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MNLP_M2_rag_dataset

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a milk man has 20 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
"explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = \ inline \ frac { 5 } { 20 } \ times 100 = 25 % % [ profit % = \ inline \ frac { profit } { cost \ : price } \ times 100 ] answer : b ) 25 %"
a ) 22 , b ) 25 , c ) 27 , d ) 29 , e ) 11
b
multiply(divide(subtract(multiply(add(add(add(20, 5), const_10), add(divide(5, const_2), const_3)), 18), multiply(20, 18)), multiply(20, 18)), const_100)
add(n1,n2)|divide(n1,const_2)|multiply(n0,n3)|add(#0,const_10)|add(#1,const_3)|add(#3,#4)|multiply(n3,#5)|subtract(#6,#2)|divide(#7,#2)|multiply(#8,const_100)|
gain
B
johnny makes $ 4.75 per hour at his work . if he works 6 hours , how much money will he earn ?
4.75 * 6 = 28.50 . answer is c .
a ) $ 30 , b ) $ 54 , c ) $ 28.50 , d ) $ 12 , e ) $ 9.60
c
multiply(4.75, 6)
multiply(n0,n1)|
physics
C
a train of 24 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 3.5 km long ?
"d = 25 * 60 + 3500 = 5000 m t = 5000 / 60 * 18 / 5 = 300 sec = 5 mins answer : c"
a ) 4 , b ) 3 , c ) 5 , d ) 7 , e ) 9
c
add(divide(multiply(add(24, const_1), 60), const_1000), 3.5)
add(n0,const_1)|multiply(n1,#0)|divide(#1,const_1000)|add(n4,#2)|
physics
C
a chemical supply company has 60 liters of a 20 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
"60 liters of a 20 % hno 3 solution means hno 3 = 12 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 12 + x = 50 % of ( 60 + x ) or x = 36 . hence , e"
a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 36
e
multiply(subtract(divide(60, const_2), divide(multiply(60, 20), const_100)), const_2)
divide(n0,const_2)|multiply(n0,n1)|divide(#1,const_100)|subtract(#0,#2)|multiply(#3,const_2)|
gain
E
the average weight of 9 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
"total increase in weight = 9 Γ— 2.5 = 22.5 if x is the weight of the new person , total increase in weight = x βˆ’ 65 = > 22.5 = x - 65 = > x = 22.5 + 65 = 87.5 answer : c"
a ) 85.5 , b ) 86.5 , c ) 87.5 , d ) 88.5 , e ) 89.5
c
add(multiply(9, 2.5), 65)
multiply(n0,n1)|add(n2,#0)|
general
C
a worker is paid rs . 20 / - for a full days work . he works 11 / 32 / 31 / 8.3 / 4 days in a week . what is the total amount paid for that worker ?
the total days worked = 1 + 0.333 + 0.667 + 0.125 + 0.75 = 2.875 days amount for 2.875 days is ( 2.875 * 20 ) 57.5 rupees answer : c
a ) 56.5 rupees , b ) 58.5 rupees , c ) 57.5 rupees , d ) 59.5 rupees , e ) 55.5 rupees
c
multiply(add(add(add(add(const_1, divide(const_1, const_3)), divide(const_2, const_3)), divide(const_1, multiply(const_2, const_4))), divide(const_3, 4)), 20)
divide(const_1,const_3)|divide(const_2,const_3)|divide(const_3,n5)|multiply(const_2,const_4)|add(#0,const_1)|divide(const_1,#3)|add(#4,#1)|add(#6,#5)|add(#7,#2)|multiply(n0,#8)
general
C
in a fuel station the service costs $ 1.15 per car , every liter of fuel costs 0.4 $ . assuming that you own 2 sports cars and 2 executive cars and all fuel tanks are empty . how much will it cost to fuel all cars together if a sports car tank is 32 liters and an executive car tank is 75 % bigger ?
"total cars = 4 1.15 * 4 = 4.6 - > service cost fuel cost in sports car = 2 * 32 * 0.4 = 25.6 fuel cost in executive car = 25.6 * 7 / 4 = 44.8 total fuel cost = 25.6 + 44.8 = 70.4 cost to fuel car = 70.4 + 4.6 = 75 answer : b"
a ) 37.5 $ , b ) 75 $ , c ) 87.5 $ , d ) 94.5 $ , e ) 98.4 $
b
add(multiply(multiply(add(32, divide(multiply(32, 75), const_100)), 2), 0.4), multiply(multiply(32, 2), 0.4))
multiply(n4,n5)|multiply(n2,n4)|divide(#0,const_100)|multiply(n1,#1)|add(n4,#2)|multiply(n3,#4)|multiply(n1,#5)|add(#6,#3)|
general
B
a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 30 % . their gross income from sales for one month increases by what percent ?
let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.3 x = 1.17 * ( p * x ) , an increase of 17 % . the answer is e .
a ) 9 % , b ) 11 % , c ) 13 % , d ) 15 % , e ) 17 %
e
subtract(subtract(30, 10), divide(30, 10))
divide(n1,n0)|subtract(n1,n0)|subtract(#1,#0)
gain
E
jennifer had $ 120 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?
"1 / 5 x $ 120 = $ 24 for sandwich 1 / 6 x $ 120 = $ 20 for museum 1 / 2 x $ 120 = $ 60 for book $ 24 + $ 20 + $ 60 = $ 104 spent $ 120 - $ 104 = $ 16 left over correct answer a"
a ) $ 16 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 0
a
subtract(120, add(add(multiply(120, divide(1, 5)), multiply(120, divide(1, 6))), multiply(120, divide(1, 2))))
divide(n1,n2)|divide(n1,n4)|divide(n1,n6)|multiply(n0,#0)|multiply(n0,#1)|multiply(n0,#2)|add(#3,#4)|add(#6,#5)|subtract(n0,#7)|
general
A
the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 500 resolutions
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : option b"
a ) 700 , b ) 704 , c ) 704 , d ) 706 , e ) 707
b
divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 500), const_100)
add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)|
physics
B
5216 x 51 = ?
"normal way of multiplication may take time . here are one alternative . 5216 x 51 = ( 5216 x 50 ) + 5216 = ( 5216 x 100 ) / 2 + 5216 = 521600 / 2 + 5216 = 260800 + 5216 = 266016 answer is b"
a ) 212016 , b ) 266016 , c ) 266436 , d ) 216314 , e ) 216318
b
multiply(divide(5216, 51), const_100)
divide(n0,n1)|multiply(#0,const_100)|
general
B
in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 128 of the workers of that company are men , how many of the workers are women ?
"set up equation : x = total number of workers 128 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 128 = 16 / 30 x x = 240 240 - 128 = 112 answer d"
a ) 80 , b ) 95 , c ) 105 , d ) 112 , e ) 210
d
multiply(divide(128, add(subtract(divide(const_1, const_3), multiply(divide(const_1, const_3), divide(20, const_100))), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))), add(multiply(divide(const_1, const_3), divide(20, const_100)), subtract(subtract(const_1, divide(const_1, const_3)), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))))
divide(const_1,const_3)|divide(n0,const_100)|divide(n1,const_100)|multiply(#0,#1)|subtract(const_1,#0)|multiply(#2,#4)|subtract(#0,#3)|add(#5,#6)|subtract(#4,#5)|add(#3,#8)|divide(n2,#7)|multiply(#9,#10)|
gain
D
a man can row at 6 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
"explanation : speed in still water = 6 kmph speed of the current = 1 kmph speed downstream = ( 6 + 1 ) = 7 kmph speed upstream = ( 6 - 1 ) = 5 kmph let the required distance be x km total time taken = 1 hour Γ’ ‑ ’ x / 7 + x / 5 = 1 Γ’ ‑ ’ 5 x + 7 x = 35 Γ’ ‑ ’ 12 x = 35 Γ’ ‑ ’ x = 2.9 km answer : option c"
a ) 2.4 km , b ) 2.6 km , c ) 2.9 km , d ) 4.4 km , e ) 5.6 km
c
divide(multiply(subtract(6, 1), const_3), 6)
subtract(n0,n1)|multiply(#0,const_3)|divide(#1,n0)|
physics
C
in what time will a train 100 meters long cross an electric pole , if its speed is 144 km / hr
"first convert speed into m / sec speed = 144 * ( 5 / 18 ) = 40 m / sec time = distance / speed = 100 / 40 = 2.5 seconds answer : d"
a ) 8.5 seconds , b ) 2.8 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
d
divide(100, multiply(144, const_0_2778))
multiply(n1,const_0_2778)|divide(n0,#0)|
physics
D
2 , 4 , 6 , 8 , 10 , . . . ?
"each number increases by 2 . 2 + 2 = 4 4 + 2 = 6 6 + 2 = 8 8 + 2 = 10 10 + 2 = 12 answer : e"
a ) 8 , b ) 5 , c ) 7 , d ) 3 , e ) 12
e
subtract(negate(8), multiply(subtract(4, 6), divide(subtract(4, 6), subtract(2, 4))))
negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)|
general
E
a positive number x is multiplied by 3 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
"we need to produce an equation from the information given in the problem stem . we are first given that x is multiplied by 2 and then the product is divided by 3 . this gives us : 2 x / 3 next we are given that the positive square root of the result ( which is 2 x / 3 ) is equal to x . this gives us √ ( 2 x / 3 ) = x 2 x / 3 = x ^ 2 2 x = 3 x ^ 2 3 x ^ 2 – 2 x = 0 x ( 3 x – 2 ) = 0 x = 0 or 3 x – 2 = 0 3 x = 2 x = 4 / 3 because x is positive , x = 4 / 3 . the answer is c ."
a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
c
divide(3, 3)
divide(n0,n1)|
general
C
the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . find the length of the rectangle ?
"let the breadth of the given rectangle be x then length is 2 x . thus area of the given rect is \ fn _ jvn { \ color { black } 2 x ^ { 2 } } after dec 5 cm from length and inc 5 cm breadth , new lenght becomes 2 x - 5 and breadth is x + 5 . thus new area = ( 2 x - 5 ) ( x + 5 ) = \ fn _ jvn { \ color { black } 2 x ^ { 2 } + 5 x - 25 } since new area is 75 units greater than original area thus \ fn _ jvn { \ color { black } 2 x ^ { 2 } + 75 = 2 x ^ { 2 } + 5 x - 25 } 5 x = 75 + 25 5 x = 100 therefore x = 20 hence length of the rectangle is 40 cm . answer : b"
a ) 10 cm , b ) 40 cm , c ) 20 cm , d ) 30 cm , e ) 50 cm
b
divide(const_100, const_3)
divide(const_100,const_3)|
geometry
B
the mean of 50 observations was 36 . it was found later that an observation 46 was wrongly taken as 23 . the corrected new mean is
"solution correct sum = ( 36 x 50 + 46 - 23 ) = 1823 . Γ’ Λ† Β΄ correct mean = 1823 / 50 = 36.46 . answer d"
a ) 35.24 , b ) 36.16 , c ) 36.24 , d ) 36.46 , e ) none
d
divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50)
multiply(n0,n1)|subtract(n0,const_2)|subtract(#1,n3)|add(#0,#2)|divide(#3,n0)|
general
D
a 70 cm long wire is to be cut into two pieces so that one piece will be 2 / 3 th of the other , how many centimeters will the shorter piece be ?
"1 : 2 / 3 = 3 : 2 2 / 5 * 70 = 28 answer : c"
a ) 35 , b ) 20 , c ) 28 , d ) 36 , e ) 30
c
subtract(70, divide(70, add(divide(2, 3), const_1)))
divide(n1,n2)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)|
physics
C
the smallest number which when diminished by 6 , is divisible by 12 , 16 , 18 , 21 and 28 is
"required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 6 = 1008 + 6 = 1014 answer : b"
a ) 1008 , b ) 1014 , c ) 1022 , d ) 1032 , e ) 1043
b
add(multiply(multiply(power(const_3, const_2.0), power(const_2.0, const_4)), add(const_3, const_4)), 6)
add(const_3,const_4)|power(const_3,const_2.0)|power(const_2.0,const_4)|multiply(#1,#2)|multiply(#0,#3)|add(#4,n0)|
general
B
a man can row upstream at 8 kmph and downstream at 13 kmph . the speed of the stream is ?
"speed of stream = 1 / 2 ( 13 - 8 ) = 2.5 kmph answer is b"
a ) 3 kmph , b ) 2.5 kmph , c ) 3.5 kmph , d ) 4.3 kmph , e ) 5 kmph
b
divide(add(8, 13), const_2)
add(n0,n1)|divide(#0,const_2)|
physics
B
for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.5 ?
"[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.5 = 6 * 0 + 2 * 7.2 + 8 - 6.5 = 0 + 14.4 + 1.5 15.7 answer d"
a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 15.7 . , e ) 16.4 .
d
subtract(add(multiply(2, 7.2), subtract(8.4, divide(const_4, const_10))), 6.5)
divide(const_4,const_10)|multiply(n1,n4)|subtract(n5,#0)|add(#1,#2)|subtract(#3,n6)|
general
D
10 men do a work in 10 days . how many men are needed to finish the work in 4 days ?
"men required to finish the work in 4 days = 10 * 10 / 4 = 25 answer is a"
a ) 25 , b ) 20 , c ) 30 , d ) 10 , e ) 15
a
divide(multiply(10, 10), 4)
multiply(n0,n1)|divide(#0,n2)|
physics
A
if the population of a certain country increases at the rate of one person every 40 seconds , by how many persons does the population increase in 1 hour ?
"answer = 1.5 * 60 = 90 answer is a"
a ) 90 , b ) 120 , c ) 150 , d ) 180 , e ) 160
a
multiply(divide(const_60, 40), 1)
divide(const_60,n0)|multiply(n1,#0)|
physics
A
if the perimeter of a rectangular garden is 680 m , its length when its breadth is 82 m is ?
"2 ( l + 82 ) = 680 = > l = 258 m answer : e"
a ) 286 m , b ) 899 m , c ) 200 m , d ) 166 m , e ) 258 m
e
subtract(divide(680, const_2), 82)
divide(n0,const_2)|subtract(#0,n1)|
physics
E
( √ 27 + √ 192 ) / √ 54 = ?
"( √ 27 + √ 192 ) / √ 54 = ( 3 √ 3 + 8 √ 3 ) / 3 √ 3 * 2 = 11 √ 3 / 3 √ 3 * 2 = 11 / ( 3 * √ 2 ) = 11 / ( 3 * √ 2 ) . hence , the correct answer is d ."
a ) 2 √ 2 , b ) 2 √ 3 , c ) 3 √ 2 , d ) 11 / ( 3 * √ 2 ) , e ) √ 2
d
divide(add(sqrt(27), sqrt(192)), sqrt(54))
sqrt(n0)|sqrt(n1)|sqrt(n2)|add(#0,#1)|divide(#3,#2)|
general
D
you enter a weight loss challenge game and manage to lose 15 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
"( 100 % - 15 % ) * ( 100 % + 2 % ) = 0.85 * 1.02 = 13.3 % the weigh in records your weight loss at 13.3 % ! the answer is a"
a ) 13.3 % , b ) 9.22 % , c ) 9 % , d ) 14 % , e ) 12 %
a
multiply(subtract(const_1, multiply(subtract(const_1, divide(15, const_100)), add(const_1, divide(2, const_100)))), const_100)
divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|subtract(const_1,#4)|multiply(#5,const_100)|
gain
A
the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 70 metres ?
"speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 70 / 5 = 14 seconds . answer : e"
a ) 22 seconds , b ) 65 seconds , c ) 78 seconds , d ) 12 seconds , e ) 14 seconds
e
divide(70, multiply(add(15, 3), const_0_2778))
add(n0,n1)|multiply(#0,const_0_2778)|divide(n2,#1)|
physics
E
the perimeter of one square is 48 cm and that of another is 28 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
"4 a = 48 4 a = 28 a = 12 a = 7 a 2 = 144 a 2 = 49 combined area = a 2 = 193 = > a = 13.9 d = 13.9 √ 2 answer : d"
a ) 13 √ 4 , b ) 13 √ 2 , c ) 23 √ 2 , d ) 13.9 √ 2 , e ) 13 √ 9
d
sqrt(multiply(add(power(divide(48, const_4), const_2), power(divide(28, const_4), const_2)), const_2))
divide(n0,const_4)|divide(n1,const_4)|power(#0,const_2)|power(#1,const_2)|add(#2,#3)|multiply(#4,const_2)|sqrt(#5)|
geometry
D
500 is increased by 30 % . find the final number .
explanation final number = initial number + 30 % ( original number ) = 500 + 30 % ( 500 ) = 500 + 150 = 650 . answer c
a ) 550 , b ) 500 , c ) 650 , d ) 600 , e ) 700
c
add(500, multiply(500, divide(30, const_100)))
divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)|
gain
C
in a recent head - to - head run - off election , 18,000 absentee ballets were cast . 3 / 7 of the absentee ballets were thrown out and 2 / 9 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
"4 / 7 * 7 / 9 ( total absentee votes ) = 4 / 9 ( total votes ) = 4 / 9 * 18000 = 8000 answer is d"
a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000
d
multiply(divide(divide(subtract(subtract(multiply(multiply(2, const_4), const_1000), multiply(multiply(multiply(2, const_4), const_1000), divide(3, 7))), multiply(subtract(multiply(multiply(2, const_4), const_1000), multiply(multiply(multiply(2, const_4), const_1000), divide(3, 7))), divide(2, 9))), const_1000), const_4), 2)
divide(n1,n2)|divide(n3,n4)|multiply(n3,const_4)|multiply(#2,const_1000)|multiply(#0,#3)|subtract(#3,#4)|multiply(#1,#5)|subtract(#5,#6)|divide(#7,const_1000)|divide(#8,const_4)|multiply(#9,n3)|
general
D
a part - time employee ’ s hourly wage was increased by 20 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
"let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 20 % wage increase , the employee makes $ 1.20 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.20 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.20 to get : new # of hours = 100 / 1.20 β‰ˆ 83 hours so , the number of hours decreases from 100 hours to ( approximately ) 83 hours . this represents a 17 % decrease ( approximately ) . answer : b"
a ) 9 % , b ) 17 % , c ) 25 % , d ) 50 % , e ) 100 %
b
multiply(divide(divide(20, const_100), divide(add(20, const_100), const_100)), const_100)
add(n0,const_100)|divide(n0,const_100)|divide(#0,const_100)|divide(#1,#2)|multiply(#3,const_100)|
general
B
a car takes 6 hours to cover a distance of 432 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
"time = 6 distence = 432 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 432 / 9 = 48 kmph a"
a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 60 kmph
a
divide(432, divide(multiply(6, 3), 2))
multiply(n0,n2)|divide(#0,n3)|divide(n1,#1)|
physics
A
a train crosses a platform of 110 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
"length of the train be Γ’ € ˜ x Γ’ € β„’ x + 110 / 15 = x + 250 / 20 4 x + 440 = 3 x + 750 x = 310 m answer : d"
a ) 150 , b ) 88 , c ) 77 , d ) 310 , e ) 52
d
subtract(multiply(250, divide(15, divide(15, const_3))), multiply(110, divide(20, divide(15, const_3))))
divide(n1,const_3)|divide(n1,#0)|divide(n3,#0)|multiply(n2,#1)|multiply(n0,#2)|subtract(#3,#4)|
physics
D
the average of first five prime numbers greater than 37 is ?
"41 + 43 + 47 + 53 + 59 = 243 / 5 = 48.6 answer : d"
a ) 32.2 , b ) 32.98 , c ) 42.3 , d ) 48.6 , e ) 32.4
d
add(37, const_1)
add(n0,const_1)|
general
D
what is the greatest possible length which can be used to measure exactly the lengths 180 m , 500 m and 15 m 20 cm ?
required length = hcf of 18000 cm , 50000 cm , 1520 cm = 80 cm answer is a
a ) 80 cm , b ) 50 cm , c ) 40 cm , d ) 10 cm , e ) 100 cm
a
multiply(20, const_4)
multiply(n3,const_4)
physics
A
john makes $ 40 a week from his job . he earns a raise and now makes $ 60 a week . what is the % increase ?
"increase = ( 20 / 40 ) * 100 = 50 % . e"
a ) 16 % , b ) 16.66 % , c ) 18 % , d ) 21 % , e ) 50 %
e
multiply(divide(subtract(60, 40), 40), const_100)
subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)|
gain
E
108 . triangle a ’ s base is 12 % greater than the base of triangle b , and a ’ s height is 12 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?
"wish the question specified that we are talking about corresponding height . base of a = 13 / 12 * base of b height of a = 11 / 12 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 13 / 12 * 11 / 12 * area of b = 143 / 144 * area of b area of a is 0.7 % less than the area of b . answer ( b )"
a ) 9 % less , b ) 0.7 % less , c ) equal to each other , d ) 1 % more , e ) 9 % more
b
divide(const_100, subtract(multiply(const_100, const_100), multiply(add(const_100, 12), subtract(const_100, 12))))
add(n1,const_100)|multiply(const_100,const_100)|subtract(const_100,n1)|multiply(#0,#2)|subtract(#1,#3)|divide(const_100,#4)|
geometry
B
a grocery shop has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
"let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 Γ— 6500 = > 34009 + x = 39000 = > x = 39000 βˆ’ 34009 = 4991 answer : d"
a ) 4857 , b ) 4184 , c ) 4012 , d ) 4991 , e ) 5291
d
subtract(multiply(6500, add(5, const_1)), add(add(add(6855, add(6435, 6927)), 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
D
find compound interest on $ 16000 at 15 % per annum for 2 years 4 months , compounded annually .
"time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 16000 x ( 1 + Β­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 16000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 22218 . : . c . i . = rs . ( 22218 - 16000 ) = $ 6218 answer c ."
a ) 6109 , b ) 6209 , c ) 6218 , d ) 6107 , e ) 6100
c
add(add(multiply(16000, divide(15, const_100)), multiply(add(16000, multiply(16000, divide(15, const_100))), divide(15, const_100))), multiply(add(add(16000, multiply(16000, divide(15, const_100))), multiply(add(16000, multiply(16000, divide(15, const_100))), divide(15, const_100))), divide(divide(15, const_100), const_3)))
divide(n1,const_100)|divide(#0,const_3)|multiply(n0,#0)|add(n0,#2)|multiply(#3,#0)|add(#2,#4)|add(#3,#4)|multiply(#6,#1)|add(#5,#7)|
gain
C
a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 90 to incur a loss 10 % ?
"production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 90 * ( 100 % + 10 % ) = $ 99 number of articles to be sold for $ 108 to incur a 20 % loss : $ 99 / $ 2.40 = 41.2 thus , solution b is correct ."
a ) 45 , b ) 41.2 , c ) 40 , d ) 50 , e ) 48
b
divide(original_price_before_loss(10, 90), divide(original_price_before_gain(20, 60), 20))
original_price_before_gain(n4,n1)|original_price_before_loss(n0,n3)|divide(#0,n0)|divide(#1,#2)|
gain
B
3 , 4.5 , 6.75 , 10.13 , 15.18 , ( . . . )
"3 ( 3 Γ£ β€” 3 ) Γ£ Β· 2 = 4.5 ( 4.5 Γ£ β€” 3 ) Γ£ Β· 2 = 6.75 ( 6.75 Γ£ β€” 3 ) Γ£ Β· 2 = 10.13 ( 10.18 Γ£ β€” 3 ) Γ£ Β· 2 = 15.18 ( 15.18 Γ£ β€” 3 ) Γ£ Β· 2 = 60.75 answer is c"
a ) 60 , b ) 60.75 , c ) 22.78 , d ) 32.52 , e ) 88
c
subtract(negate(10.13), multiply(subtract(4.5, 6.75), divide(subtract(4.5, 6.75), subtract(3, 4.5))))
negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)|
general
C
what is the total number of positive integers that are less than 1000 and that have no positive factor in common with 1000 other than 1 ?
"since 1000 = 2 ^ 3 * 5 ^ 3 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 500 odd numbers from 1 to 1000 . we then need to eliminate the 100 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 995 . there are a total of 500 - 100 = 400 such numbers between 1 and 1000 . the answer is d ."
a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
d
subtract(subtract(1000, 1), subtract(add(add(divide(subtract(subtract(1000, const_2), const_2), const_2), 1), add(divide(subtract(subtract(1000, divide(1000, const_100)), divide(1000, const_100)), divide(1000, const_100)), 1)), add(divide(subtract(subtract(1000, const_10), const_10), const_10), 1)))
divide(n0,const_100)|subtract(n0,n2)|subtract(n0,const_2)|subtract(n0,const_10)|subtract(#2,const_2)|subtract(n0,#0)|subtract(#3,const_10)|divide(#4,const_2)|divide(#6,const_10)|subtract(#5,#0)|add(#7,n2)|add(n2,#8)|divide(#9,#0)|add(#12,n2)|add(#10,#13)|subtract(#14,#11)|subtract(#1,#15)|
general
D
a rectangular carpet has an area of 60 sq . m . if its diagonal and longer side together equal 5 times the shorter side , the length of the carpet is :
let , length = x meters and breadth = y meters then xy = 60 and ( x 2 + y 2 ) + x = 5 therefore , x = 60 and ( x 2 + y 2 ) = ( 5 y - x ) 2 or xy = 60 and 24 y 2 - 10 xy = 0 . therefore , 24 y 2 - 10 * 60 = 0 or y 2 = 25 or = 5 . therefore , x = ( 60 / 5 ) m = 12 m . so , length of the carpet = 12 m answer : b
['a ) 5 m', 'b ) 12 m', 'c ) 13 m', 'd ) 14.5 m', 'e ) 15.5 m']
b
divide(60, sqrt(divide(multiply(60, const_10), subtract(power(5, const_2), const_1))))
multiply(n0,const_10)|power(n1,const_2)|subtract(#1,const_1)|divide(#0,#2)|sqrt(#3)|divide(n0,#4)
geometry
B
a man distributed rs . 100 equally among his friends . if there had been 5 more friends , each would have received one rupee less . how many friends had he ?
firstly we have 20 friends and money wiill be distribute each of them 5 rupee then 5 more friends it means total no frnd = 25 each recv 4 rupee which means all recv 1 less rupee answer : b
a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
b
add(divide(100, 5), 5)
divide(n0,n1)|add(n1,#0)
general
B
a baseball card decreased in value 10 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
"consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.9 = 90 after second year price = 90 * 0.9 = 81 final decrease = [ ( 100 - 81 ) / 100 ] * 100 = 19 % correct answer - a"
a ) 19 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 72 %
a
subtract(const_100, multiply(multiply(subtract(const_1, divide(10, const_100)), subtract(const_1, divide(10, const_100))), const_100))
divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(const_100,#5)|
gain
A
2 , 3 , 6 , 15 , _ , 123 ?
answer : a
a ) 42 , b ) 38 , c ) 28 , d ) 29 , e ) 11
a
subtract(negate(15), multiply(subtract(3, 6), divide(subtract(3, 6), subtract(2, 3))))
negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)|
general
A
a train is running with a speed of 60 kmph and its length is 110 metres . calculate the time by which it will pass a man running opposite with speed of 6 kmph
explanation : from the given question , we will first calculate the speed of train relative to man , = > ( 60 + 6 ) = 66 km / hr ( we added 6 because man is running opposite ) convert it in metre / second = 66 Γ£ β€” 5 / 18 = 55 / 3 m / sec time it will take to pass man = 110 Γ£ β€” 3 / 55 = 6 seconds answer is c
a ) 2 second , b ) 4 second , c ) 6 second , d ) 8 second , e ) 10 second
c
divide(110, multiply(add(60, 6), const_0_2778))
add(n0,n2)|multiply(#0,const_0_2778)|divide(n1,#1)
physics
C
the average height of 35 boys in a class was calculated as 181 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
"calculated average height of 35 boys = 181 cm . wrong total height of 35 boys = 181 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - 60 / 35 cm = 181 cm - 1.71 cm = 179.29 cm . answer : b"
a ) 178.27 cm , b ) 179.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
b
floor(divide(add(subtract(multiply(35, 181), 166), 106), 35))
multiply(n0,n1)|subtract(#0,n2)|add(n3,#1)|divide(#2,n0)|floor(#3)|
general
B
what is the units digit of ( 493 ) ( 913 ) ( 381 ) ( 756 ) ( 29 )
"just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 3 . imo d ."
a ) 0 , b ) 1 , c ) 4 , d ) 3 , e ) 6
d
divide(add(multiply(factorial(493), factorial(913)), multiply(factorial(493), factorial(756))), 493)
factorial(n0)|factorial(n1)|factorial(n3)|multiply(#0,#1)|multiply(#0,#2)|add(#3,#4)|divide(#5,n0)|
general
D
at an international conference , β€œ red ” world countries and β€œ blue ” world countries are the only participants . the ratio of β€œ red ” world participants to β€œ blue ” world participants is 10 : 5 . if one - third of β€œ red ” world participants are left - handed and two - thirds of β€œ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ?
red : blue = 10 : 5 let red = 10 x and blue = 5 x 1 / 3 of red are left handed = > 1 / 3 * 10 x = 10 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 5 x = 10 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 10 x / 3 + 10 x / 3 ) / ( 10 x + 5 x ) = 20 / 45 = 4 / 9 answer : b
a ) 4 / 10 , b ) 4 / 9 , c ) 6 / 5 , d ) 9 / 2 , e ) 6 / 4
b
divide(add(multiply(10, const_0_33), multiply(5, divide(const_2, const_3))), add(10, 5))
add(n0,n1)|divide(const_2,const_3)|multiply(n0,const_0_33)|multiply(n1,#1)|add(#2,#3)|divide(#4,#0)
other
B
the average height of 20 girls out of a class of 50 is 142 cm . and that of the remaining girls is 149 cm . the average height of the whole class is :
"explanation : average height of the whole class = ( 20 Γ— 142 + 30 Γ— 149 / 50 ) = 146.2 cms answer a"
a ) 146.2 cms , b ) 146.5 cms , c ) 146.9 cms , d ) 142.2 cms , e ) 136.2 cms
a
divide(add(multiply(142, 20), multiply(149, const_10)), 50)
multiply(n0,n2)|multiply(n3,const_10)|add(#0,#1)|divide(#2,n1)|
general
A
if a 2 + b 2 + c 2 = 390 and ab + bc + ca = 5 , then a + b + c is
by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 390 and ab + bc + ca = 5 , ( a + b + c ) ^ 2 = 390 + 2 ( 5 ) = 400 = 20 ^ 2 therefore : a + b + c = 20 answer : b
a ) 19 , b ) 20 , c ) 25 , d ) 30 , e ) 64
b
sqrt(add(390, multiply(5, const_2)))
multiply(n4,const_2)|add(n3,#0)|sqrt(#1)
general
B
a housing society has been allotted a square piece of land measuring 2550.25 sq . m . what is the side of the plot ?
solution side = √ 2550.25 = √ 255025 / 100 = 505 / 10 = 50.5 m . answer b
['a ) 50.25 m', 'b ) 50.5 m', 'c ) 50.65 m', 'd ) 50.85', 'e ) none']
b
sqrt(2550.25)
sqrt(n0)
physics
B
a wire can be bent in the form of a circle of radius 56 cm . if it is bent in the form of a square , then its area will be ?
length of wire = 2 pier = 2 * ( 22 / 7 ) * 56 = 352 cm side of the square = 352 / 4 = 88 cm area of the square = 88 * 88 = 7744 sq cm answer : a
['a ) 7744', 'b ) 8844', 'c ) 5544', 'd ) 4444', 'e ) 3444']
a
power(divide(circumface(56), const_4), const_2)
circumface(n0)|divide(#0,const_4)|power(#1,const_2)
geometry
A
a dishonest dealer professes to sell goods at the cost price but uses a weight of 700 grams per kg , what is his percent ?
"700 - - - 300 100 - - - ? = > 42.8 % answer : a"
a ) 42.8 % , b ) 25 % , c ) 55 % , d ) 28 % , e ) 55 %
a
subtract(multiply(divide(const_100, 700), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)
add(const_2,const_3)|divide(const_100,n0)|multiply(#0,const_2)|multiply(#2,const_100)|multiply(#1,#3)|subtract(#4,const_100)|
gain
A
the average weight of a group of boys is 35 kg . after a boy of weight 40 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
let the number off boys in the group originally be x . total weight of the boys = 35 x after the boy weighing 40 kg joins the group , total weight of boys = 35 x + 40 so 35 x + 40 = 36 ( x + 1 ) = > x = 5 . answer : b
a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
b
add(subtract(40, add(35, 1)), const_1)
add(n0,n2)|subtract(n1,#0)|add(#1,const_1)
general
B
two brother x and y appeared for an exam . the probability of selection of x is 1 / 3 and that of b is 2 / 5 . find the probability that both of them are selected .
"explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 3 , p ( b ) = 2 / 5 . let c be the event that both are selected . p ( c ) = p ( a ) Γ£ β€” p ( b ) as a and b are independent events : = ( 1 / 3 ) Γ£ β€” ( 2 / 5 ) = 2 / 15 answer : b ) 2 / 15"
a ) 2 / 69 , b ) 2 / 15 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10
b
multiply(divide(1, 3), divide(2, 5))
divide(n0,n1)|divide(n2,n3)|multiply(#0,#1)|
general
B
in a theater , the first row has 14 seats and each row has 2 more seats than previous row . if the last row has 56 seats , what is the total number of seats in the theater ?
"the number of seats in the theater is 14 + ( 14 + 2 ) + . . . + ( 14 + 42 ) = 22 ( 14 ) + 2 ( 1 + 2 + . . . + 21 ) = 22 ( 14 ) + 2 ( 21 ) ( 22 ) / 2 = 22 ( 14 + 21 ) = 22 ( 35 ) = 770 the answer is a ."
a ) 770 , b ) 780 , c ) 790 , d ) 800 , e ) 810
a
multiply(divide(add(14, 56), const_2), divide(add(subtract(56, 14), 2), 2))
add(n0,n2)|subtract(n2,n0)|add(n1,#1)|divide(#0,const_2)|divide(#2,n1)|multiply(#3,#4)|
general
A
a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 1.1 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
"72 km / hr = 1.2 km / min the total distance is 1.2 km . 1.2 / 1.2 = 1 minute the answer is a ."
a ) 1.0 , b ) 1.2 , c ) 1.4 , d ) 1.6 , e ) 1.8
a
multiply(divide(add(1.1, divide(100, const_1000)), 72), const_60)
divide(n0,const_1000)|add(n2,#0)|divide(#1,n1)|multiply(#2,const_60)|
physics
A
what is the positive difference between the sum of the squares of the first 8 positive integers and the sum of the prime numbers between the first square and fourth square ?
"forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 8 ^ 2 = 204 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 204 is 163 . so the answer is ( c ) ."
a ) 161 , b ) 162 , c ) 163 , d ) 164 , e ) 165
c
subtract(add(add(add(add(add(const_1, power(const_2, const_2)), power(const_3, const_2)), power(const_4, const_2)), power(add(const_4, const_1), const_2)), power(8, const_2)), add(add(add(const_4, const_3), 8), add(add(add(add(const_2, const_3), add(const_4, const_1)), add(const_4, const_3)), add(add(const_2, const_3), 8))))
add(const_1,const_4)|add(const_3,const_4)|add(const_2,const_3)|power(const_2,const_2)|power(const_3,const_2)|power(const_4,const_2)|power(n0,const_2)|add(#3,const_1)|add(n0,#1)|add(#2,#0)|add(n0,#2)|power(#0,const_2)|add(#7,#4)|add(#9,#1)|add(#12,#5)|add(#13,#10)|add(#14,#11)|add(#8,#15)|add(#16,#6)|subtract(#18,#17)|
general
C
if a farmer sells 5 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 10 more chickens , he will run out of feed 3 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
"say farmer has n chicken and he is good for d days . : - we have 3 equations given in question : - ( n - 5 ) * d + 4 = ( n + 10 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 10 d - 3 n = 30 4 n - 5 d = 20 = > n = 20 ans c it is !"
a ) 12 , b ) 24 , c ) 20 , d ) 55 , e ) 60
c
multiply(add(const_2, 4), multiply(3, 4))
add(const_2,n1)|multiply(n1,n3)|multiply(#0,#1)|
general
C
cuboid volume and base area are 144 m ^ 3 and 18 m ^ 3 respectively . find the height of a cuboid ?
height of the cuboid = volume * base area = 144 / 18 = 8 metre answer is option d
['a ) 5 m', 'b ) 12 m', 'c ) 6 m', 'd ) 8 m', 'e ) 10 m']
d
divide(144, 18)
divide(n0,n2)
geometry
D
circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 2 more revolutions than gear p ?
"gear q makes 30 more revolutions each 60 seconds . the time to make 2 = 30 / 15 more revolutions is 60 / 15 = 4 seconds . the answer is a ."
a ) 4 , b ) 8 , c ) 10 , d ) 12 , e ) 15
a
divide(2, subtract(divide(40, const_60), divide(10, const_60)))
divide(n1,const_60)|divide(n0,const_60)|subtract(#0,#1)|divide(n2,#2)|
physics
A
convert 400 miles into meters ?
"1 mile = 1609.34 meters 400 mile = 400 * 1609.34 = 643736 meters answer is e"
a ) 784596 , b ) 845796 , c ) 804670 , d ) 784596 , e ) 643736
e
divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 400), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)))
add(const_2,const_3)|multiply(#0,const_2)|multiply(#1,#1)|multiply(n0,#2)|divide(#3,#2)|
physics
E
in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 27 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
"200 are sophomores . the number of freshmen is 600 - 160 - 0.27 ( 800 ) = 224 the answer is c ."
a ) 12 , b ) 18 , c ) 24 , d ) 30 , e ) 36
c
subtract(divide(multiply(subtract(subtract(subtract(const_100, multiply(divide(160, 800), const_100)), 27), subtract(const_100, 75)), 800), const_100), divide(multiply(subtract(const_100, 75), 800), const_100))
divide(n3,n0)|subtract(const_100,n2)|multiply(#0,const_100)|multiply(n0,#1)|divide(#3,const_100)|subtract(const_100,#2)|subtract(#5,n1)|subtract(#6,#1)|multiply(n0,#7)|divide(#8,const_100)|subtract(#9,#4)|
gain
C
a student has to obtain 60 % of the total marks to pass . he got 160 marks and failed by 20 marks . the maximum marks are ?
"let the maximum marks be x then , 60 % of x = 160 + 20 60 x / 100 = 180 60 x = 180 * 100 = 18000 x = 300 answer is c"
a ) 210 , b ) 280 , c ) 300 , d ) 320 , e ) 340
c
divide(add(160, 20), divide(60, const_100))
add(n1,n2)|divide(n0,const_100)|divide(#0,#1)|
general
C
machines x and y produce bottles at their respective constant rates . machine x produces k bottles in 6 hours and machine y produces k bottles in 12 hours . how many hours does it take machines x and y , working simultaneously , to produce 24 k bottles ?
"x rate = k / 6 y rate = k / 12 k / 6 + k / 12 = 24 k / t solving t = 96 answer e"
a ) 48 , b ) 42 , c ) 45 , d ) 98 , e ) 96
e
divide(multiply(24, divide(add(6, 12), 12)), 12)
add(n0,n1)|divide(#0,n1)|multiply(n2,#1)|divide(#2,n1)|
physics
E
the present worth of a certain bill due sometime hence is rs . 400 and the true discount is rs . 20 . what is the banker ' s discount ?
"explanation : bg = ( td ) 2 / pw = 202 / 400 = rs . 1 bg = bd – td = > 1 = bd - 20 = > bd = 1 + 20 = rs . 21 answer : option d"
a ) rs . 19 , b ) rs . 22 , c ) rs . 20 , d ) rs . 21 , e ) none of these
d
add(20, divide(power(20, const_2), 400))
power(n1,const_2)|divide(#0,n0)|add(n1,#1)|
gain
D
a train speeds past a pole in 20 seconds and a platform 100 m long in 25 seconds . its length is ?
"let the length of the train be x meters and its speed be y m / sec . they , x / y = 20 = > y = x / 20 x + 100 / 25 = x / 20 x = 400 m . answer : e"
a ) 188 m , b ) 876 m , c ) 251 m , d ) 150 m , e ) 400 m
e
multiply(100, subtract(const_2, const_1))
subtract(const_2,const_1)|multiply(n1,#0)|
physics
E
a man sitting in a train which is traveling at 70 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
"relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 70 ) kmph = 42 kmph . answer : e"
a ) 50 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 42 kmph
e
subtract(multiply(divide(280, 9), const_3_6), 70)
divide(n2,n1)|multiply(#0,const_3_6)|subtract(#1,n0)|
physics
E
how many seconds does sandy take to cover a distance of 500 meters , if sandy runs at a speed of 15 km / hr ?
"15 km / hr = 15000 m / 3600 s = ( 150 / 36 ) m / s = ( 25 / 6 ) m / s time = 500 / ( 25 / 6 ) = 120 seconds the answer is b ."
a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180
b
divide(500, multiply(15, const_0_2778))
multiply(n1,const_0_2778)|divide(n0,#0)|
physics
B
if the compound interest on a certain sum of money for 7 years at 10 % per annum be rs . 993 , what would be the simple interest ?
"let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 7 yrs = ( 3000 x 10 x 7 ) / 100 = 2100 / - answer : d ."
a ) rs . 880 , b ) rs . 890 , c ) rs . 895 , d ) rs . 2100 , e ) none
d
divide(multiply(multiply(multiply(multiply(const_3.0, const_100), 10), 10), 7), const_100)
multiply(const_3.0,const_100)|multiply(n1,#0)|multiply(n1,#1)|multiply(n0,#2)|divide(#3,const_100)|
gain
D
a bakery has 6 employees . it pays annual salaries of $ 16,000 to each of 2 employees , $ 18,000 to 1 employee , and $ 19,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
"average = 2 ( 16000 ) + ( 18000 ) + 3 ( 19000 ) / 6 = $ 17,833 the answer is c ."
a ) $ 17,200 , b ) $ 17,500 , c ) $ 17,800 , d ) $ 18,000 , e ) $ 18,400
c
divide(add(add(multiply(add(add(add(const_10, const_10), 1), 1), 3), multiply(subtract(add(const_10, const_10), 1), 2)), add(add(const_10, const_10), 1)), 6)
add(const_10,const_10)|add(#0,n4)|subtract(#0,n4)|add(#1,n4)|multiply(#2,n2)|multiply(#3,n6)|add(#5,#4)|add(#6,#1)|divide(#7,n0)|
general
C
the width of a rectangular hall is Β½ of its length . if the area of the hall is 288 sq . m , what is the difference between its length and breadth ?
"let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 288 = x * 1 x / 2 x Β² = 576 x = 24 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 24 / 2 = 12 m answer : c"
a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m
c
divide(sqrt(divide(288, divide(const_1, const_2))), const_2)
divide(const_1,const_2)|divide(n0,#0)|sqrt(#1)|divide(#2,const_2)|
geometry
C
what is ( 21 ^ 7 + 21 ) / 21 ?
( 21 ^ 7 + 21 ) / 21 = 21 * ( 21 ^ 6 + 1 ) / 21 = 21 ^ 6 + 1 clearly this is a number which ends with a 2 in the units place . the answer is d .
a ) 82216043 , b ) 83786095 , c ) 84316108 , d ) 85766122 , e ) 86426237
d
divide(add(power(21, 7), 21), 21)
power(n0,n1)|add(n0,#0)|divide(#1,n0)
general
D
the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 735 , krishan has ?
ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 735 : n & there n = 289 x 735 / 49 = rs . 4335 answer : a
a ) s . 4335 , b ) s . 2330 , c ) s . 1190 , d ) s . 1620 , e ) s . 2680
a
multiply(divide(multiply(divide(735, 7), 17), 7), 17)
divide(n4,n0)|multiply(n1,#0)|divide(#1,n0)|multiply(n1,#2)
other
A
if $ 1092 are divided between worker a and worker b in the ratio 5 : 8 , what is the share that worker b will get ?
"worker b will get 8 / 13 = 61.54 % the answer is b ."
a ) 60.32 % , b ) 61.54 % , c ) 62.21 % , d ) 62.76 % , e ) 63.87 %
b
divide(1092, add(5, 8))
add(n1,n2)|divide(n0,#0)|
other
B
find the simple interest on $ 6000 at 15 % per annum for 9 months ?
"p = $ 6000 r = 15 % t = 9 / 12 years = 3 / 4 years s . i . = p * r * t / 100 = 6000 * 15 * 3 / 400 = $ 675 answer is c"
a ) $ 492 , b ) $ 512 , c ) $ 675 , d ) $ 745 , e ) $ 1020
c
multiply(6000, divide(15, const_100))
divide(n1,const_100)|multiply(n0,#0)|
gain
C
a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 13 brown mice in the experiment , how many mice in total are in the experiment ?
"let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 13 = > m = 39 answer a"
a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 10
a
subtract(divide(13, divide(2, 3)), 13)
divide(n0,n1)|divide(n2,#0)|subtract(#1,n2)|
general
A
a tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
"the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 2,500 = 7,500 gallons and sodium chloride is 700 gallons ( 7 % of initial solution of 10,000 gallons ) then sodium chloride is 700 / 7,500 * 100 = ~ 9.33 % of the remaining solution of 7,500 gallons . answer : c ."
a ) 1.25 % , b ) 3.75 % , c ) 9.33 % , d ) 10.67 % , e ) 11.7 %
c
multiply(divide(multiply(multiply(const_100, const_100), divide(7, const_100)), subtract(multiply(const_100, const_100), add(multiply(add(const_2, const_3), multiply(multiply(add(const_2, const_3), const_2), const_100)), multiply(add(const_2, const_3), const_100)))), const_100)
add(const_2,const_3)|divide(n1,const_100)|multiply(const_100,const_100)|multiply(#1,#2)|multiply(#0,const_2)|multiply(#0,const_100)|multiply(#4,const_100)|multiply(#0,#6)|add(#7,#5)|subtract(#2,#8)|divide(#3,#9)|multiply(#10,const_100)|
gain
C
john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 5 % and the mobile phone at a profit of 10 % . overall how much he make a profit .
let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 5 / 100 ) = 15000 - 750 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 750 + 800 = rs . 50 as this is positive , an overall profit of rs . 50 was made . d
a ) s . 90 , b ) s . 120 , c ) s . 200 , d ) s . 50 , e ) s . 290
d
subtract(multiply(10, divide(8000, const_100)), multiply(5, divide(15000, const_100)))
divide(n1,const_100)|divide(n0,const_100)|multiply(n3,#0)|multiply(n2,#1)|subtract(#2,#3)
gain
D
a cube of edge 15 cm is imersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in waer level .
sol . increase in volume = volume of the cube = ( 15 * 15 * 15 ) cm ³ . ∴ rise in water level = [ volume / area ] = [ 15 * 15 * 15 / 20 * 15 ] cm = 11.25 cm . answer a
['a ) 11.25 cm .', 'b ) 12.25 cm', 'c ) 13.25 cm', 'd ) 14.25 cm', 'e ) none of these']
a
divide(volume_cube(15), multiply(15, 20))
multiply(n0,n1)|volume_cube(n0)|divide(#1,#0)
geometry
A
a sum was put a simple interest at a certain rate for 5 years . had it been put at 2 % higher rate , it would have fetched rs . 250 more . the sum is :
"explanation : let the sub be rs . x and the initial rate be r % . then x Γ£ β€” ( r + 2 ) Γ£ β€” 5 / 100 Γ’ Λ† ’ x Γ£ β€” r Γ£ β€” 5 / 100 = 250 Γ’ ‑ ’ x Γ£ β€” 2 Γ£ β€” 5 / 100 = 250 Γ’ ‑ ’ x Γ£ β€” 5 / 100 = 125 Γ’ ‑ ’ 5 x = 12500 Γ’ ‑ ’ x = 2500 answer : option b"
a ) s . 2000 , b ) s . 2500 , c ) s . 3000 , d ) s . 3500 , e ) s . 4000
b
multiply(divide(divide(250, 5), 2), const_100)
divide(n2,n0)|divide(#0,n1)|multiply(#1,const_100)|
gain
B
10 machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ?
"another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 10 = 15 so we need 15 - 10 = 5 more machines . answer : d"
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 8
d
subtract(divide(multiply(10, add(const_4, const_1)), 12), add(const_4, const_1))
add(const_1,const_4)|multiply(n0,#0)|divide(#1,n1)|subtract(#2,#0)|
physics
D
a train 500 m long can cross an electric pole in 20 sec and then find the speed of the train ?
"length = speed * time speed = l / t s = 500 / 20 s = 25 m / sec speed = 25 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 90 kmph answer : d"
a ) 87 kmph , b ) 97 kmph , c ) 72 kmph , d ) 90 kmph , e ) 19 kmph
d
divide(divide(500, const_1000), divide(20, const_3600))
divide(n0,const_1000)|divide(n1,const_3600)|divide(#0,#1)|
physics
D
out of 3 consecutive odd numbers 9 times the first number is equal to addition of twice the third number and adding 9 to twice the second . what is the first number ?
description : = > 9 x = 2 ( x + 2 ) + 9 + 2 ( x + 4 ) = > 9 x = 4 x + 21 = > 5 x = 21 x = 21 / 5 answer e
a ) 20 / 21 , b ) 23 / 25 , c ) 24 / 23 , d ) 22 / 5 , e ) 21 / 5
e
divide(subtract(multiply(9, 3), multiply(const_2, const_3)), add(3, const_2))
add(n0,const_2)|multiply(n0,n1)|multiply(const_2,const_3)|subtract(#1,#2)|divide(#3,#0)
general
E
a palindrome is a word or a number that reads the same forward and backward . for example , 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits 1 , 2 , 3 , 4 , 5 , and 6 , how many palindromes are possible ?
"there are 6 choices for each of the first three digits . the number of possible palindromes is 6 ^ 3 = 216 . the answer is d ."
a ) 36 , b ) 96 , c ) 132 , d ) 216 , e ) 256
d
power(5, 3)
power(n2,n5)|
general
D
if the wheel is 21 cm then the number of revolutions to cover a distance of 1056 cm is ?
"2 * 22 / 7 * 21 * x = 1056 = > x = 8 answer : a"
a ) 8 , b ) 27 , c ) 10 , d ) 7 , e ) 19
a
divide(1056, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 21))
multiply(const_100,const_3)|multiply(const_1,const_10)|add(#0,#1)|add(#2,const_4)|divide(#3,const_100)|multiply(#4,const_2)|multiply(n0,#5)|divide(n1,#6)|
physics
A
there are 16 bees in the hive , then 8 more fly . how many bees are there in all ?
16 + 8 = 24 . answer is d .
a ) 7 , b ) 33 , c ) 12 , d ) 24 , e ) 25
d
add(16, 8)
add(n0,n1)|
general
D
if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 18 - m ) then m = ?
"2 m = 18 - m 3 m = 18 m = 6 the answer is c ."
a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
c
divide(18, add(2, const_1))
add(n0,const_1)|divide(n3,#0)|
general
C
45 % of the employees of a company are men . 60 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
"no of employees = 100 ( say ) men = 45 women = 55 men speaking french = 0.6 * 45 = 27 employees speaking french = 0.55 * 100 = 55 therefore women speaking french = 55 - 42 = 13 and women not speaking french = 55 - 13 = 42 % of women not speaking french = 42 / 55 * 100 = 76.36 % answer c"
a ) 4 % , b ) 10 % , c ) 76.36 % , d ) 90.16 % , e ) 20 %
c
multiply(divide(subtract(divide(subtract(const_100, 45), const_100), subtract(divide(40, const_100), multiply(divide(45, const_100), divide(60, const_100)))), divide(subtract(const_100, 45), const_100)), const_100)
divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|subtract(const_100,n0)|divide(#3,const_100)|multiply(#1,#2)|subtract(#0,#5)|subtract(#4,#6)|divide(#7,#4)|multiply(#8,const_100)|
gain
C
jake took a bus from home to market , that travels at 10 kmph . while walking back at 2 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 50 kmph . find the average speed .
let the distance be 2 x ( one way ) time taken by bus = 2 x / 10 , by walking = x / 2 , by cycling = x / 50 hours : . average speed = total distance / total time = 2 x / x / 5 + x / 2 + x / 50 = 2 * 60 / 12 + 30 + 1.2 = 1.67 answer : b
a ) 1.17 kmph , b ) 1.67 kmph , c ) 0.69 kmph , d ) 1.45 kmph , e ) none of these
b
divide(multiply(50, 2), add(add(10, 2), 50))
add(n0,n1)|multiply(n1,n2)|add(n2,#0)|divide(#1,#2)
physics
B
if x / ( 12 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
"x / ( 12 p ) = odd prime number x = odd prime number * 11 p least value of x = lowest odd prime number * 11 * lowest value of p = 3 * 12 * 2 = 72 answer e"
a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 72
e
multiply(multiply(const_3, 12), const_2)
multiply(n0,const_3)|multiply(#0,const_2)|
general
E
30 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
"capacity of the tank = 30 Γ£ β€” 13.5 = 405 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 405 Γ’  β€ž 9 = 45 answer c"
a ) 30 , b ) 32 , c ) 45 , d ) data inadequate , e ) none of these
c
divide(multiply(13.5, 30), 9)
multiply(n0,n1)|divide(#0,n2)|
physics
C
the sum of all possible two digit numbers formed from 3 different one digit natural numbers when divided by the sum of the original 3 numbers is equal to ?
let the one digit numbers x , y , z sum of all possible two digit numbers = ( 10 x + y ) + ( 10 x + z ) + ( 10 y + x ) + ( 10 y + z ) + ( 10 z + x ) + ( 10 z + y ) = 22 ( x + y + z ) therefore sum of all possible two digit numbers when divided by sum of one digit numbers gives 22 . answer e
a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
e
multiply(divide(add(multiply(3, const_10), const_3), 3), const_2)
multiply(n0,const_10)|add(#0,const_3)|divide(#1,n0)|multiply(#2,const_2)
general
E
in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 48 people were made to stand in a column , how many columns could be formed ?
16 * 30 = 48 * n n = 10 the answer is a .
a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
a
divide(30, divide(48, 16))
divide(n2,n1)|divide(n0,#0)
other
A
the average weight of 16 girls in a class is 50.25 kg and that of the remaining 8 girls is 45.15 kg . find the average weights of all the girls in the class .
required average = ( 50.25 x 16 + 45.15 x 8 ) / ( 16 + 8 ) = ( 804 + 361.20 ) / 24 = 1165.20 / 24 = 48.55 kg answer is a
a ) a ) 48.55 , b ) b ) 49 , c ) c ) 51 , d ) d ) 61 , e ) e ) 62
a
divide(add(multiply(16, 50.25), multiply(8, 45.15)), add(16, 8))
add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)
general
A
in a certain accounting class of 90 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 65 % , and the students on the make - up date had an average score of 85 % , what was the average score for the entire class ?
"70 % of the students took the final exam on the assigned day - - > 0.7 * 90 = 63 students took the final exam on the assigned day , with an average score of 65 . the rest of the students took the exam on a make - up date - - > 90 - 63 = 27 students took the exam on a make - up date , with an average score of 85 . ( average score ) = ( sum of the scores ) / ( total students ) = ( 63 * 65 + 27 * 85 ) / 90 = 71 . answer : b ."
a ) 68 % , b ) 71 % , c ) 73 % , d ) 75 % , e ) 79 %
b
divide(add(multiply(70, 65), multiply(85, subtract(90, 70))), 90)
multiply(n1,n2)|subtract(n0,n1)|multiply(n3,#1)|add(#0,#2)|divide(#3,n0)|
general
B
the racing magic takes 90 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
"time taken by racing magic to make one circle = 90 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 90 seconds = 90 seconds time taken for them to meet at the starting point for the second time = 2 * 90 sec = 180 seconds = 3 mins answer a"
a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
a
multiply(divide(multiply(multiply(90, divide(90, 40)), const_2), 90), const_2)
divide(n0,n1)|multiply(#0,n0)|multiply(#1,const_2)|divide(#2,n0)|multiply(#3,const_2)|
physics
A