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ericsun153
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mathqa_shuffle_question_test

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Rationale
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annotated_formula
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linear_formula
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of the 120 passengers on flight 750 , 60 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?
"answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are red and 40 % are blue . since we know that there are only three colors , the remaining 40 % must be green . 40 % blue of 10 % brass widgets leads to 4 % green brass widgets out of the total 10,550 widgets . 10,500 / 100 * 4 = 420 . answer d ."
a ) 480 , b ) 840 , c ) 1050 , d ) 420 , e ) 2100
d
multiply(multiply(multiply(multiply(divide(10, const_100), divide(40, const_100)), divide(add(10, const_2), 10)), const_100), const_100)
add(n1,const_2)|divide(n1,const_100)|divide(n3,const_100)|divide(#0,n1)|multiply(#1,#2)|multiply(#3,#4)|multiply(#5,const_100)|multiply(#6,const_100)|
gain
a box measuring 49 inches long by 21 inches wide by 14 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
"speed of the train relative to man = 250 / 20 m / sec = 25 / 2 m / sec . = 25 / 2 x 18 / 5 km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 10 ) km / hr . x - 10 = 45 = 55 km / hr . answer : c"
a ) 100 , b ) 60 , c ) 55 , d ) 50 , e ) 45
c
divide(divide(subtract(250, multiply(multiply(10, const_0_2778), 10)), 10), const_0_2778)
multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n1)|divide(#3,const_0_2778)|
physics
among the two clocks , clock a gains 20 seconds per minute . if clock a and b are set at 2 0 ' clock , when clock a is at 7 : 20 , what does clock b show ?
"solution start with 17 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 17 + 1 which is 9 , so you ' re left with 17 - 9 = 8 . peter takes 1 baseball card from you : 8 - 1 = 7 baseball cards . paul triples the number of baseball cards you have : 7 ã — 3 = 21 baseball cards . so you have 21 at the end . correct answer : e"
a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
e
multiply(subtract(subtract(subtract(17, const_4), const_4), 1), const_3)
subtract(n0,const_4)|subtract(#0,const_4)|subtract(#1,n1)|multiply(#2,const_3)|
general
tanks p and b are each in the shape of a right circular cylinder . the interior of tank p has a height of 10 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 p is what percent of the capacity of tank b ?
average = 2 ( 19000 ) + ( 21000 ) + 3 ( 22000 ) / 6 = $ 20,833 the answer is c .
a ) $ 20,200 , b ) $ 20,500 , c ) $ 20,800 , d ) $ 21,000 , e ) $ 21,400
c
divide(divide(add(multiply(22000, 3), add(multiply(19000, 2), 21000)), const_1000), 6)
multiply(n1,n2)|multiply(n5,n6)|add(n3,#0)|add(#2,#1)|divide(#3,const_1000)|divide(#4,n0)
general
a scuba diver descends at a rate of 40 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 3000 feet below the sea level . . how long will he take to reach the ship ?
"total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 15 = 16 * 15 = 240 $ total charge = 126 + 240 = 366 $ answer a"
a ) $ 336 , b ) $ 289 , c ) $ 282 , d ) $ 274 , e ) $ 286
a
add(multiply(18.00, add(const_3, const_4)), multiply(15.00, subtract(23, add(const_3, const_4))))
add(const_3,const_4)|multiply(n0,#0)|subtract(n2,#0)|multiply(n1,#2)|add(#1,#3)|
general
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 ?
"other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . ans : a"
a ) 120 , b ) 147 , c ) 251 , d ) 451 , e ) 258
a
rectangle_area(15, sqrt(subtract(power(17, const_2), power(15, const_2))))
power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)|sqrt(#2)|rectangle_area(n0,#3)|
geometry
in a lottery there are 100 prizes and 300 blanks . a lottery is drawn at random . what is the probability of getting a prize ?
after the reservoir is filled to 75 gallons the amount of water is at 37.5 % - which means that 62.5 % of the reservoir is empty . to figure out what that 62.5 % is approximate : 75 gallons / 37.5 percent = x gallons / 62.5 percent , therefore , x = 125 gallons , answer choices a , b , c , d are below 125 . we know that the reservoir must be short more than 125 gallons , therefore , the only possible choice is e .
a ) 90 , b ) 114 , c ) 124 , d ) 120 , e ) 127
e
divide(divide(multiply(75, const_100), 37.5), const_2)
multiply(n1,const_100)|divide(#0,n2)|divide(#1,const_2)|
general
a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 44000 . what is the share of c ?
first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that t increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , t will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c
a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84
c
add(multiply(subtract(24, 6), divide(subtract(100, 60), subtract(60, 30))), 24)
subtract(n4,n3)|subtract(n3,n2)|subtract(n1,n0)|divide(#0,#1)|multiply(#3,#2)|add(n1,#4)
general
excluding stoppages , the speed of a bus is 80 km / hr and including stoppages , it is 70 km / hr . for how many minutes does the bus stop per hour ?
let the numbers be x and ( 184 - x ) . then , ( x / 3 ) - ( 184 - x ) / 7 = 8 7 x - 3 ( 184 - x ) = 168 10 x = 720 , x = 72 . hence the correct answer is option a ) 72 .
a ) 72 , b ) 64 , c ) 84 , d ) 12 , e ) 92
a
divide(add(multiply(184, const_3), multiply(multiply(add(const_3, const_4), const_3), 8)), add(add(const_3, const_4), const_3))
add(const_3,const_4)|multiply(n0,const_3)|add(#0,const_3)|multiply(#0,const_3)|multiply(n1,#3)|add(#1,#4)|divide(#5,#2)
general
a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 28 adults have their meal , find the total number of children that can be catered with the remaining food .
"my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : q = 2550 + ( 100 * 50 ) = 7550 . b"
a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
b
multiply(divide(add(200, 102), const_2), add(divide(subtract(200, 102), const_2), const_1))
add(n2,n3)|subtract(n3,n2)|divide(#1,const_2)|divide(#0,const_2)|add(#2,const_1)|multiply(#4,#3)|
general
a man bought 20 shares of rs . 50 at 5 discount , the rate of dividend being 13 . the rate of interest obtained is :
explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 15 * 20 / 100 = 3 answer : option d
a ) 4 , b ) 5 , c ) 2 , d ) 3 , e ) 1
d
multiply(divide(20, const_100), 15)
divide(n1,const_100)|multiply(n0,#0)|
gain
the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 216 sq . cm , what is the width of the rectangle ?
let y gets rs x . then we can say x gets rs ( x + 20 ) and y gets rs ( x + 35 ) . x + 20 + x + x + 35 = 385 3 x = 330 x = 110 . r ’ s share = rs ( 110 + 35 ) = rs . 145 b
a ) rs . 130 , b ) rs . 145 , c ) rs . 154 , d ) rs . 160 , e ) rs . 164
b
add(15, add(divide(subtract(385, add(15, add(20, 20))), const_3), 20))
add(n1,n1)|add(n2,#0)|subtract(n0,#1)|divide(#2,const_3)|add(n1,#3)|add(n2,#4)
general
uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 16 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
case 1 n = 5,8 , 11,14 , 17,20 case 2 m = 5 , 9,13 , 17,21 therefore n = 17 remainder of 17 / 16 will be 1 a
a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2
a
floor(divide(add(add(const_12, const_3), add(const_2, const_4)), 16))
add(const_12,const_3)|add(const_2,const_4)|add(#0,#1)|divide(#2,n4)|floor(#3)
general
26 : 62 : : 32 : ?
"original number of men = 8 * 28 / ( 28 - 20 ) = 28 answer is b"
a ) 60 , b ) 28 , c ) 40 , d ) 50 , e ) 25
b
divide(multiply(8, 28), subtract(28, 20))
multiply(n1,n2)|subtract(n2,n0)|divide(#0,#1)|
physics
danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 1536 , what is the area of the side face of the box ?
"280 - 180 = 100 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 100 - 36 = 64 sq m of the wallpaper overlaps in three layers . 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m . answer ( b ) ."
a ) 5 square meters , b ) 32 square meters , c ) 42 square meters , d ) 83.3 square meters , e ) 120 square meters
b
divide(subtract(subtract(280, 180), 36), const_2)
subtract(n0,n1)|subtract(#0,n2)|divide(#1,const_2)|
geometry
find the sum of first 70 odd numbers
explanation : numbers from 1 to 60 , which are divisible by 6 are : 6 , 1218 , 24 , 30 , 3642 , 48 , 54 , 60 . there are 10 such numbers . numbers from 1 to 60 , the sum of whose digits is 6 are : 6 , 15 , 24 , 33 , 42 , 51 , 60 . there are 7 such numbers of which 4 are common to the above ones . so , there are 3 such uncommon numbers . numbers from 1 to 60 , which have 6 as one of the digits are 6 , 16 , 26 , 36 , 46 , 56 , 60 . clearly , there are 4 such uncommon numbers . so , numbers ' not connected with 6 ' = 60 - ( 10 + 3 + 4 ) = 43 . answer : d
a ) 18 , b ) 22 , c ) 42 , d ) 43 , e ) 45
d
subtract(60, add(add(const_10, const_3), const_4))
add(const_10,const_3)|add(#0,const_4)|subtract(n6,#1)
general
if taxi fares were $ 2.00 for the first 1 / 5 mile and $ 0.40 for each 1 / 5 mile there after , then the taxi fare for a 4 - mile ride was
"cost of kit = $ 67.50 if filters are purchased individually - $ 7.45 * 2 + $ 10.05 * 2 + $ 14.50 = $ 49.50 amount saved = $ 67.50 - $ 49.50 = $ 18 required % age = ( $ 18 / $ 67.50 ) * 100 = 26.66 % so , the correct answer is b ."
a ) 25.66 % , b ) 26.66 % , c ) 27.66 % , d ) 28.66 % , e ) 29.66 %
b
divide(multiply(subtract(67.50, add(14.50, add(multiply(2, 7.45), multiply(2, 10.05)))), const_100), 67.50)
multiply(n2,n3)|multiply(n2,n5)|add(#0,#1)|add(n7,#2)|subtract(n1,#3)|multiply(#4,const_100)|divide(#5,n1)|
general
what is difference between biggest and smallest fraction among 1 / 3 , 3 / 4 , 4 / 5 and 5 / 6
"largest 4 - digit number = 9999 90 ) 9999 ( 111 9990 - - - - - - - - - - - - largest number divisible by 90 is 9990 answer : e"
a ) 9935 , b ) 9939 , c ) 9944 , d ) 9954 , e ) 9990
e
square_area(const_pi)
square_area(const_pi)|
general
company a imported 10,500 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 10 percent of the widgets are made of brass and of those 20 percent are painted red and 40 percent are painted blue how many brass widgets painted green were imported ?
20 ! = 1 * 2 * 3 * 4 * 5 . . . * 19 * 20 ( this is 20 factorial written as 20 ! ) n = 1 * 2 * 3 * 4 * 5 * 6 * 7 . . . . . * 19 * 20 how many 2 s are there in n ? one 2 from 2 two 2 s from 4 one two from 6 three 2 s from 8 and so on . . . when you count them all , you get 18 . answer : d
a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
d
add(add(add(divide(20, 2), divide(20, power(2, const_2))), floor(divide(20, power(power(2, const_2), 2)))), floor(divide(20, power(2, const_3))))
divide(n1,n2)|power(n2,const_2)|power(n2,const_3)|divide(n1,#1)|divide(n1,#2)|power(#1,n2)|add(#0,#3)|divide(n1,#5)|floor(#4)|floor(#7)|add(#6,#9)|add(#10,#8)
general
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
"explanation : let the journey be x km then , 1 x / 2 + 1 x / 4 + 4 = x 3 x + 16 = 4 x x = 16 km answer : option b"
a ) 18 km , b ) 16 km , c ) 12 km , d ) 24 km , e ) 25 km
b
multiply(4, 4)
multiply(n3,n4)|
general
the population of a town increased from 1 , 34,800 to 2 , 42,500 in a decade . the average percent increase of population per year is :
"explanation : since every third number starting from 10 will be divisible by 3 , so total number of numbers divisible by 3 are 90 / 3 = 30 numbers which are divisible by 3 and 5 both are numbers which are multiple of 15 . for the range 10 to 99 , 15 is the first number divisible by 15 and 90 is the last number . so total number of numbers divisible by 15 are : ( 90 - 15 ) / 15 + 1 = 5 + 1 = 6 number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6 . so number of numbers divisible by 3 and not by 5 are : 30 - 6 = 24 so total probability = 24 / 90 = 4 / 15 answer : c"
a ) 1 / 15 , b ) 2 / 15 , c ) 4 / 15 , d ) 7 / 15 , e ) none of these
c
divide(subtract(multiply(multiply(5, const_2), 3), multiply(3, const_2)), multiply(multiply(5, const_2), multiply(3, 3)))
multiply(n1,const_2)|multiply(n0,const_2)|multiply(n0,n0)|multiply(n0,#0)|multiply(#0,#2)|subtract(#3,#1)|divide(#5,#4)|
probability
jim ’ s taxi service charges an initial fee of $ 2.45 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
"given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 21 % ( 700 ) = rs . 147 answer : e"
a ) 2287 , b ) 140 , c ) 128 , d ) 797 , e ) 147
e
multiply(subtract(divide(300, divide(30, const_100)), 300), divide(21, const_100))
divide(n1,const_100)|divide(n0,const_100)|divide(n2,#1)|subtract(#2,n2)|multiply(#0,#3)|
gain
the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 13 and 31 inclusive .
"45 workers * 8 hours / 30 meters = x * 6 / 35 x = 70 total workers 70 - 45 = 30 new workers the answer is c ."
a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
c
subtract(multiply(multiply(45, divide(8, 6)), divide(35, 30)), 45)
divide(n3,n2)|divide(n1,n4)|multiply(n0,#1)|multiply(#0,#2)|subtract(#3,n0)|
physics
evaluate : 60 - 12 * 3 * 2 = ?
"lots of ways to tackle this . 25 % of 180 = 45 1 / 3 of 45 = 15 so , 1 / 3 less than 45 is equal to 45 - 15 = 30 answer : b"
a ) 15 , b ) 30 , c ) 35 , d ) 40 , e ) 45
b
subtract(multiply(divide(25, const_100), 180), multiply(divide(const_1, const_3), multiply(divide(25, const_100), 180)))
divide(n0,const_100)|divide(const_1,const_3)|multiply(n1,#0)|multiply(#1,#2)|subtract(#2,#3)|
general
a salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100 . if the sale price of each machine was $ 10,000 and the salesperson received a $ 32,000 commission , how many machines did she sell ?
"if an object travels at 8 feet per second it covers 8 x 60 feet in one minute , and 8 x 60 x 45 feet in forty five minutes . answer = 21600 answer : c"
a ) 18000 , b ) 24000 , c ) 21600 , d ) 18000 , e ) 22000
c
multiply(multiply(const_3, const_60), const_60)
multiply(const_3,const_60)|multiply(#0,const_60)|
physics
in a particular state , 60 % of the counties received some rain on monday , and 65 % of the counties received some rain on tuesday . no rain fell either day in 25 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?
explanation : let arun ’ s weight by x kg . according to arun , 65 < x < 72 according to arun ’ s brother , 60 < x < 70 . according to arun ’ s mother , x < = 68 the values satisfying all the above conditions are 66 , 67 and 68 . required average = [ 66 + 67 + 68 / 3 ] = [ 201 / 3 ] = 67 kg answer b
a ) 66 kg , b ) 67 kg , c ) 68 kg , d ) 69 kg , e ) none of these
b
divide(add(add(subtract(68, const_1), subtract(subtract(68, const_1), const_1)), 68), const_3)
subtract(n4,const_1)|subtract(#0,const_1)|add(#0,#1)|add(n4,#2)|divide(#3,const_3)
general
8597 - ? = 7429 - 4358
approach 1 at - least 1 paper back = total - no paper back 8 c 4 - 5 c 4 = 65 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 3 c 1 * 5 c 3 + 3 c 2 * 5 c 2 + 3 c 3 * 5 c 1 = 65 answer is e
a ) a ) 40 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 65
e
subtract(choose(8, 4), choose(5, 4))
choose(n0,n3)|choose(n2,n3)|subtract(#0,#1)
probability
the l . c . m . of 2 numbers is 72 . the numbers are in the ratio 2 : 3 . find their sum ?
"sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 500 â ‡ ” 20 / 100 x = 500 â ‡ ” x = 500 ã — 5 = 2500 . answer a"
a ) rs . 2500 , b ) rs . 3500 , c ) rs . 1500 , d ) rs . 500 , e ) rs . 2000
a
multiply(500, add(const_4, const_1))
add(const_1,const_4)|multiply(n4,#0)|
gain
the amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5 . if they worked a combined total of 128 hours , how many hours did the secretary who worked the longest spend on the project ?
"given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 418 = 242 answer : c"
a ) 152 , b ) 209 , c ) 242 , d ) 171 , e ) 181
c
multiply(multiply(8, subtract(11, 8)), 11)
subtract(n2,n1)|multiply(n1,#0)|multiply(n2,#1)|
other
16.02 ã — 0.1 = ?
"total salary = rs . 15000 / - borrowed money = 7280 / - balance salary = 15000 - 7280 = 7720 paid amount = 18500 / - incentive amount = 18500 - 7720 = 10780 / - answer is c"
a ) 9500 , b ) 12500 , c ) 10780 , d ) 10500 , e ) 8600
c
subtract(18500, 7280)
subtract(n2,n1)|
general
the owner of a furniture shop charges his customer 42 % more than the cost price . if a customer paid rs . 8300 for a computer table , then what was the cost price of the computer table ?
"3 : 4 = x : 200 4 x = 3 * 400 x = 300 answer : d"
a ) 130 , b ) 100 , c ) 200 , d ) 300 , e ) 120
d
multiply(400, 3)
multiply(n0,n2)|
other
the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 65.0 . what is the quiz score of the student who dropped the class ?
one man can consume the same food in 40 * 20 = 800 days . 10 more men join , the total number of men = 50 the number of days the food will last = 800 / 50 = 16 days . answer : d
a ) 22 days , b ) 30 days , c ) 23 days , d ) 16 days , e ) 17 days
d
divide(multiply(40, 20), add(40, 10))
add(n0,n2)|multiply(n0,n1)|divide(#1,#0)
physics
if it takes a tub 5 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ?
"original price = 100 cp = 70 s = 70 * ( 150 / 100 ) = 105 100 - 105 = 5 % answer : e"
a ) 7 % , b ) 62 % , c ) 12 % , d ) 19 % , e ) 5 %
e
multiply(subtract(divide(divide(multiply(subtract(const_100, 30), add(const_100, 50)), const_100), const_100), const_1), const_100)
add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|divide(#3,const_100)|subtract(#4,const_1)|multiply(#5,const_100)|
gain
three unbiased coins are tossed . what is the probability of getting 3 heads and 1 tail ?
"explanation : number of cubes = ( 20 x 20 x 20 ) / ( 5 x 5 x 5 ) = 64 answer : b"
a ) 36 , b ) 64 , c ) 216 , d ) 484 , e ) none of these
b
divide(volume_cube(20), volume_cube(divide(5, const_100)))
divide(n0,const_100)|volume_cube(n1)|volume_cube(#0)|divide(#1,#2)|
probability
if x / 4 years ago roger was 14 years old and x / 4 years from now he will be 4 x years old , how old will he be 3 x years from now ?
"this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 450 pounds . we sum the two variables to obtain : f + s = 450 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 450 3 f = 750 f = 250 answer is a ."
a ) 250 , b ) 275 , c ) 325 , d ) 350 , e ) 400
a
divide(add(450, 300), const_3)
add(n0,n1)|divide(#0,const_3)|
general
in a certain pond , 80 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
"the total number of books is 150 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 108 books , thus the number of un - returned books is 150 - 108 = 42 books . 0.35 x = 42 x = 120 the answer is e ."
a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
e
divide(subtract(150, 108), subtract(const_1, divide(65, const_100)))
divide(n1,const_100)|subtract(n0,n2)|subtract(const_1,#0)|divide(#1,#2)|
gain
arun is travelling on his cycle and has calculated to reach point a at 2 pm if he travels at 10 kmph . he will reach there at 12 noon if he travels at 15 kmph . at what speed must he travel to reach a at 1 pm ?
distance travelled by ramu = 45 * 4 = 180 km somu travelled the same distance in 6 hours . his speed = 180 / 6 = 30 km / hr hence in the conditional case , ramu ' s speed = 45 - 9 = 36 km / hr and somu ' s speed = 30 + 10 = 40 km / hr . therefore travel time of ramu and somu would be 5 hours and 4.5 hours respectively . hence difference in the time taken = 0.5 hours = 30 minutes . answer : b
a ) 23 minutes , b ) 30 minutes , c ) 43 minutes , d ) 23 minutes , e ) 33 minutes
b
multiply(subtract(divide(multiply(45, 4), subtract(45, 9)), divide(multiply(45, 4), add(divide(multiply(45, 4), 6), 10))), const_60)
multiply(n0,n1)|subtract(n0,n3)|divide(#0,#1)|divide(#0,n2)|add(n4,#3)|divide(#0,#4)|subtract(#2,#5)|multiply(#6,const_60)
general
what least number should be added to 1022 , so that the sum is completely divisible by 25 ?
"explanation : given : 240 * 80 / 60 + 40 / 10 = ? substituting the coded symbols for mathematical operations , we get , 240 / 80 - 60 * 40 - 10 = ? 3 - 2400 - 10 = - 2407 answer : b"
a ) - 2305 , b ) - 2407 , c ) 2509 , d ) - 2101 , e ) none of these
b
add(multiply(divide(60, 40), divide(240, 80)), 10)
divide(n2,n3)|divide(n0,n1)|multiply(#0,#1)|add(n4,#2)|
general
a merchant marks his goods up by 30 % and then offers a discount of 20 % on the marked price . what % profit does the merchant make after the discount ?
"4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 6 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : c ."
a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
c
subtract(multiply(const_4.0, 12), 42.00)
multiply(const_4.0,n2)|subtract(#0,n3)|
general
due to construction , the speed limit along an 5 - mile section of highway is reduced from 60 miles per hour to 40 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 ?
"let the numbers be 2 x and 3 x . then , their l . c . m = 6 x . so , 6 x = 48 or x = 8 . the numbers are 16 and 24 . hence , required sum = ( 16 + 24 ) = 40 . answer : c"
a ) 28 , b ) 30 , c ) 40 , d ) 50 , e ) 60
c
divide(multiply(2, 48), 3)
multiply(n0,n1)|divide(#0,n2)|
other
what is the angle between the minute and the hour hand of the clock which shows 12 : 24 ?
let the side of the square be x m . ∴ perimeter of the square = 48 × 2 = 4 x ∴ x = 24 m ∴ area = ( 24 ) 2 = 576 m 2 answer d
['a ) 133 cm 2', 'b ) 276 cm 2', 'c ) 2500 cm 2', 'd ) 576 cm 2', 'e ) none of these']
d
square_area(divide(48, 2))
divide(n0,n1)|square_area(#0)
physics
the denominator of a fraction is 6 greater than the numerator . if the numerator and the denominator are increased by 1 , the resulting fraction is equal to 4 ⠁ „ 5 . what is the value of the original fraction ?
area of a parallelogram = base * height = 20 * 10 = 200 cm 2 answer : e
['a ) 290 cm 2', 'b ) 380 cm 2', 'c ) 270 cm 2', 'd ) 280 cm 2', 'e ) 200 cm 2']
e
multiply(20, 10)
multiply(n0,n1)
geometry
of the 14,210 employees of the anvil factory , 3 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
"in 84 liters of drink a , there are 48 liters of milk and 36 liters of juice . with 48 liters of milk , we need a total of 64 liters of juice to make drink b . we need to add 28 liters of juice . the answer is b ."
a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
b
subtract(divide(multiply(multiply(divide(4, add(4, 3)), 84), 4), 3), multiply(divide(3, add(4, 3)), 84))
add(n0,n1)|divide(n0,#0)|divide(n1,#0)|multiply(n4,#1)|multiply(n4,#2)|multiply(n0,#3)|divide(#5,n1)|subtract(#6,#4)|
general
√ 4 percent of 4 √ 4 =
"explanation : convert first all terms into cm . i . e . 1265 cm , 1525 cm , 1065 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 5 . option b"
a ) 45 cm , b ) 5 cm , c ) 4 cm , d ) 15 cm , e ) 50 cm
b
floor(divide(add(multiply(12, const_100), 65), add(multiply(15, const_100), 25)))
multiply(n0,const_100)|multiply(n2,const_100)|add(n1,#0)|add(n3,#1)|divide(#2,#3)|floor(#4)|
physics
how long does a train 120 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?
"we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result r will be 8 - 5 = 3 and answer b"
a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
b
subtract(5, 2)
subtract(n1,n0)|
general
a sum of money deposited at c . i . amounts to rs . 500 in 3 years and to rs . 650 in 4 years . find the rate percent ?
"sol . let the number of grils be x . then , number of boys = ( 620 - x ) . then , ( 11 3 / 4 × 620 ) ⇔ 11 x + 12 ( 620 - x ) ⇔ x = 7440 - 7285 ⇔ 155 . answer c"
a ) 150 , b ) 200 , c ) 155 , d ) 350 , e ) none
c
subtract(multiply(12, 620), multiply(add(11, divide(9, 12)), 620))
divide(n4,n1)|multiply(n0,n1)|add(n2,#0)|multiply(n0,#2)|subtract(#1,#3)|
general
excluding stoppages , the speed of a bus is 80 km / hr and including stoppages , it is 70 km / hr . for how many minutes does the bus stop per hour ?
"relative speed = 60 + 90 = 150 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 150 hr = 1 / / 75 hr = 3600 / 75 seconds = 1200 / 25 = 240 / 5 = 48 seconds answer is e ."
a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
e
multiply(divide(add(1.10, 0.9), add(60, 90)), const_3600)
add(n2,n3)|add(n0,n1)|divide(#0,#1)|multiply(#2,const_3600)|
physics
john paid a sum of money for purchasing 20 pens , which he recovered in full when he sold 10 of them . what was his percentage of profit or loss per pen ?
clearly , the two will meet when they are 1000 m apart to be 20 + 14 = 34 km apart , they take 1 hour to be 1000 m apart , they take 34 * 1000 / 1000 = 34 min . answer is c
a ) 50 min , b ) 40 min , c ) 34 min , d ) 25 min , e ) 20 min
c
add(20, 14)
add(n1,n2)
general
each of the integers from 1 to 17 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?
"sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 90 * 80 / ( 90 - 80 ) = rs . 720 . answer c"
a ) 1360 , b ) 1450 , c ) 720 , d ) 1800 , e ) none
c
divide(multiply(90, 80), subtract(90, 80))
multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)|
gain
the sector of a circle has radius of 14 cm and central angle 135 o . find its perimeter ?
"explanation : 2 x 3 x 5 x 2 x 2 = 120 answer : option c"
a ) 140 , b ) 160 , c ) 120 , d ) 150 , e ) 250
c
multiply(multiply(power(const_3, const_3), multiply(power(const_2, const_3), power(add(const_4, const_1), const_2))), divide(divide(divide(divide(divide(24, const_2), const_2), const_3), add(const_4, const_1)), add(const_4, const_1)))
add(const_1,const_4)|divide(n2,const_2)|power(const_2,const_3)|power(const_3,const_3)|divide(#1,const_2)|power(#0,const_2)|divide(#4,const_3)|multiply(#2,#5)|divide(#6,#0)|multiply(#7,#3)|divide(#8,#0)|multiply(#10,#9)|
physics
a clock shows the time as 9 a . m . if the minute hand gains 6 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
speed = 4.5 * 5 / 18 = 1.25 m / sec time taken = 750 / 1.25 = 600 sec ie . 10 mins . answer : c
a ) 5 , b ) 30 , c ) 10 , d ) 12 , e ) 15
c
multiply(divide(divide(750, const_1000), 4.5), const_60)
divide(n1,const_1000)|divide(#0,n0)|multiply(#1,const_60)
physics
if x / y = 7 / 4 , then ( x + y ) / ( x - y ) = ?
x ^ 2 + 2 x - 24 = ( x + 6 ) ( x - 4 ) = 0 then x = - 6 or x = 4 . x ^ 2 - 5 x + 4 = ( x - 4 ) ( x - 1 ) = 0 then x = 4 or x = 1 . thus x = 4 . the answer is a .
a ) 4 , b ) - 4 , c ) - 3 , d ) - 6 , e ) 1
a
divide(add(4, 24), add(2, 5))
add(n2,n6)|add(n0,n5)|divide(#0,#1)
general
the sector of a circle has radius of 14 cm and central angle 108 o . find its perimeter ?
sol . since the month begins with a sunday , so there will be five sundays in the month . ∴ required average = [ 510 x 5 + 240 x 25 / 30 ] = 8550 / 30 = 285 answer d
a ) 250 , b ) 276 , c ) 280 , d ) 285 , e ) none
d
divide(add(multiply(add(const_4, const_1), 510), multiply(multiply(add(const_4, const_1), add(const_4, const_1)), 240)), 30)
add(const_1,const_4)|multiply(n0,#0)|multiply(#0,#0)|multiply(n1,#2)|add(#1,#3)|divide(#4,n2)
general
a cat leaps 5 leaps for every 4 leaps of a dog , but 2 leaps of the dog are equal to 3 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?
pony take 20 hours and horse take 12 hours . . . then distance chased by them is 320 * 12 . so speed of pony is ( 320 * 12 ) / 20 = 192 kmph . answer is b
a ) 182 kmph , b ) 192 kmph , c ) 193 kmph , d ) 196 kmph , e ) 190 kmph
b
divide(multiply(12, 320), add(12, 8))
add(n0,n1)|multiply(n1,n2)|divide(#1,#0)
physics
in right triangle abc , ac is the hypotenuse . if ac is 40 and ab + bc = 60 , what is the area of the triangle abc ?
"ratio of the capitals of a , b and c = 10000 ã — 6 + 5000 ã — 6 : 10000 ã — 6 + 6000 ã — 6 : 10000 ã — 6 + 16000 ã — 6 = 90000 : 96000 : 156000 = 90 : 96 : 156 b â € ™ s share = ( 34200 ã — 96 ⠁ „ 342 ) = 9600 answer a"
a ) 9,600 , b ) 21,200 , c ) 28,200 , d ) 20,500 , e ) none of these
a
divide(add(multiply(subtract(const_12, 6), 4000), multiply(multiply(const_2, multiply(const_100, const_100)), 6)), multiply(const_100, const_10))
multiply(const_100,const_100)|multiply(const_10,const_100)|subtract(const_12,n1)|multiply(n3,#2)|multiply(#0,const_2)|multiply(n1,#4)|add(#3,#5)|divide(#6,#1)|
gain
if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 6 ?
"let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.10 x = 50 x = 39.52 hence , the correct option is a"
a ) 39.52 $ , b ) 40.63 $ , c ) 41.63 $ , d ) 42.15 $ , e ) 41.15 $
a
divide(50, add(divide(add(10, 15), const_100), const_1))
add(n1,n2)|divide(#0,const_100)|add(#1,const_1)|divide(n0,#2)|
general
a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 51.84 , the number of the member is the group is :
"explanation : distance = ( 300 x 6 ) = 1800 km . speed = distance / time speed = 1800 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 1800 x 3 / 5 km / hr = 1080 km / hr . answer : option c"
a ) 1008 kmph , b ) 760 kmph , c ) 1080 kmph , d ) 1070 kmph , e ) none
c
divide(divide(multiply(300, 6), add(const_1, divide(const_2, const_3))), const_2)
divide(const_2,const_3)|multiply(n0,n1)|add(#0,const_1)|divide(#1,#2)|divide(#3,const_2)|
physics
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 ?
"surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 150 / 2 = 75 answer is d"
a ) 10 , b ) 25 , c ) 50 , d ) 75 , e ) 100
d
divide(150, const_2)
divide(n0,const_2)|
general
calculate the area of a triangle , if the sides of are 52 cm , 48 cm and 20 cm , what is its area ?
"let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 25 = = > 27 x + 17 y = 25 x + 25 y = = > 2 x = 8 y = = > x / y = 4 / 1 . answer : b"
a ) 3 / 1 , b ) 4 / 1 , c ) 3 / 3 , d ) 3 / 5 , e ) 5 / 2
b
divide(subtract(27, 25), subtract(25, 17))
subtract(n0,n2)|subtract(n2,n1)|divide(#0,#1)|
physics
the wages earned by robin is 40 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
"concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 15 ) / ( 15 - 0 ) = 3 / 1 1 / x = 3 / 1 x = 1 / 3 answer : b"
a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
b
divide(15, subtract(60, 15))
subtract(n0,n1)|divide(n1,#0)|
gain
in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 5 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight
"4 miles on the highway = 4 / 32 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 32 + 4 / 20 = 13 / 40 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 13 / 40 - 8 / 32 ) / ( 8 / 32 ) = 0.30 . answer : e ."
a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 30 %
e
multiply(divide(subtract(add(multiply(divide(const_1, 20), 4), multiply(4, divide(const_1, 32))), multiply(8, divide(const_1, 32))), multiply(8, divide(const_1, 32))), const_100)
divide(const_1,n1)|divide(const_1,n0)|multiply(n2,#0)|multiply(n2,#1)|multiply(n4,#1)|add(#2,#3)|subtract(#5,#4)|divide(#6,#4)|multiply(#7,const_100)|
general
the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 66 kmph ?
let p be the original price paid by the retailer . 1.25 * p = 100 p = 80 the profit is $ 20 . the answer is c .
a ) $ 10 , b ) $ 16 , c ) $ 20 , d ) $ 24 , e ) $ 25
c
subtract(100, multiply(divide(const_1, add(divide(25, 100), const_1)), 100))
divide(n1,n0)|add(#0,const_1)|divide(const_1,#1)|multiply(n0,#2)|subtract(n0,#3)
gain
a garrison of 500 men has provisions for 20 days . at the end of 14 days , a reinforcement arrives , and it is now found that the provisions will last only for 3 days more . what is the reinforcement ?
easy way to solve this question is start from the answer and then conform the information provided in the question . we can start from option d i . e 20 . . . as a quantity of juice p in x because it is the only one option that gets divided by 4 is 20 . . . since in the x the juice p to t ratio is 4 : 1 this gives us that quantity of juice p in x = 20 therefore quantity of juice t will be 5 . . . hence ratio = 4 : 1 this will lead to quantity of juice p in x = 4 and quantity of juice t = 20 . . . hence ratio 1 : 5 if we calculate total juice p = 24 and total of juice v = 25 it fits because totals are same as what mentioned in the question . . . thus ans is d
a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
d
subtract(24, divide(subtract(multiply(4, 25), 24), subtract(multiply(4, 5), 1)))
multiply(n1,n2)|multiply(n2,n5)|subtract(#0,n0)|subtract(#1,n3)|divide(#2,#3)|subtract(n0,#4)
other
by selling 22 pens for a rupee a woman loses 10 % . how many for a rupee should he sell in order to gain 50 % ?
{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 75 - { both correctly } + 15 { both correctly } = 75 . answer : d .
a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
d
subtract(add(add(85, 75), 15), const_100)
add(n0,n1)|add(n2,#0)|subtract(#1,const_100)
other
if a lends rs . 1200 to b at 10 % per annum and b lends the same sum to c at 18 % per annum then the gain of b in a period of 2 years is ?
"let the number of students in class a be = x 1 + x 2 + . . . . . . + a 1 ( where a 1 = remaining students ) now the remaining avg of the students be a 1 / t = 60 a 1 = 60 t ( we are not sure on the number of students , assuming it as t ) . a = x 1 + x 2 + . . . . . . + a 1 ( first set of students + remaining students ) . one third of a students avg is 60 . a / 3 = 69 = > a = 207 . now x 1 + x 2 + . . . . . . + a 1 = 207 . x 1 + x 2 + . . . . . . = 207 - 60 t . we are not sure about the number of students in the remaining class + whole class and without that we ca n ' t solve this . answer : e is correct option ."
a ) 61 . , b ) 63 . , c ) 65 , d ) 67 , e ) it depends how many people are there in the class .
e
add(multiply(divide(60, const_3), const_2), divide(69, const_3))
divide(n0,const_3)|divide(n1,const_3)|multiply(#1,const_2)|add(#0,#2)|
general
a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 8 km ?
"4 years answer : d"
a ) 6 years , b ) 9 years , c ) 5 years , d ) 4 years , e ) 6 years
d
floor(add(divide(log(const_2), log(add(const_1, divide(25, const_100)))), const_1))
divide(n0,const_100)|log(const_2)|add(#0,const_1)|log(#2)|divide(#1,#3)|add(#4,const_1)|floor(#5)|
general
in a graduate physics course , 70 percent of the students are male and 40 percent of the students are married . if two - sevenths of the male students are married , what fraction of the female students is single ?
"total number of enrolled students = 29 number of students who did not take test = 5 hence , number of students who took test = 29 - 5 = 24 number of students who answered q 2 correctly = 24 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 22 . number of students who answered both q 1 & q 2 correctly = 22 . answer : c"
a ) 18 , b ) 19 , c ) 22 , d ) 20 , e ) 19
c
subtract(add(add(24, 22), 5), 29)
add(n1,n3)|add(n5,#0)|subtract(#1,n0)|
other
a rower can row 5 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
7 m - 20 = 2 m so , 5 m = 20 so , m + 7 = 11 answer : c
a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
c
add(divide(20, subtract(7, 2)), 7)
subtract(n0,n2)|divide(n1,#0)|add(n0,#1)
general
a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 16 days . in how many days b alone can do the work ?
"66 greater than 16 . answer : b"
a ) 1.6 , b ) 66 , c ) 6 , d ) - 6 , e ) 6.1
b
divide(divide(divide(divide(divide(divide(16, const_4), const_3), const_4), const_3), const_2), const_2)
divide(n0,const_4)|divide(#0,const_3)|divide(#1,const_4)|divide(#2,const_3)|divide(#3,const_2)|divide(#4,const_2)|
general
the length of a train and that of a platform are equal . if with a speed of 90 kmph the train crosses the platform in one minute , then the length of the train in metres is
"sol . = ( 2 × 1 + 1 ) = 3 , = ( 2 × 3 + 1 ) = 7 , = ( 2 × 4 + 1 ) = 9 , which is not prime . therefore n = 4 . answer b"
a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
b
add(2, 2)
add(n0,n0)|
general
find the number of different prime factors of 25650
two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have all even ( being multiple of 8 ) probability of number selected being odd = total odd numbers / total available numbers probability = 100 / 500 = 0.2 = 20 % answer : option a
a ) 20 % , b ) 25 % , c ) 40 % , d ) 50 % , e ) 80 %
a
multiply(divide(100, 500), const_100)
divide(n0,n4)|multiply(#0,const_100)
general
in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 4720 votes were polled , then how many valid votes did b get ?
"whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 3 / 5 x + 5 x - 1 / 2 x - 3 / 5 x = 5 x = 12 km option : e"
a ) 13 , b ) 17 , c ) 42 , d ) 15 , e ) 12
e
multiply(5, inverse(subtract(1, add(divide(1, 3), divide(1, 4)))))
divide(n0,n1)|divide(n2,n3)|add(#0,#1)|subtract(n0,#2)|inverse(#3)|multiply(n4,#4)|
physics
if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 20 , then n =
"perimeter of the sector = length of the arc + 2 ( radius ) = ( 108 / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) = 26.4 + 28 = 54.4 cm answer : b"
a ) 52 cm , b ) 54.4 cm , c ) 60 cm , d ) 65 cm , e ) 70 cm
b
multiply(multiply(const_2, divide(multiply(subtract(14, const_3), const_2), add(const_4, const_3))), 14)
add(const_3,const_4)|subtract(n0,const_3)|multiply(#1,const_2)|divide(#2,#0)|multiply(#3,const_2)|multiply(n0,#4)|
physics
45 x ? = 25 % of 900
( 1 mph + 10 mph ) / 2 = 5.5 mph correct option is : b
a ) 8 mph , b ) 5.5 mph , c ) 3.5 mph , d ) 4 mph , e ) 0.5 mph
b
divide(add(1, 10), const_2)
add(n0,n1)|divide(#0,const_2)
physics
the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 130 inclusive is the digital sum a multiple of 7 ?
"let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( x / 100 ) ] * p i . e . 100 - x = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . x = 6.25 answer : option d"
a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2
d
divide(multiply(25, 25), const_100)
multiply(n0,n0)|divide(#0,const_100)|
general
the average age of 15 students of a class is 14 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?
when trying the first time the probability denise does n ' t pick the correct combination = 3999 / 4000 second time , as the total number of possible combinations reduced by one , not picking the right one would be 3998 / 3999 . third time 3997 / 3998 . . . and the same 75 times . so we get : 3999 / 4000 ∗ 3998 / 3999 ∗ . . . ∗ 3925 / 39263999 / 4000 ∗ 3998 / 3999 ∗ . . . ∗ 3925 / 3926 every denominator but the first will cancel out and every nominator but the last will cancel out as well . we ' ll get 3925 / 4000 = 157 / 160 . answer : c .
a ) 1 , b ) 159 / 160 , c ) 157 / 160 , d ) 4 3 / 160 , e ) 0
c
divide(subtract(4000, 75), 4000)
subtract(n0,n1)|divide(#0,n0)
probability
the length of minute hand of a clock is 5.6 cm . what is the area covered by this in 10 minutes
"12 rupees = 1200 paisa ' s 36 / 1200 × 100 = 3 / 12 12 / 3 = 3 % b"
a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 %
b
multiply(divide(36, 12), const_100)
divide(n0,n1)|multiply(#0,const_100)|
gain
a can do a piece of work 30 days . b can do work in 45 days . in how many days they will complete the work together ?
"main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer q = 44 . d"
a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
d
multiply(divide(divide(8, divide(const_1, const_2)), const_12), multiply(0.33, 100))
divide(const_1,const_2)|multiply(n1,n2)|divide(n0,#0)|divide(#2,const_12)|multiply(#3,#1)|
general
marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 35 % . what percent of the projected revenue was the actual revenue ?
sphere volume ( v ) = 4 / 3 π r ( power 3 ) : 4 / 3 π r ( power 3 ) = 4 ( power 3 ) : 3 ( power 3 ) = 64 : 27 answer is d .
['a ) 64 : 13', 'b ) 13 : 64', 'c ) 27 : 64', 'd ) 64 : 27', 'e ) none of them']
d
divide(volume_sphere(4), volume_sphere(3))
volume_sphere(n0)|volume_sphere(n1)|divide(#0,#1)
other
the average score of a cricketer in 6 matches is 27 and in other 4 matches is 32 . then find the average score in all the 10 matches ?
"time taken to cross a moving person = length of train / relative speed time taken = 420 / ( ( 45 - 9 ) ( 5 / 18 ) = 420 / 36 * ( 5 / 18 ) = 420 / 10 = 42 sec answer : b"
a ) 56 sec , b ) 42 sec , c ) 36 sec , d ) 29 sec . , e ) 19 sec .
b
divide(420, subtract(divide(45, const_3_6), divide(divide(9, const_2), const_3_6)))
divide(n1,const_3_6)|divide(n2,const_2)|divide(#1,const_3_6)|subtract(#0,#2)|divide(n0,#3)|
physics
the cost price of a radio is rs . 2550 and it was sold for rs . 2130 , find the loss % ?
"lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 1536 l * 1.5 l * 2 l = 1536 l = 8 side face area = l * d = l * 2 l = 8 * 2 * 8 = 128 e is the answer"
a ) 34 , b ) 65 , c ) 88 , d ) 90 , e ) 128
e
divide(power(multiply(const_3, power(1536, const_2)), divide(const_1, const_3)), 1.5)
divide(const_1,const_3)|power(n1,const_2)|multiply(#1,const_3)|power(#2,#0)|divide(#3,n0)|
geometry
pipe a can fill the tank in 30 minutes and pipe b can empty the tank in 90 minutes . how long it will take to fill the tank if both pipes are operating together ?
"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 276 + 2 * 150 a + b + c = â ˆ š 576 = 24 answer d"
a ) 22 , b ) 18 , c ) 26 , d ) 24 , e ) 32
d
sqrt(add(276, multiply(150, const_2)))
multiply(n2,const_2)|add(n1,#0)|sqrt(#1)|
general
what percent of 5.2 kg is 16 gms ?
i got two equations : 3 x - 2 y = 25 x + y = 14 3 x - 2 ( 14 - x ) = 25 3 x - 28 + 2 x = 25 5 x = 53 x = 10.6 or between 10 and 11 . ( ans e )
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
e
divide(add(subtract(multiply(2, subtract(14, 2)), multiply(3, 2)), 31), add(3, 2))
add(n0,n2)|multiply(n0,n2)|subtract(n1,n2)|multiply(n2,#2)|subtract(#3,#1)|add(n3,#4)|divide(#5,#0)
general
the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if arthur and david have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?
let the distance travelled be x km . total time = ( x / 2 ) / 40 + ( x / 2 ) / 10 = 15 = > x / 80 + x / 20 = 15 = > ( x + 4 x ) / 80 = 15 = > x = 240 km answer : a
a ) 240 , b ) 230 , c ) 260 , d ) 220 , e ) 340
a
multiply(divide(15, add(divide(multiply(const_2, 40), const_10), divide(multiply(const_2, 10), const_10))), multiply(multiply(divide(multiply(const_2, 40), const_10), divide(multiply(const_2, 10), const_10)), const_10))
multiply(n1,const_2)|multiply(n2,const_2)|divide(#0,const_10)|divide(#1,const_10)|add(#2,#3)|multiply(#2,#3)|divide(n0,#4)|multiply(#5,const_10)|multiply(#6,#7)
physics
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 9 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 8 * 2 / 5 = 1 / 20 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 1 / 20 = 1 / 5 = 20 % the answer is a .
a ) 20 % , b ) 23 % , c ) 15 % , d ) 18 % , e ) 16 %
a
add(subtract(subtract(const_100, 40), multiply(divide(3, 4), subtract(const_100, 40))), subtract(40, multiply(divide(7, 8), 40)))
divide(n2,n3)|divide(n0,n1)|subtract(const_100,n4)|multiply(#0,#2)|multiply(n4,#1)|subtract(#2,#3)|subtract(n4,#4)|add(#5,#6)
general
from a group of 4 boys and 4 girls , 4 children are to be randomly selected . what is the probability that 2 boys and 2 girls will be selected ?
the part of the tank filled by three pipes in one hour = 1 / 8 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 8 = 1 / 12 . the tank can be filled in 12 hours . answer : b
a ) 11 hours , b ) 12 hours , c ) 15 hours , d ) 16 hours , e ) 17 hours
b
inverse(multiply(divide(const_2, const_3), divide(const_1, 8)))
divide(const_2,const_3)|divide(const_1,n0)|multiply(#0,#1)|inverse(#2)
physics
the banker â € ™ s discount of a certain sum of money is rs . 90 and the true discount on the same sum for the same time is rs . 60 . the sum due is
"the # of factors 220 has is 12 ; so out of 12 factors only three are multiples of 55 : 55 , 110 and 220 , itself ; so , the probability is 3 / 12 = 1 / 4 . answer : e ."
a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
e
divide(divide(choose(55, const_1), 55), power(const_3, const_2))
choose(n1,const_1)|power(const_3,const_2)|divide(#0,n1)|divide(#2,#1)|
other
what percent is 36 paisa ' s of 12 rupees ?
"increase = ( 30 / 40 ) * 100 = ( 3 / 4 ) * 100 = 75 % . e"
a ) 16 % , b ) 16.66 % , c ) 76.69 % , d ) 76.98 % , e ) 75 %
e
multiply(divide(subtract(70, 40), 40), const_100)
subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)|
gain
jane and ashley take 8 days and 40 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an eight day leave from work . this led to jane ' s working for four extra days on her own to complete the project . how long did it take to finish the project ?
"total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 72 percent of the votes cast number of votes for winning candidate = ( 72 / 100 ) * 525 = 378 percent of total membership that voted for winning candidate = ( 378 / 1260 ) * 100 = 30 % answer c"
a ) 75 % , b ) 58 % , c ) 30 % , d ) 34 % , e ) 25 %
c
multiply(divide(multiply(divide(72, const_100), 525), multiply(const_100, power(const_4, const_2))), const_100)
divide(n2,const_100)|power(const_4,const_2)|multiply(n1,#0)|multiply(#1,const_100)|divide(#2,#3)|multiply(#4,const_100)|
gain
jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 4 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
"let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34009 + x = 39000 = > x = 39000 − 34009 = 4991 answer is c ."
a ) 4551 , b ) 4771 , c ) 4991 , d ) 4881 , e ) 4661
c
subtract(multiply(add(5, const_1), 6500), add(add(add(add(6435, 6927), 6855), 7230), 6562))
add(n5,const_1)|add(n0,n1)|add(n2,#1)|multiply(n6,#0)|add(n3,#2)|add(n4,#4)|subtract(#3,#5)|
general
what will be the compound interest on rs . 25000 a ō er 3 years at the rate of 12 % per annum
"explanation : x / 2 – x / 3 = 4 = > x = 24 2 + 4 = 6 a"
a ) 6 , b ) 9 , c ) 11 , d ) 12 , e ) 15
a
add(reminder(multiply(4, const_4), const_10), const_1)
multiply(n0,const_4)|reminder(#0,const_10)|add(#1,const_1)|
general
a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 11,900 sedans in anytown , how many motorcycles are there ?
explanation : let the number of bricks be ' n ' 10 x 4 / 100 x 6 x 90 / 100 = 25 / 100 x 15 / 100 x 8 / 100 x n 10 x 4 x 6 x 90 = 15 x 2 x n = > n = 720 . answer is a
a ) 720 , b ) 600 , c ) 660 , d ) 6000 , e ) none of these
a
divide(multiply(multiply(multiply(10, divide(4, const_100)), 6), subtract(const_1, divide(10, const_100))), multiply(multiply(divide(25, const_100), divide(15, const_100)), divide(8, const_100)))
divide(n4,const_100)|divide(n3,const_100)|divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|multiply(n3,#0)|multiply(#3,#4)|subtract(const_1,#1)|multiply(n5,#5)|multiply(#2,#6)|multiply(#8,#7)|divide(#10,#9)
physics
a 100 - litre mixture of milk and water contains 30.25 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ?
"let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 3 x ) ^ 2 = 9 x ^ 2 . the answer is a ."
a ) 9 , b ) 8 , c ) 6 , d ) 3 , e ) 2
a
multiply(const_4, const_4)
multiply(const_4,const_4)|
geometry
a certain junior class has 1,000 students and a certain senior class has 800 students . among these students , there are 20 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
hcf x lcm = product of numbers 8 x 48 = 24 x the other number other number = ( 8 x 48 ) / 24 other number = 16 answer : d
a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 20
d
divide(multiply(8, 48), 24)
multiply(n0,n1)|divide(#0,n2)
physics
john makes $ 50 a week from his job . he earns a raise and now makes $ 60 a week . what is the % increase ?
the rooms which were not rented is 2 / 5 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 2 / 5 ) = 1 / 2 = 50 % the answer is a .
a ) 50 % , b ) 55 % , c ) 60 % , d ) 65 % , e ) 70 %
a
multiply(divide(multiply(subtract(const_1, divide(2, 3)), multiply(divide(3, 5), const_100)), subtract(const_100, multiply(divide(3, 5), const_100))), const_100)
divide(n0,n1)|divide(n2,n0)|multiply(#0,const_100)|subtract(const_1,#1)|multiply(#2,#3)|subtract(const_100,#2)|divide(#4,#5)|multiply(#6,const_100)
gain
a certain bacteria colony doubles in size every day for 19 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
"speed = 144 * 5 / 18 = 40 m / sec time taken = 180 / 40 = 4.5 sec . answer : d"
a ) 2.5 sec , b ) 1.9 sec , c ) 8.9 sec , d ) 4.5 sec , e ) 2.9 sec
d
divide(180, multiply(144, const_0_2778))
multiply(n1,const_0_2778)|divide(n0,#0)|
physics
the price of an article is cut by 10 % . to restore it to the former value . the new price must be increased by ?
"take the task of building palindromes and break it intostages . stage 1 : select the 7 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 6 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways stage 3 : select the 5 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 3 in 10 ways stage 4 : select the 5 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 4 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 5 : select the hundreds digit this digit must be the same as the thousands digit ( which we already chose in stage 2 ) so , we can complete this stage in 1 way . stage 6 : select the tens digit this digit must be the same as the thousands digit ( which we already chose in stage 2 ) so , we can complete this stage in 1 way . stage 7 : select the units digit this digit must be the same as the ten - thousands digit ( which we already chose in stage 1 ) so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 7 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 9000 ways ) answer : d"
a ) 100 , b ) 610 , c ) 729 , d ) 9000 , e ) 1000
d
multiply(multiply(multiply(multiply(7, const_10), const_10), const_10), const_10)
multiply(n0,const_10)|multiply(#0,const_10)|multiply(#1,const_10)|multiply(#2,const_10)|
general
in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 12 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
"manager ' s monthly salary = rs . ( 2700 * 26 - 2500 * 25 ) = rs . 7700 answer : a"
a ) rs . 7700 , b ) rs . 3618 , c ) rs . 3600 , d ) rs . 3619 , e ) rs . 3610
a
subtract(multiply(add(2500, 200), add(25, const_1)), multiply(2500, 25))
add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)|
general
the difference between the place value and the face value of 6 in the numeral 856973 is
"let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 49 2 x + 1 = 49 2 x = 48 x = 24 therefore larger number is x + 1 = 25 answer : c"
a ) 42 , b ) 43 , c ) 25 , d ) 45 , e ) 46
c
add(add(power(add(add(divide(subtract(subtract(49, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(49, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(49, const_10), const_2), const_4), const_2), power(add(divide(subtract(subtract(49, const_10), const_2), const_4), const_2), const_2)))
subtract(n0,const_10)|subtract(#0,const_2)|divide(#1,const_4)|add(#2,const_2)|power(#2,const_2)|add(#3,const_2)|power(#3,const_2)|add(#5,const_2)|add(#4,#6)|power(#5,const_2)|power(#7,const_2)|add(#9,#10)|add(#11,#8)|
physics
a certain college ' s enrollment at the beginning of 1992 was 30 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 10 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
"let x be the amount of money we started with . 0.7 x = 1400 x = 2000 the answer is a ."
a ) $ 2000 , b ) $ 2100 , c ) $ 2200 , d ) $ 2300 , e ) $ 2400
a
divide(1400, subtract(const_1, divide(30, const_100)))
divide(n1,const_100)|subtract(const_1,#0)|divide(n0,#1)|
gain