a 58 - sided convex polygon have ?

"if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 415 not divisible by a hence , we need to add 1 to this number for it to be divisible by 8 correct option : a"

a ) $ 214.16 , b ) $ 214.17 , c ) $ 214.18 , d ) $ 214.19 , e ) $ 214.20

a

add(214.15, divide(const_3, const_100))

divide(const_3,const_100)|add(n1,#0)|

general

due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?

"lots of calculations . 1.50 * 4 + 3 * . 35 * 32 + 2 * ( 7 / 4 ) * 32 * . 35 answer = $ 78.80 the correct option is a"

a ) $ 78.80 , b ) $ 79.80 , c ) $ 78.90 , d ) $ 79.90 , e ) $ 77.80

a

multiply(multiply(0.35, 2), 3)

multiply(n1,n3)|multiply(n2,#0)|

general

the area of a triangle will be when a = 1 m , b = 4 m , c = 5 m , a , b , c being lengths of respective sides ?

"let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which y is 40 % of 80 hence , d is the answer"

a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50

d

divide(80, const_2)

divide(n3,const_2)|

general

two bullet trains of equal lengths take 10 seconds and 30 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?

"trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , b , d , e the answer to be c again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 5120 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 5120 = 12500 hence , correct answer = c"

a ) 5113 , b ) 5117 , c ) 5120 , d ) 8119 , e ) 10115

c

divide(12500, power(add(divide(1, 4), 1), 4))

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

general

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

explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 714 = 272 answer : b

a ) 240 , b ) 272 , c ) 379 , d ) 277 , e ) 122

b

multiply(divide(714, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))

add(n1,n3)|multiply(n0,n2)|multiply(n1,n2)|subtract(n0,n3)|subtract(const_12,n2)|multiply(#3,#4)|multiply(#0,#4)|add(#1,#5)|add(#2,#6)|add(#7,#8)|divide(n5,#9)|multiply(#7,#10)

gain

the captain of a cricket team of 11 members is 29 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?

"d = 60 * 5 / 18 = 35 = 583 – 120 = 463 answer : c"

a ) 338 , b ) 277 , c ) 463 , d ) 456 , e ) 271

c

subtract(multiply(35, multiply(60, const_0_2778)), 120)

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

physics

there are 32 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?

"an easy way to solve this question is by number plugging . assume there are 100 marbles in jar b then in jar a there will be 106 marbles . now , for both jars to have equal marbles we should move 3 marbles from a to b , which is 3 / 106 = ~ 2.8 % of a . answer : a ."

a ) 2.8 % , b ) 3.0 % , c ) 3.2 % , d ) 3.4 % , e ) 3.6 %

a

multiply(divide(divide(6, const_2), add(6, const_100)), const_100)

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

gain

a and b can do a piece of work in 30 days and 30 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?

"given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes t in this range . answer : a ."

a ) none , b ) one , c ) two , d ) three , e ) four

a

divide(add(factorial(6), 6), add(factorial(6), 6))

factorial(n2)|add(n2,#0)|divide(#1,#1)|

general

the l . c . m . of 2 numbers is 72 . the numbers are in the ratio 2 : 3 . find their sum ?

"so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 200 , thus 0.2 x = $ 200 - - > x = $ 1,000 . since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,000 = $ 2,000 . answer : c"

a ) 3000 , b ) 5000 , c ) 2000 , d ) 4000 , e ) 6000

c

multiply(divide(multiply(divide(400, 2), divide(400, 2)), subtract(605, 400)), 2)

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

gain

what is the length of a bridge ( in meters ) , which a train 166 meters long and travelling at 45 km / h can cross in 40 seconds ?

"the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.4 ( 6 ) = 2.4 gallons at the start , the amount of water is 0.6 ( 6 ) = 3.6 gallons after 4 hours , the amount of water is 3.6 - 0.5 ( 4 ) = 1.6 gallons the concentration of water is 1.6 / ( 2.4 + 1.6 ) = 40 % the answer is a ."

a ) 40 % , b ) 44 % , c ) 48 % , d ) 52 % , e ) 56 %

a

multiply(divide(subtract(divide(multiply(4, subtract(const_100, 40)), const_100), multiply(0.5, 4)), subtract(4, multiply(0.5, 4))), const_100)

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

gain

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

"answer : option b explanation : 5 : 1 = x : 10 x = 50 answer : option b"

a ) 74 , b ) 50 , c ) 94 , d ) 59 , e ) 48

b

multiply(10, 5)

multiply(n0,n2)|

other

a lady starts from p towards q and realizes that at a point r , if he walks 50 km further he will be at a point s , which is as far away from r as it is from q . what is the distance between p and q if the distance between p and r is half the distance from r to q ? ( assume that p , q , r and s are all on the same straight line )

"s = 125 / 5 * 18 / 5 = 90 kmph answer : e"

a ) 229 , b ) 108 , c ) 278 , d ) 126 , e ) 90

e

multiply(divide(125, 5), const_3_6)

divide(n0,n1)|multiply(#0,const_3_6)|

physics

what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 3 , and 5 if each digit can be used only once in each number ?

"due to stoppages , it covers 10 km less . time taken to cover 10 km = 10 / 80 * 60 = 8 min . answer : c"

a ) 11 min , b ) 10 min , c ) 8 min , d ) 6 min , e ) 5 min

c

multiply(const_60, divide(subtract(80, 70), 80))

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

physics

when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of t ?

"1 / 7 + 1 / 14 + 1 / 28 = 7 / 28 = 1 / 4 all three can finish the work in 4 days answer : a"

a ) 4 , b ) 9 , c ) 2 , d ) 11 , e ) none

a

inverse(add(inverse(28), add(inverse(7), inverse(14))))

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

physics

a farm has chickens , cows and sheep . there are 6 times the number of chickens and cows than sheep . if there are more cows than chickens or sheep , and together , cows and chickens have a total of 100 feet and heads , how many sheep live at the farm ?

total = 200 not working = 100 having family = 75 like to sing in shower = 125 working = 200 - 100 = 100 not having family = 200 - 75 = 125 like to sing in shower = 125 largest possible number is the lowest possible among the above thus 100 c

a ) 125 , b ) 150 , c ) 100 , d ) 130 , e ) 140

c

subtract(add(add(100, 75), 125), 200)

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

general

in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.45 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?

"explanation : number students behind the nitin in rank = ( 49 - 18 ) = 31 nitin is 32 nd from the last answer : c ) 32"

a ) 33 , b ) 38 , c ) 32 , d ) 28 , e ) 19

c

subtract(49, 18)

subtract(n1,n0)|

other

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

6 minutes is 360 seconds . lamp a and lamp b will flash together every 24 seconds . 360 / 24 = 15 . in the time period , lamp a and lamp b will flash together 15 times . lamp a and lamp c will flash together every 30 seconds . 360 / 30 = 12 . in the time period , lamp a and lamp c will flash together 12 times . lamp b and lamp c will flash together every 40 seconds . 360 / 40 = 9 . in the time period , lamp b and lamp c will flash together 9 times . all three lights will flash together every 2 * 2 * 2 * 3 * 5 = 120 seconds . 360 / 120 = 3 . we have counted these triple flashes three times , so we need to subtract three times the number of times that all three lights flash together . the number of times that exactly two lights flash together is 15 + 12 + 9 - 9 = 27 times . the answer is d .

a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28

d

subtract(add(add(divide(multiply(6, const_60), lcm(6, 8)), divide(multiply(6, const_60), lcm(6, 10))), divide(multiply(6, const_60), lcm(8, 10))), multiply(divide(multiply(6, const_60), lcm(lcm(6, 8), 10)), 3))

lcm(n0,n1)|lcm(n0,n2)|lcm(n1,n2)|multiply(n0,const_60)|divide(#3,#0)|divide(#3,#1)|divide(#3,#2)|lcm(n2,#0)|add(#4,#5)|divide(#3,#7)|add(#8,#6)|multiply(n3,#9)|subtract(#10,#11)

physics

albert is 2 times mary ’ s age and 4 times as old as betty . mary is 12 years younger than albert . how old is betty ?

"ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . q = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616"

a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784

b

divide(59.32, subtract(2, floor(2)))

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

general

how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 5 ?

speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 12 * 60 = 2000 m answer is a

a ) 2000 , b ) 1492 , c ) 1667 , d ) 1254 , e ) 1112

a

multiply(divide(multiply(10, const_1000), const_60), 12)

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

gain

$ 378 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?

30 % of 1000 gives 300 . so 300 attends chess and 10 % of 300 gives 30 . so 30 enrolled for swimming answer : d

a ) 1 , b ) 10 , c ) 100 , d ) 30 , e ) 20

d

divide(multiply(divide(multiply(30, 1000), const_100), 10), const_100)

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

gain

each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 53 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?

"cost price = 800 profit = 10 % = 10 % of 800 = 80 selling price = cp + profit sp = 880 a discount of 10 % to employees means 10 % off on 880 so 10 % of 880 = 88 ans b"

a ) 86 , b ) 88 , c ) 90 , d ) 92 , e ) 94

b

divide(add(divide(multiply(800, 10), const_100), 800), multiply(divide(800, 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

what is the value of 3 x ^ 2 − 1.8 x + 0.7 for x = 0.6 ?

"let ' s assume there are 100 reporters - - > 15 reporters cover local politics . now , as 25 % of the reporters who cover all politics do not cover local politics then the rest 75 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 75 % of them equal to 15 ( # of reporters who cover local politics ) : 0.75 x = 15 - - > x = 20 , hence 20 reporters cover politics and the rest 100 - 20 = 80 reporters do not cover politics at all . answer : d ."

a ) 20 % , b ) 42 % , c ) 44 % , d ) 80 % , e ) 84 %

d

multiply(subtract(const_1, divide(15, subtract(const_100, 25))), const_100)

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

gain

a lawn is in the form of a rectangle having its sides in the ratio 2 : 3 . the area of the lawn is ( 1 / 6 ) hectares . find the length and breadth of the lawn .

"i ii iii 150 120 100 120 - - - - - - - - - - 150 100 - - - - - - - - - - - ? = > 125 % answer : a"

a ) 125 % , b ) 97 % , c ) 118 % , d ) 52 % , e ) 83 %

a

subtract(const_100, multiply(divide(add(50, const_100), add(20, const_100)), const_100))

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

gain

in a manufacturing plant , it takes 36 machines 4 hours of continuous work to fill 6 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ?

"total = 70 thrower = 43 rest = 70 - 43 = 27 left handed = 27 / 3 = 9 right handed = 18 if all thrower are right handed then total right handed is 43 + 18 = 61 so c . 61 is the right answer"

a ) 54 , b ) 59 , c ) 61 , d ) 71 , e ) 92

c

add(multiply(subtract(const_1, divide(const_1, const_3)), subtract(70, 43)), 43)

divide(const_1,const_3)|subtract(n0,n1)|subtract(const_1,#0)|multiply(#2,#1)|add(n1,#3)|

general

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

"speed = 36 * 5 / 18 = 10 m / s time = 100 / 10 = 10 seconds the answer is c ."

a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14

c

divide(100, multiply(const_0_2778, 36))

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

physics

a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 10 as remainder . find the no . is ?

"s . p . of each of the article = 1000 / 2 = $ 500 let m . p = $ x 90 % of x = 500 x = 500 * 100 / 90 = $ 555.55 answer is a"

a ) $ 555.55 , b ) $ 500 , c ) $ 350 , d ) $ 400 , e ) $ 600

a

divide(multiply(subtract(const_100, 10), divide(1000, const_2)), const_100)

divide(n0,const_2)|subtract(const_100,n1)|multiply(#0,#1)|divide(#2,const_100)|

gain

how many multiples of 5 are there between 70 and 358 ?

"the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 5 / 10 ) = 150 / 3000 = 0.05 option a"

a ) 0.05 , b ) 0.9 , c ) 9 , d ) 90 , e ) none of the above

a

divide(multiply(15, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100)

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

gain

if a speaks the truth 65 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time

let the train fare between the two places for one person be rs . t bus fare between the two places for two persons rs . 4 / 3 t = > 6 / 2 ( 4 / 3 t ) + 8 ( t ) = 1512 = > 12 t = 1512 = > t = 126 . answer : a

a ) rs . 126 , b ) rs . 132 , c ) rs . 120 , d ) rs . 114 , e ) none of these

a

divide(1512, add(multiply(divide(6, const_2), divide(4, const_3)), 8))

divide(n1,const_2)|divide(n0,const_3)|multiply(#0,#1)|add(n2,#2)|divide(n3,#3)

general

in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 120 marks , the number of questions he attempts correctly , is :

"in 2 minutes , he ascends = 1 metre â ˆ ´ 15 metres , he ascends in 30 minutes . â ˆ ´ he reaches the top in 31 st minute . answer a"

a ) 31 st , b ) 22 nd , c ) 23 rd , d ) 24 th , e ) none of these

a

subtract(multiply(2, 17), 1)

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

physics

the population of a town increased from 1 , 75,000 to 2 , 62,500 in a decade . what is the average percent increase of population per year ?

e 270 m

a ) 220 m , b ) 250 m , c ) 280 m , d ) 210 m , e ) 270 m

e

subtract(multiply(multiply(72, const_0_2778), 26), 250)

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

physics

the average age of 36 students in a group is 14 years . when teacher ' s age is included to it , the average increases by one . find out the teacher ' s age in years ?

"explanation : let the cp of the article = rs . 100 . then labeled price = rs . 140 . sp = rs . 140 - 10 % of 140 = rs . 140 - 14 = rs . 126 . gain = rs . 126 â € “ rs . 100 = rs . 26 therefore , gain / profit percent = 26 % . answer : option a"

a ) 26 % , b ) 20 % , c ) 17 % , d ) 18 % , e ) none of these

a

subtract(subtract(add(const_100, 40), multiply(add(const_100, 40), divide(10, const_100))), const_100)

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

gain

how long does a train 125 m long running at the speed of 78 km / hr takes to cross a bridge 125 m length ?

"36 ^ 5 = 6 ^ 7 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 7 ( dont actually calculate full values ) and answer is d : 3"

a ) 1 , b ) 7 , c ) 5 , d ) 3 , e ) 9

d

floor(divide(reminder(power(36, reminder(5, add(const_4, const_1))), const_100), const_10))

add(const_1,const_4)|reminder(n1,#0)|power(n0,#1)|reminder(#2,const_100)|divide(#3,const_10)|floor(#4)|

general

a car traveling at a certain constant speed takes 30 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 30 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?

"according to order of operations , inner brackets first . hence | 6 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 6 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 6 + 72 | - | 5 - 11 | = | 78 | - | - 6 | = 78 - 6 = 72 correct answer c ) 72"

a ) 40 , b ) 50 , c ) 72 , d ) 70 , e ) 80

c

subtract(subtract(6, multiply(8, subtract(3, 12))), negate(subtract(5, 11)))

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

general

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 ?

"i = ( 500 * 9 * 6 ) / 100 = 270 answer : b"

a ) 287 , b ) 270 , c ) 276 , d ) 129 , e ) 211

b

multiply(500, divide(9, const_100))

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

gain

in a class of 60 students , 20 did not opt for math . 15 did not opt for science and 5 did not opt for either . how many students of the class opted for both math and science ?

"according to order of operations , 12 ÷ 4 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 4 × 2 = 3 × 2 = 6 hence 60 - 12 ÷ 4 × 2 = 60 - 6 = 54 correct answer is b ) 54"

a ) a ) 45 , b ) b ) 54 , c ) c ) 63 , d ) d ) 72 , e ) e ) 81

b

subtract(60, multiply(multiply(12, 4), 2))

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

general

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

the time to go 42 miles was 22 / 11 + 20 / 10 = 2 + 2 = 4 hours . the average speed for the return trip was 42 miles / 5 hours = 8.4 mph . the answer is e .

a ) 7.6 , b ) 7.8 , c ) 8 , d ) 8.2 , e ) 8.4

e

divide(add(22, 20), subtract(9, add(divide(22, 11), divide(20, 10))))

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

physics

the difference of a larger number and a smaller number is 6 . the sum of the larger number and twice the smaller is 15 . what is the larger number ?

"explanation : number of pages increased = 100 now , the number of pages of book = 240 number of pages of the books before increase = 240 – 100 = 140 % increase in the number of pages in the book = 100 / 140 x 100 % = 71.4 % d"

a ) 20 % , b ) 305 , c ) 50 % , d ) 71.4 % , e ) 60 %

d

subtract(multiply(divide(240, subtract(240, 100)), const_100), const_100)

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

general

the difference between the place values of 7 and 3 in the prime number 527435 is

answer 3 / 10 + 5 / 100 + 8 / 1000 = 0.3 + 0.05 + 0.008 = 0.358 correct option : b

a ) 0.853 , b ) 0.358 , c ) 3.58 , d ) 8.35 , e ) none

b

add(divide(8, 1000), add(divide(3, 10), divide(5, 100)))

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

general

a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 25 hour to row to a place and come back , how far is the place ?

if a = 1 , r = 2 then a = 1 , b = 2 , c = 4 then abs ( a + b - c ) = 1 if a = 1 , r = 3 then a = 1 , a = 3 , a = 9 then abs ( 1 + 3 - 9 ) = 5 if a = 2 , r = 2 , then a = 2 , b = 4 , c = 8 then abs ( 2 + 4 - 8 ) = 2 if a = 1 , r = - 2 then a = 1 , b = - 2 , c = 4 the abs ( 1 - 2 - 4 ) = 5 if a = 1 , r = - 3 then a = 1 , b = - 3 , c = 9 then abs ( 1 - 3 - 9 ) = 11 if a = 2 , r = - 2 then a = 2 , b = - 4 , c = - 8 then abs ( 2 - 4 - 8 ) = 10 so total 5 abs ( ) values answer : d

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

d

add(3, const_2)

add(n0,const_2)

general

sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 07 : 00 and starts climbing at a constant pace . ken starts climbing only at 09 : 00 , when sari is already 700 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?

"sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 19 odd numbers = 19 ^ 2 = 361 answer : c"

a ) 341 , b ) 351 , c ) 361 , d ) 371 , e ) 381

c

multiply(multiply(19, const_2), divide(19, const_2))

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

general

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

"1 . no . of coaches = 9 sqr root = 3 speed decreases by 12 12 = k * 3 k = 4 no . of coaches = 25 swr root = 5 decrease = 5 * 4 = 20 new speed = 90 - 20 = 70 e"

a ) 90 , b ) 85 , c ) 80 , d ) 60 , e ) 70

e

subtract(90, multiply(sqrt(25), divide(subtract(90, 78), sqrt(9))))

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

physics

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

"explanation : let the length of train be l m . acc . to question ( 264 + l ) / 20 = l / 8 2112 + 8 l = 20 l l = 2112 / 12 = 176 m answer b"

a ) 188 , b ) 176 , c ) 175 , d ) 96 , e ) none of these

b

multiply(divide(264, subtract(20, 8)), 8)

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

physics

what is the tens digit of 36 ^ 5 ?

"step 1 ) took lcm of 10 and 12 . . came as 30 . just multiplied by 10 . . . ( to make easy calculation ) step 2 ) 300 distance between b to c . . . do 300 / 12 hence 25 gallons used step 3 ) twice distance . . hence 300 * 2 = 600 . . . do as above . . 600 / 10 = 60 gallons used step 4 ) total gallons . . 25 + 60 = 85 gallons step ) total miles = 300 + 600 = 900 miles hence . . average of whole journey = 900 / 85 which comes to 10.6 answer : d"

a ) 11.5 , b ) 9.5 , c ) 13.5 , d ) 10.6 , e ) 14.5

d

divide(add(multiply(12, const_10), divide(multiply(12, const_10), const_2)), add(divide(multiply(12, const_10), 10), divide(divide(multiply(12, const_10), const_2), 12)))

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

general

the average runs scored by a batsman in 20 matches is 40 . in the next 30 matches the batsman scored an average of 20 runs . find his average in all the 50 matches ?

"explanation : the total number of mangoes bought by the shopkeeper be 12 . if he buys 4 a rupee , his cp = 3 he selling at 3 a rupee , his sp = 4 profit = sp - cp = 4 - 3 = 1 profit percent = 1 / 3 * 100 = 33 1 / 3 % answer : c"

a ) 73 1 / 3 % , b ) 13 1 / 3 % , c ) 33 1 / 3 % , d ) 23 1 / 3 % , e ) 93 1 / 3 %

c

divide(multiply(3, const_100), 4)

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

gain

a train 150 m long passes a km stone in 15 seconds and another train of the same length travelling in opposite direction in 8 seconds . the speed of the second train is

"length of train = 12 × 15 = 180 m . then , speed of train = 180 ⁄ 18 = 10 m / s now , length of train = 10 × 15 = 150 m ∴ required time = 150 ⁄ 10 = 15 sec . answer c"

a ) 18 sec , b ) 12 sec , c ) 15 sec , d ) 20 sec , e ) none of these

c

divide(subtract(multiply(12, 15), 15), divide(multiply(12, 15), 18))

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

physics

if x and y are both odd prime numbers and x < y , how many distinct positive integer e factors does 2 xy have ?

"let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 16 . . 4 x + 12 = 16 . . x = 1 . . ans = x + 4 = 1 + 4 = 5 answer a"

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

a

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

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

general

if $ 120 invested at a certain rate of simple interest amounts to $ 180 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?

40 pages - - - - - - - > 1 min 2 hrs except 20 mints means = 2 * 60 = 120 - 20 = 100 mints i . e . , 100 * 40 = 4,000 pages printed . answer : a

a ) 4,000 , b ) 12,880 , c ) 14,880 , d ) 8,880 , e ) 18,880

a

divide(multiply(subtract(multiply(2, const_60), 20), 40), multiply(const_10, const_100))

multiply(n1,const_60)|multiply(const_10,const_100)|subtract(#0,n2)|multiply(n0,#2)|divide(#3,#1)

general

a reduction of 50 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?

"speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 450 m at 50 / 3 m / sec = 450 * 3 / 50 sec = 27 sec answer : c ."

a ) 5 sec , b ) 39 sec , c ) 27 sec , d ) 15 sec , e ) 18 sec

c

divide(450, multiply(subtract(68, 8), const_0_2778))

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

physics

in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 90 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?

4 / 10 of all the vehicles were not rented . ( 3 / 5 ) ( 2 / 5 ) = 6 / 25 of all the vehicles are 4 wds that were not rented . ( 6 / 25 ) / ( 4 / 10 ) = 3 / 5 is the fraction of non - rented vehicles that were 4 wds 1 - 3 / 5 = 40 % of non - rented vehicles were not 4 wds . the answer is c .

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

c

multiply(divide(divide(multiply(const_2, 40), add(const_3, const_2)), 40), const_100)

add(const_2,const_3)|multiply(n2,const_2)|divide(#1,#0)|divide(#2,n2)|multiply(#3,const_100)

gain

if 100 cats kill 100 mice in 100 days , then 4 cats would kill 4 mice in how many days ?

"we have : 1 ) x < y < z 2 ) y - x > 5 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c and e we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 7 the least value for y - x must be 11 , the least value for x must be 2 , and , thus , the least possible value for y must be 11 ( y - 2 = 9 , y = 11 ) 2 < 11 < z , since z is odd , the least possible value for z is 13 z - x = 13 - 2 = 11 answer c"

a ) 6 , b ) 7 , c ) 11 , d ) 8 , e ) 10

c

add(add(7, const_2), const_2)

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

general

a pump can fill a tank with water in 3 hours . because of a leak , it took 3 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in ?

"a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 1000 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 100000 n = 1000 satisfies this . e"

a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000

e

multiply(const_1000, divide(1, 100000))

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

general

a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area w covered by the two roads ?

"the number of miles to drive to finish his journey is given by 1200 - 1096 = 104 miles correct answer a"

a ) 104 miles , b ) 432 miles , c ) 456 miles , d ) 887 miles , e ) 767 miles

a

subtract(1200, 1096)

subtract(n1,n0)|

physics

a rectangular lawn of dimensions 120 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?

"number of days taken by ram to complete task = 18 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 18 days is 18 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 18 w / 3 w = 6 days answer d"

a ) 16 days , b ) 12 days , c ) 8 days , d ) 6 days , e ) 18 days

d

inverse(add(divide(const_1, 18), divide(const_1, divide(18, const_2))))

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

physics

if y > 0 , ( 2 y ) / 20 + ( 3 y ) / 10 is what percent of y ?

"external radius = 4 cm , internal radius = 3 cm . volume of iron = ( 22 / 7 x [ ( 4 ) ^ 2 - ( 3 ) ^ 2 ] x 21 ) cm ^ 3 ( 22 / 7 x 7 x 1 x 21 ) cm ^ 3 462 cm ^ 3 . weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg . answer b"

a ) 3.6 kg , b ) 3.696 kg , c ) 36 kg , d ) 36.9 kg , e ) 3.06 kg

b

divide(multiply(subtract(volume_cylinder(divide(8, const_2), 21), volume_cylinder(subtract(divide(8, const_2), 1), 21)), 8), const_1000)

divide(n1,const_2)|subtract(#0,n2)|volume_cylinder(#0,n0)|volume_cylinder(#1,n0)|subtract(#2,#3)|multiply(n1,#4)|divide(#5,const_1000)|

general

what is the length of the diagonal of a square whose area is 4 times of another square with diagonal as 5 v 2 cm ?

"total weight increases = 7 × 1.5 = 10.5 kg so the weight of new person = 65 + 10.5 = 75.5 kg answer c"

a ) 76 kg , b ) 77 kg , c ) 75.5 kg , d ) data inadequate , e ) none of these

c

add(65, multiply(7, 1.5))

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

general

three cubes of iron whose edges are 6 cm , 8 cm and 10 cm respectively are melted and formed into a single cube . the edge of the new cube formed is

explanation : let the initial amount be x , amount given to his wife = ( 40 / 100 ) x = 2 x / 5 balance = ( x - ( 2 x / 5 ) ) = 3 x / 5 amount given to his wife = ( 20 / 100 ) * ( 3 x / 5 ) = 3 x / 25 balance = 3 x / 5 - 3 x / 25 = 12 x / 25 amountt spent on miscellaneous items = ( 1 / 2 ) * ( 12 x / 25 ) = 6 x / 25 which is equal to 12000 hence , = > 6 x / 25 = 12000 = > x = 50000 answer : c

a ) 40000 , b ) 45000 , c ) 50000 , d ) 62000 , e ) none of these

c

divide(12000, multiply(divide(divide(const_100, const_2), const_100), multiply(subtract(const_1, divide(40, const_100)), subtract(const_1, divide(20, const_100)))))

divide(const_100,const_2)|divide(n0,const_100)|divide(n1,const_100)|divide(#0,const_100)|subtract(const_1,#1)|subtract(const_1,#2)|multiply(#4,#5)|multiply(#3,#6)|divide(n3,#7)

gain

the bus fare for two persons for travelling between agra and aligarh id 4 - thirds the train fare between the same places for one person . the total fare paid by 6 persons travelling by bus and 8 persons travelling by train between the two places is rs . 1512 . find the train fare between the two places for one person ?

"let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 170 + p c + m = 170 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 170 / 2 = 85 . answer : d"

a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95

d

divide(170, const_2)

divide(n0,const_2)|

general

the average age of 15 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . the age of the 15 th student is ?

"amount with ci = 10000 [ 1 + ( 12 / 2 * 100 ) ] 2 = rs . 11236 therefore , ci = 11236 – 10000 = rs . 1236 answer : b"

a ) rs . 1036 , b ) rs . 1236 , c ) rs . 1186 , d ) rs . 1206 , e ) rs . 1226

b

subtract(multiply(power(add(const_1, divide(divide(12, const_4), const_100)), const_3), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100))), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100)))

divide(n1,const_4)|multiply(const_4,const_4)|sqrt(const_100)|divide(#0,const_100)|multiply(#1,const_100)|add(#3,const_1)|multiply(#4,#2)|power(#5,const_3)|multiply(#6,#7)|subtract(#8,#6)|

gain

if an object travels 90 feet in 2 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )

22 * 200 = 4400 . the other 3 onions weigh a total of 720 grams . the average weight is 720 / 3 = 240 grams . the answer is c .

a ) 200 , b ) 220 , c ) 240 , d ) 260 , e ) 280

c

divide(subtract(multiply(5.12, const_1000), multiply(22, 200)), 3)

multiply(n1,const_1000)|multiply(n3,n4)|subtract(#0,#1)|divide(#2,n2)

general

4 dice are thrown simultaneously on the board . find the probability which show the same face ?

"a profit of rs . 600 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 360 and 240 . difference in profit share = 360 - 240 = 120 answer : b"

a ) s . 220 , b ) s . 120 , c ) s . 320 , d ) s . 50 , e ) s . 90

b

subtract(divide(divide(600, add(divide(1, 2), divide(1, 3))), 2), divide(divide(600, add(divide(1, 2), divide(1, 3))), 3))

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

general

john makes $ 40 a week from his job . he earns a raise and now makes $ 70 a week . what is the % increase ?

"let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 10 ) ( y + 10 ) = m and so ( 2 ) xy + 10 x + 10 y + 100 = m + 144 let ' s subtract equation ( 1 ) from equation ( 2 ) . 8 x + 8 y + 96 = 144 2 x + 2 y = 12 , which is the perimeter of the photograph . the answer is b ."

a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18

b

divide(subtract(144, subtract(power(multiply(5, const_2), const_2), power(multiply(1, const_2), const_2))), const_2)

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

geometry

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

total number of votes polled = ( 1000 + 2000 + 4000 ) = 7000 required percentage = 4000 / 7000 * 100 = 57 % ( approximately ) answer : option c

a ) 30 % , b ) 50 % , c ) 57 % , d ) 62 % , e ) 75 %

c

multiply(divide(4000, add(add(1000, 2000), 4000)), const_100)

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

general

if f ( x ) = 3 x ^ 4 - 4 x ^ 3 - 2 x ^ 2 + 6 x , then f ( - 1 ) =

s = ( 3 + 5 + 10 ) / 2 = 9 answer : d

a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 1

d

divide(add(add(3, 5), 10), 5)

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

geometry

if the perimeter of a rectangular garden is 600 m , its length when its breadth is 100 m is ?

"10 ( 11111 ) * 4 ! - 10 ( 1111 ) 3 ! = 2599980 answer : a"

a ) 2599980 , b ) 235500 , c ) 923580 , d ) 765432 , e ) 765434

a

multiply(divide(add(divide(subtract(subtract(const_1000, 5), add(add(multiply(multiply(5, 5), const_10), multiply(5, 5)), 5)), 1,2), const_1), 0), add(subtract(const_1000, 5), add(add(multiply(multiply(5, 5), const_10), multiply(5, 5)), 5)))

multiply(n0,n0)|subtract(const_1000,n0)|multiply(#0,const_10)|add(#2,#0)|add(n0,#3)|add(#4,#1)|subtract(#1,#4)|divide(#6,n2)|add(#7,const_1)|divide(#8,n1)|multiply(#5,#9)|

probability

6 persons in an organization including x and y were to be divided in two groups of 3 members each . the total number of groups containing both x and y is what fraction of the total number of groups which can be formed ?

"let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 64 ( x - y ) - - > x + y = 64 . answer : d ."

a ) 24 , b ) 26 , c ) 30 , d ) 64 , e ) 40

d

floor(64)

floor(n0)|

general

the height of a cylinder is 60 cm and the diameter of its base is 5 cm . the total surface area of the cylinder is

"alcohol in the 20 litres of mix . = 40 % of 20 litres = ( 40 * 20 / 100 ) = 8 litres water in it = 20 - 8 = 12 litres new quantity of mix . = 20 + 8 = 28 litres quantity of alcohol in it = 8 litres percentage of alcohol in new mix . = 8 * 100 / 28 = 50 / 3 = 28.57 % answer is c"

a ) 26.32 % , b ) 35.14 % , c ) 28.57 % , d ) 25 % , e ) 31.14 %

c

multiply(divide(subtract(add(20, 8), add(multiply(divide(subtract(const_100, 40), const_100), 20), 8)), add(20, 8)), const_100)

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

gain

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 60 people bought tickets to the concert , what was the total revenue from ticket sales ?

"we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional values the productivity in 1 st case is 0.5 bears / hour and in the 2 nd case it is 1 bear / hour hence the productivity is double with the assistant i . e . the increase in productivity is 120 % d"

a ) 20 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 200 %

d

multiply(divide(10, subtract(subtract(const_100, 90), 10)), const_100)

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

physics

what is the sum of all the odd numbers between 24 and 50 , inclusive ?

"= 12.036 / 0.04 = 1203.6 / 4 = 300.9 answer is b ."

a ) 30.09 , b ) 300.9 , c ) 30.06 , d ) 100.9 , e ) 300.6

b

divide(12.036, 0.04)

divide(n0,n1)|

general

the ratio of the volumes of two cubes is 343 : 512 . what is the ratio of their total surface areas ?

"the amount of chemical x in the solution is 20 + 0.05 ( 80 ) = 24 liters . 24 liters / 100 liters = 24 % the answer is a ."

a ) 24 % , b ) 26 % , c ) 28 % , d ) 30 % , e ) 32 %

a

add(20, multiply(divide(5, const_100), 80))

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

general

how many distinct prime numbers are factors of 33150 ?

"( 4.4 miles / 8 minutes ) * 60 minutes / hour = 33 mph let x be the original speed . x - 5 ( 3 ) = 33 x = 48 mph the answer is c ."

a ) 35 , b ) 40 , c ) 48 , d ) 51 , e ) 54

c

add(add(add(add(divide(4.4, divide(8, const_60)), 3), 3), 3), 3)

divide(n1,const_60)|divide(n2,#0)|add(n0,#1)|add(n0,#2)|add(n0,#3)|add(n0,#4)|

general

find the average of all prime numbers between 30 and 50

"a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean r = 74 . answer : a ."

a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82

a

divide(add(multiply(58, 3), multiply(98, 2)), add(2, 3))

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

general

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

"speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 240 = 600 meter time = distance / speed = 600 * ( 2 / 25 ) = 48 seconds answer : e"

a ) 65 seconds , b ) 46 seconds , c ) 40 seconds , d ) 97 seconds , e ) 48 seconds

e

divide(add(360, 240), divide(multiply(45, const_1000), const_3600))

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

physics

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

"x * 110 / 100 * 90 / 100 = 7920 x * 0.99 = 7920 x = 7920 / 0.99 = > 8000 answer : b"

a ) 8008 , b ) 8000 , c ) 8022 , d ) 8021 , e ) 8022

b

divide(divide(7920, subtract(const_1, divide(10, const_100))), add(const_1, divide(10, const_100)))

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

general

in a box of 11 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?

"let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 135 % of $ 640 = $ 864 d"

a ) $ 480 , b ) $ 450 , c ) $ 960 , d ) $ 864 , e ) $ 660

d

add(divide(multiply(divide(add(832, 448), const_2), 35), const_100), divide(add(832, 448), const_2))

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

gain

if annual decrease in the population of a town is 5 % and the present number of people is 40000 what will the population be in 2 years ?

"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 = 3720 * ( 6 / 31 ) = 120 * 6 = 720 . answer : option a"

a ) 720 , b ) 700 , c ) 800 , d ) 900 , e ) none of these

a

multiply(3720, 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

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

3 hrs 25 min = 205 min first 15 min - - - - - - > $ 2 time left is 190 min . . . now , 60 min costs $ 6 1 min costs $ 6 / 60 190 min costs $ 6 / 60 * 190 = > $ 19 so , total cost will be $ 19 + $ 2 = > $ 21 the answer will be ( d ) $ 21

a ) $ 22 , b ) $ 3 , c ) $ 15 , d ) $ 21 , e ) $ 30

d

add(multiply(divide(6, const_60), subtract(add(multiply(3, const_60), 25), 15)), 2)

divide(n3,const_60)|multiply(n4,const_60)|add(n5,#1)|subtract(#2,n1)|multiply(#0,#3)|add(n0,#4)

physics

machine a produces 100 parts thrice as fast as machine b does . machine b produces 100 parts in 30 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 6 minutes ?

"area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 30 = 25500 p in rs = 25500 / 100 = rs 255 answer : a"

a ) s 255 , b ) s 780 , c ) s 880 , d ) s 480 , e ) s 980

a

divide(multiply(subtract(multiply(110, 65), multiply(subtract(110, multiply(2.5, const_2)), subtract(65, multiply(2.5, const_2)))), 30), const_100)

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

physics

a certain galaxy is known to comprise approximately 5 x 10 ^ 11 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?

amount of work done by john and andrew in 1 day = 1 / 9 amount of work done by john and andrew in 6 days = 6 ã — ( 1 / 9 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 john completes 1 / 3 work in 6 days amount of work john can do in 1 day = ( 1 / 3 ) / 6 = 1 / 18 = > john can complete the work in 18 days answer : c

a ) 30 days , b ) 60 days , c ) 18 days , d ) 80 days , e ) 90 days

c

divide(6, subtract(const_1, divide(6, 9)))

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

physics

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

"the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 14.3 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . a"

a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %

a

multiply(multiply(divide(divide(divide(3, 7), 3), add(divide(divide(3, 7), 3), subtract(const_1, divide(3, 7)))), const_100), const_3)

divide(n1,n2)|divide(#0,n1)|subtract(const_1,#0)|add(#1,#2)|divide(#1,#3)|multiply(#4,const_100)|multiply(#5,const_3)|

general

consider a lady took a loan from a bank at the rate of 12 % p . a . simple interest . after 3 years she had to pay rs . 9900 interest only for the period . the principal amount borrowed by her was

"1 kg = 1000 gm 400 / 1000 ã — 100 = 40000 / 1000 = 40 % answer is b"

a ) 25 % , b ) 40 % , c ) 10 % , d ) 8 % , e ) 12 %

b

multiply(divide(400, 1), const_100)

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

gain

if a and b are positive integers , and a = 5 b + 20 , the greatest common divisor of a and b can not be

"explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 160 x + ( x - 160 ) = 208 2 x = 368 x = 184 runs answer : a"

a ) 184 , b ) 367 , c ) 269 , d ) 177 , e ) 191

a

divide(add(160, subtract(multiply(60, 46), multiply(58, subtract(46, const_2)))), const_2)

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

general

pipe a fills a tank in 42 minutes . pipe b can fill the same tank 6 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?

"explanation : given that a + b = 14 + b + c = > a ? c = 14 + b ? b = 14 = > c is younger than a by 14 years answer : option d"

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

d

multiply(14, const_1)

multiply(n0,const_1)|

general

p software has coding line 5 % more than n , n software has coding line 1 / 2 more than m . m software has 100 lines of coding . find p lines .

"price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 3500 net price of the car in 02 = 18700 + 3500 = $ 22200 correct option : c"

a ) $ 18,400 , b ) $ 19,500 , c ) $ 22,200 , d ) $ 20,400 , e ) $ 21,100

c

multiply(const_2, const_10)

multiply(const_10,const_2)|

gain

on a trip , a cyclist averaged 11 miles per hour for the first 22 miles and 10 miles per hour for the remaining 20 miles . if the cyclist returned immediately via the same route and took a total of 9 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?

l - b = 23 . . . ( 1 ) perimeter = 206 2 ( l = b ) = 206 l + b = 103 . . . ( 2 ) ( 1 ) + ( 2 ) 2 l = 23 + 103 = 126 l = 126 / 2 = 63 metre substituting the value of l in ( 1 ) , we get 63 - b = 23 b = 63 - 23 = 40 metre area = lb = 63 ã — 40 = 2520 m 2 answer : a

['a ) 2520', 'b ) 2510', 'c ) 2525', 'd ) 2025', 'e ) 2020']

a

rectangle_area(add(divide(subtract(206, multiply(const_2, 23)), const_4), 23), divide(subtract(206, multiply(const_2, 23)), const_4))

multiply(n0,const_2)|subtract(n1,#0)|divide(#1,const_4)|add(n0,#2)|rectangle_area(#3,#2)

geometry

george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 5 % of the money for taxi fare and buys 25 mangoes . how many oranges can he buy ?

"explanation : volume of water displaced = ( 5 x 2 x 0.01 ) m 3 = 0.10 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.10 x 1000 ) kg = 100 kg . answer : a"

a ) 100 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none of these

a

multiply(multiply(multiply(5, 2), divide(1, const_100)), const_1000)

divide(n2,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(#2,const_1000)|

physics

1394 x 1394

as 100 cats kill 100 mice in 100 days 1 cats kill 1 mouse in 100 days then 4 cats kill 4 mice in 100 days answer : d

a ) 1 day , b ) 4 days , c ) 40 days , d ) 100 days , e ) 50 days

d

divide(multiply(multiply(4, 100), 100), multiply(100, 4))

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

physics

positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 36 . what is the value of x ?

"unit digit in 7105 = unit digit in [ ( 74 ) 26 * 7 ] but , unit digit in ( 74 ) 26 = 1 unit digit in 7105 = ( 1 * 7 ) = 7 answer : c"

a ) 1 , b ) 5 , c ) 7 , d ) 9 , e ) 11

c

circle_area(divide(7105, multiply(const_2, const_pi)))

multiply(const_2,const_pi)|divide(n0,#0)|circle_area(#1)|

general

the ratio of the volumes of two cubes is 343 : 512 . what is the ratio of their total surface areas ?

total - neither = all air conditioning + all power windows - both or 55 - neither = 40 + 25 - 12 = 53 . = > neither = 2 , hence d . answer : d

a ) 15 , b ) 8 , c ) 10 , d ) 2 , e ) 18

d

subtract(55, subtract(add(40, 25), 12))

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

other

it takes 10 days for digging a trench of 100 m long , 50 m broad and 10 m deep . what length of trench , 25 m broad and 15 m deep can be dug in 30 days ?

"easiest way for me : 49 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 24 * 2 + 1 ) ^ 37 - ( 24 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : c"

a ) 2 , b ) 1 , c ) 0 , d ) 3 , e ) none of these

c

reminder(multiply(74, 49), 5)

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

general

the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 15 % profit ?

"d 4 % s . i . = ( 14400 - 13400 ) = 1000 . rate = ( 100 x 1000 ) / ( 13400 x 2 ) % = 4 %"

a ) 2 % , b ) 1 % , c ) 6 % , d ) 4 % , e ) 8 %

d

multiply(divide(divide(const_3, 2), add(multiply(const_3, 2), add(const_0_25, const_0_25))), const_100)

add(const_0_25,const_0_25)|divide(const_3,n2)|multiply(const_3,n2)|add(#0,#2)|divide(#1,#3)|multiply(#4,const_100)|

gain

if you write down all the numbers from 1 to 100 , then how many times do you write 1 ?

"p - 420 = ( p * 5 * 8 ) / 100 p = 700 the answer is c ."

a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900

c

divide(420, subtract(const_1, divide(multiply(5, 8), const_100)))

multiply(n0,n1)|divide(#0,const_100)|subtract(const_1,#1)|divide(n2,#2)|

gain

after 6 games , team b had an average of 65 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?

"explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 30 : : 18 : x [ please pay attention , we have written 27 : 30 rather than 30 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 30 \ times 18 } { 27 } } x = 20 so 20 days will be required to get work done by 27 men . answer : a"

a ) 20 , b ) 77 , c ) 36 , d ) 25 , e ) 13

a

divide(multiply(18, 30), 27)

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

physics

at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 400 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 200 ?

200 = 2 ^ 3 * 5 ^ 2 if 200 divides n ^ 2 , then n must be divisible by 2 ^ 2 * 5 = 20 the answer is c .

a ) 10 , b ) 15 , c ) 20 , d ) 36 , e ) 50

c

multiply(sqrt(divide(200, 2)), 2)

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

general

oil cans x and y are right circular cylinders and the height and radius of y are each 5 times those of x . if the oil in can x filled to capacity sells for $ 1 , how much does the oil in y sell for if y is only 1 / 5 th filled ?

a 100 % if the sum he paid whilst purchasing 20 pens = a , then the cost price of each pen = a / 20 . since the amount he got whilst selling 10 pens is also = a then the selling price of each pen = a / 10 . since selling price > cost price , he made a profit . profit per pen = selling price - cost price = a / 10 - a / 20 = a / 20 . profit percentage per pen = profit per pen / cost per pen x 100 = ( a / 20 ) / ( a / 20 ) x 100 = 100 %

a ) 100 % , b ) 150 % , c ) 90 % , d ) 80 % , e ) 95 %

a

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

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

gain

find a sum for first 8 prime numbers ?

"1 / 3 of sqrt ( x ) = 3 x , which means that sqrt ( x ) = 9 x or x = 81 x ^ 2 - > divide by x 1 = 81 x x = 1 / 81 c ."

a ) 1 / 3 , b ) 1 / 9 , c ) 1 / 81 , d ) 1 , e ) 81

c

power(3, multiply(3, const_3))

multiply(n1,const_3)|power(n1,#0)|

general

joe drives 240 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?

smallest number of six digits is 100000 . required number must be divisible by l . c . m . of 25,35 , 45,15 i . e 1575 , on dividing 100000 by 1575 , we get 800 as remainder . therefore , required number = 100000 + ( 1575 â € “ 800 ) = 100775 . answer is b .

a ) 100555 , b ) 100775 , c ) 100885 , d ) 100995 , e ) 100665

b

multiply(power(const_100, const_2), const_10)

power(const_100,const_2)|multiply(#0,const_10)

general

a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 24 , find the sum of money ?

"let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 21 s = ( 27 x + 17 y ) / ( x + y ) = 21 = ( 27 x + 17 y ) / = 21 ( x + y ) = 6 x = 4 y = x / y = 4 / 6 = 2 / 3 i . e 2 : 3 answer : c"

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

c

divide(subtract(27, 21), subtract(21, 17))

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

physics

25 is subtracted from 75.00001 % of a number , the result is 50 . find the number ?

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

multiply(divide(const_1, add(const_3, const_1)), const_100)

add(const_1,const_3)|divide(const_1,#0)|multiply(#1,const_100)

general

if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 4 other contributions made before john ' s , what is the size of his donation ?

"2 / 3 filled in 6 mint 1 / 3 filled in 3 mint thn 2 / 3 + 1 / 3 = 6 + 3 = 9 minutes answer : d"

a ) 90 seconds , b ) 70 seconds , c ) 60 seconds , d ) 9 minutes , e ) 120 seconds

d

multiply(divide(6, const_2), const_3)

divide(n0,const_2)|multiply(#0,const_3)|

physics

in a box of 11 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?

"let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 76 = 17 x or x = ( 76 – 48 ) = 28 . answer b"

a ) 36 , b ) 28 , c ) 42 , d ) 45 , e ) none of the above

b

add(subtract(76, multiply(17, 3)), 3)

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

general