Problem
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Rationale
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37
300
correct
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annotated_formula
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linear_formula
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6 values
16 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
"required number of machines = 16 * 10 / 40 = 4 answer is c"
a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5
c
divide(multiply(16, 10), 40)
multiply(n0,n1)|divide(#0,n2)|
physics
the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 15000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
"answer average salary = 8000 + 5000 + 15000 + 7000 + 9000 / 5 = rs . 8800 correct option : c"
a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8800 , d ) rs . 9000 , e ) none
c
divide(add(add(add(add(8000, 5000), 15000), 7000), 9000), add(const_4, const_1))
add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)|
general
if n is a prime number greater than 19 , what is the remainder when n ^ 2 is divided by 12 ?
"there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 19 , square it and see what would be the remainder upon division of it by 12 . n = 23 - - > n ^ 2 = 529 - - > remainder upon division 529 by 12 is 1 . a...
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
b
subtract(power(add(19, 2), 2), multiply(12, const_4))
add(n0,n1)|multiply(n2,const_4)|power(#0,n1)|subtract(#2,#1)|
general
total number of 4 digit number do not having the digit 3 or 6 .
answer : d
a ) 22 , b ) 28 , c ) 27 , d ) 19 , e ) 11
d
add(add(add(add(6, 3), 4), 3), 3)
add(n1,n2)|add(n0,#0)|add(n1,#1)|add(n1,#2)
general
the average weight of a , b and c is 43 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
"let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 129 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 37 . b ' s wei...
a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 36 kg , e ) 37 kg
e
subtract(add(multiply(40, const_2), multiply(43, const_2)), multiply(43, const_3))
multiply(n1,const_2)|multiply(n2,const_2)|multiply(n0,const_3)|add(#0,#1)|subtract(#3,#2)|
general
the length of rectangle is thrice its breadth and its perimeter is 80 m , find the area of the rectangle ?
"2 ( 3 x + x ) = 80 l = 36 b = 10 lb = 36 * 10 = 360 a"
a ) 360 , b ) 376 , c ) 299 , d ) 276 , e ) 111
a
multiply(multiply(divide(80, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(80, add(multiply(const_3, const_2), multiply(const_1, const_2))))
multiply(const_2,const_3)|multiply(const_1,const_2)|add(#0,#1)|divide(n0,#2)|multiply(#3,const_3)|multiply(#3,#4)|
geometry
a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability r that both selected dogs are not littermates ?
"we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one ...
a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
c
divide(const_5, 6)
divide(const_5,n1)|
other
a train running at the speed of 60 km / hr crosses a pole in 21 seconds . what is the length of the train ?
"speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 21 ) m = 350 m . answer : a"
a ) 350 m , b ) 278 m , c ) 876 m , d ) 150 m , e ) 267 m
a
multiply(divide(multiply(60, const_1000), const_3600), 21)
multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|
physics
a number when divided by 214 gives a remainder 35 , what remainder will be obtained by dividing the same number 14 ?
"explanation : 214 + 35 = 249 / 14 = 11 ( remainder ) answer : c"
a ) 7 , b ) 10 , c ) 11 , d ) 2 , e ) 3
c
subtract(35, multiply(14, const_2))
multiply(n2,const_2)|subtract(n1,#0)|
general
a number whose fifth part increased by 3 is equal to its fourth part diminished by 3 is ?
"answer let the number be n . then , ( n / 5 ) + 3 = ( n / 4 ) - 3 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 6 â ‡ ’ ( 5 n - 4 n ) / 20 = 6 â ˆ ´ n = 120 option : a"
a ) 120 , b ) 180 , c ) 200 , d ) 220 , e ) none
a
divide(add(3, 3), subtract(divide(const_1, 3), divide(const_1, add(const_1, 3))))
add(n0,n1)|add(const_1,n0)|divide(const_1,n0)|divide(const_1,#1)|subtract(#2,#3)|divide(#0,#4)|
general
a military camp has a food reserve for 250 personnel for 40 days . if after 15 days 50 more personnel are added to the camp , find the number of days the reserve will last for ?
explanation : as the camp has a reserve for 250 personnel that can last for 40 days , after 10 days the reserve left for 250 personnel is for 30 days . now 50 more personnel are added in the camp . hence , the food reserve for 300 personnel will last for : 250 : 300 : : x : 30 … … . . ( it is an indirect proportion as ...
a ) 25 , b ) 67 , c ) 26 , d ) 29 , e ) 18
a
add(divide(multiply(250, subtract(40, 15)), add(250, 50)), const_3)
add(n0,n3)|subtract(n1,n2)|multiply(n0,#1)|divide(#2,#0)|add(#3,const_3)
general
what is x if x + 2 y = 12 and y = 3 ?
"x = 12 - 2 y x = 12 - 6 . x = 6 answer : c"
a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2
c
subtract(12, multiply(2, 3))
multiply(n0,n2)|subtract(n1,#0)|
general
in how many years rs 200 will produce the same interest at 10 % as rs . 1000 produce in 2 years at 12 %
explanation : clue : firstly we need to calculate the si with prinical 1000 , time 2 years and rate 12 % , it will be rs . 240 then we can get the time as time = ( 100 * 240 ) / ( 200 * 10 ) = 12 option d
a ) 13 , b ) 9 , c ) 11 , d ) 12 , e ) 10
d
divide(multiply(divide(multiply(1000, 12), const_100), 2), multiply(divide(10, const_100), 200))
divide(n1,const_100)|multiply(n2,n4)|divide(#1,const_100)|multiply(n0,#0)|multiply(n3,#2)|divide(#4,#3)
gain
a store ’ s selling price of $ 2240 for a certain computer would yield a profit of 40 percent of the store ’ s cost for the computer . what selling price would yield a profit of 60 percent of the computer ’ s cost ?
"1.4 x = 2240 x = 2240 / 1.4 so , 1.6 x = 2240 * 1.6 / 1.4 = 2560 answer : - c"
a ) $ 2400 , b ) $ 2464 , c ) $ 2560 , d ) $ 2732 , e ) $ 2800
c
multiply(2240, divide(add(const_100, 60), add(const_100, 40)))
add(n2,const_100)|add(n1,const_100)|divide(#0,#1)|multiply(n0,#2)|
gain
a person buys 18 local tickets for rs 110 . each first class ticket costs rs 10 and each second class ticket costs rs 3 . what will another lot of 18 tickets in which the numbers of first class and second class tickets are interchanged cost ?
explanation : let , there are x first class ticket and ( 18 - x ) second class tickets . then , 110 = 10 x + 3 ( 18 − x ) . = > 110 = 10 x + 54 − 3 x . = > 7 x = 56 . = > x = 8 . if the number of the first class and second class tickets are interchanged , then the total cost would be 10 × 10 + 3 × 8 = 124 . answer : d
a ) 112 , b ) 118 , c ) 121 , d ) 124 , e ) none of these
d
add(multiply(divide(subtract(110, multiply(18, 3)), subtract(10, 3)), 3), multiply(10, 10))
multiply(n0,n3)|multiply(n2,n2)|subtract(n2,n3)|subtract(n1,#0)|divide(#3,#2)|multiply(n3,#4)|add(#5,#1)
physics
for all numbers a and b , the operationis defined by ab = ( a + 2 ) ( b – 3 ) . if 3 y = – 30 , then y =
( 3 + 2 ) ( y - 3 ) = - 30 . . x - 3 = - 6 . . x = - 3 c
a ) – 15 , b ) – 6 , c ) - 3 , d ) 6 , e ) 15
c
negate(divide(30, 3))
divide(n3,n1)|negate(#0)
general
a train 250 m long running at 72 kmph crosses a platform in 40 sec . what is the length of the platform ?
"d = 72 * 5 / 18 = 40 = 800 â € “ 250 = 450 m answer : a"
a ) 450 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m
a
subtract(multiply(40, multiply(72, const_0_2778)), 250)
multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)|
physics
out of 3 given numbers , the first one is twice the second and 3 times the third . if the average of these numbers is 88 , then the difference between first and third is .
sum of three number is = 88 * 3 = 264 let three numbers are a , b , c and a is the highest and c is the lowest then , 2 b = a so b = a / 2 and 3 c = a so c = a / 3 we can write , a + b + c = 264 a + a / 2 + a / 3 = 264 11 a / 6 = 264 a = 144 so , c = 144 / 3 = 48 so there difference is = 144 - 48 = 96 answer d
a ) 92 , b ) 39 , c ) 87 , d ) 96 , e ) none
d
add(88, add(const_4, const_4))
add(const_4,const_4)|add(n2,#0)
general
an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 32 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
"without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 40 % , thus he must pay slightly more than $ 60 . only answer choice e fits . answer : e ."
a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 70.00
e
multiply(subtract(10, divide(multiply(32, 8), const_100)), 10)
multiply(n2,n4)|divide(#0,const_100)|subtract(n0,#1)|multiply(#2,n0)|
gain
r is the set of positive odd integers less than 200 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
"r is the set of positive odd integers less than 200 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 1,3 , 5,7 , 9,11 , 13,15 . . . s = 1 , 9,25 , 49,81 . . . numbers : 1 , 9 , 25 , 49 , 81 , 121 , and 169 are odd integers ( less than 200 ) that ...
a ) none , b ) two , c ) four , d ) five , e ) seven
e
subtract(subtract(200, const_4), const_4)
subtract(n0,const_4)|subtract(#0,const_4)|
physics
the cost to park a car in a certain parking garage is $ 9.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
"total cost of parking for 9 hours = 9 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 9 + 7 * 1.75 = 21.25 thus the average parking price = 21.25 / 9 = 2.36 $ d is the correct answer ."
a ) $ 1.09 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.36 , e ) $ 2.50
d
divide(add(9.00, multiply(1.75, subtract(9, 2))), 9)
subtract(n4,n1)|multiply(n2,#0)|add(n0,#1)|divide(#2,n4)|
general
find the compound interest on $ 30000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
"principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 30000 * ( 1 + 2 / 100 ) ^ 4 = 30000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 32472.96 c . i . = 32472.96 - 10000 = $ 2472.96 answer is d"
a ) $ 645.56 , b ) $ 824.32 , c ) $ 954.26 , d ) $ 2472.96 , e ) $ 1020.45
d
subtract(multiply(power(add(divide(divide(4, const_100), 2), const_1), 4), 30000), 30000)
divide(n2,const_100)|divide(#0,n1)|add(#1,const_1)|power(#2,n2)|multiply(n0,#3)|subtract(#4,n0)|
gain
the average waight of a , b , c is 45 kg . the avg wgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .
". let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer is e ."
a ) 34 kg , b ) 40 kg , c ) 42 kg , d ) 41 kg , e ) 31 kg
e
subtract(multiply(40, const_2), subtract(multiply(45, const_3), multiply(43, const_2)))
multiply(n1,const_2)|multiply(n0,const_3)|multiply(n2,const_2)|subtract(#1,#2)|subtract(#0,#3)|
general
of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents z watch all of the shows ?
oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is z = 3.5 % of 600 , is 21 . d is...
a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21
d
divide(subtract(subtract(add(add(multiply(600, divide(35, const_100)), multiply(600, divide(40, const_100))), multiply(600, divide(50, const_100))), 600), multiply(divide(18, const_100), 600)), 2)
divide(n1,const_100)|divide(n2,const_100)|divide(n3,const_100)|divide(n5,const_100)|multiply(n0,#0)|multiply(n0,#1)|multiply(n0,#2)|multiply(n0,#3)|add(#4,#5)|add(#8,#6)|subtract(#9,n0)|subtract(#10,#7)|divide(#11,n6)
gain
john ' s marks wrongly entered as 82 instead of 62 . due to that the average marks for the class got increased by half ( 1 / 2 ) . the number of john in the class is ?
otal increase in marks = x x 1 = x 2 2 x / 2 = ( 82 - 62 ) x / 2 = 40 x = 80 . c
a ) 70 , b ) 78 , c ) 80 , d ) 84 , e ) 90
c
multiply(divide(subtract(82, 62), divide(1, 2)), 2)
divide(n2,n3)|subtract(n0,n1)|divide(#1,#0)|multiply(n3,#2)
general
a train running at the speed of 90 km / hr crosses a pole in 10 seconds . find the length of the train .
"speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time 25 * 10 = 250 meter answer : c"
a ) 150 , b ) 180 , c ) 250 , d ) 200 , e ) 225
c
multiply(divide(multiply(90, const_1000), const_3600), 10)
multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|
physics
milk is poured from a full rectangular container with dimensions 4 inches by 9 inches by 10 inches into a cylindrical container with a diameter of 6 inches . if the milk does not overflow , how many inches high will the milk reach ?
let the height of level of milk in the cylinder = h since , volume of milk is constant . therefore 4 * 9 * 10 = π π * 3 ^ 2 * h = > π * h = 40 = > h = 40 / ( π ) answer c
['a ) 60 / π', 'b ) 24', 'c ) 40 / π', 'd ) 10', 'e ) 3 π']
c
divide(divide(volume_rectangular_prism(4, 9, 10), 9), const_pi)
volume_rectangular_prism(n0,n1,n2)|divide(#0,n1)|divide(#1,const_pi)
geometry
if 65 % of a number is greater than 5 % of 60 by 23 , what is the number ?
"explanation : 65 / 100 * x - 5 / 100 * 60 = 23 65 / 100 * x - 3 = 23 65 / 100 * x = 26 x = 26 * 100 / 65 x = 40 answer : option b"
a ) 65 , b ) 40 , c ) 55 , d ) 30 , e ) 60
b
multiply(const_100, divide(add(23, multiply(divide(60, const_100), 5)), 65))
divide(n2,const_100)|multiply(n1,#0)|add(n3,#1)|divide(#2,n0)|multiply(#3,const_100)|
gain
8 men and 2 boys working together can do 4 times as much work as a man and a boy . working capacity of man and boy is in the ratio
explanation : let 1 man 1 day work = x 1 boy 1 day work = y then 8 x + 2 y = 4 ( x + y ) = > 4 x = 2 y = > x / y = 2 / 4 = > x : y = 1 : 2 option a
a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 1 , d ) 2 : 3 , e ) none of these
a
divide(subtract(4, 2), subtract(8, 4))
subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)
other
the difference between the place value and the face value of 7 in the numeral 856973 is
( place value of 7 ) - ( face value of 7 ) = ( 70 - 7 ) = 63 answer : option a
a ) 63 , b ) 6973 , c ) 5994 , d ) 6084 , e ) none of these
a
subtract(multiply(const_10, 7), 7)
multiply(n0,const_10)|subtract(#0,n0)
general
if a person walks at 15 km / hr instead of 5 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
"let the actual distance traveled be x km . then , x / 5 = ( x + 20 ) / 15 10 x - 100 = > x = 10 km . answer : d"
a ) 50 km , b ) 76 km , c ) 18 km , d ) 10 km , e ) 97 km
d
multiply(5, divide(20, subtract(15, 5)))
subtract(n0,n1)|divide(n2,#0)|multiply(n1,#1)|
general
the diameter of a cylindrical tin is 4 cm and height is 5 cm . find the volume of the cylinder ?
"r = 2 h = 5 π * 2 * 2 * 5 = 20 π cc answer : c"
a ) 33 , b ) 45 , c ) 20 , d ) 77 , e ) 21
c
divide(volume_cylinder(divide(4, const_2), 5), const_pi)
divide(n0,const_2)|volume_cylinder(#0,n1)|divide(#1,const_pi)|
geometry
the sum of 3 consecutive numbers is definitely
"if 1 st term is x : x + ( x + 1 ) + ( x + 2 ) = 3 x + 3 - - - > always divisible by 3 if 2 nd term is x : ( x - 1 ) + x + ( x + 1 ) = 3 x - - - > always divisible by 3 if 3 rd term is x : ( x - 2 ) + ( x - 1 ) + x = 3 x - 3 - - - > always divisible by 3 answer : d"
a ) positive . , b ) divisible by 2 . , c ) divisible by 4 . , d ) divisible by 3 . , e ) divisible by 5 .
d
add(divide(subtract(3, const_1), multiply(const_2, const_1)), const_1)
multiply(const_1,const_2)|subtract(n0,const_1)|divide(#1,#0)|add(#2,const_1)|
physics
for all even integers n , h ( n ) is defined to be the sum of the even integers between 6 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?
"concept : when terms are in arithmetic progression ( a . p . ) i . e . terms are equally spaced then mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 6 + 18 ) / 2 ] * 7 = 84 h ( 10 ) = ( 6 + 10 ) / 2 ] * 3 = 24 h ( 18 ) / h ( 10 ) = ( 84 ) / ( 24 ) ~ 4 answer : b"
a ) 1.8 , b ) 4 , c ) 6 , d ) 18 , e ) 60
b
divide(divide(multiply(add(18, 6), add(divide(subtract(18, 6), const_2), const_1)), const_2), divide(multiply(add(divide(subtract(10, 6), const_2), const_1), add(6, 10)), const_2))
add(n0,n1)|add(n0,n2)|subtract(n1,n0)|subtract(n2,n0)|divide(#2,const_2)|divide(#3,const_2)|add(#4,const_1)|add(#5,const_1)|multiply(#0,#6)|multiply(#7,#1)|divide(#8,const_2)|divide(#9,const_2)|divide(#10,#11)|
general
20 % of a 6 litre solution and 60 % of 4 litre solution are mixed . what percentage of the mixture of solution
20 % of 6 litre is ( 6 * 20 / 100 ) = 1.2 litre 60 % of 4 litre is ( 60 * 4 / 100 ) = 2.4 litre the mixture is 3.6 litre so the percentage is ( 3.6 * 100 / 10 ) = 36 % answer : a
a ) 36 % , b ) 35 % , c ) 34 % , d ) 33 % , e ) 32 %
a
multiply(divide(add(divide(multiply(60, 4), const_100), divide(multiply(20, 6), const_100)), add(6, 4)), const_100)
add(n1,n3)|multiply(n2,n3)|multiply(n0,n1)|divide(#1,const_100)|divide(#2,const_100)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)
gain
population of a city decreases by 10 % at the end of first year and increases by 10 % at the end of second year and again decreases by 10 % at the end of third year . if the population of the city at the end of third year is 4455 , then what was the population of the city at the beginning of the first year ?
m . f = 90 / 100 * 110 * 100 * 90 / 100 = 81 * 11 / 1000 population before 3 yrs = i . q / m . f = 4455 * 1000 / 81 * 11 = 5000 answer : a
a ) 5000 , b ) 4500 , c ) 4950 , d ) 1000 , e ) 2000
a
divide(4455, multiply(multiply(subtract(const_1, divide(10, const_100)), add(const_1, divide(10, const_100))), subtract(const_1, divide(10, const_100))))
divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#0)|multiply(#1,#2)|multiply(#3,#2)|divide(n3,#4)
gain
a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many days was he absent ?
30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = 10 b
a ) 8 , b ) 10 , c ) 15 , d ) 17 , e ) 19
b
subtract(30, divide(add(multiply(7.5, 30), 425), add(7.5, 25)))
add(n1,n2)|multiply(n0,n2)|add(n3,#1)|divide(#2,#0)|subtract(n0,#3)
physics
stalin and heather are 20 miles apart and walk towards each other along the same route . stalin walks at constant rate that is 1 mile per hour faster than heather ' s constant rate of 5 miles / hour . if heather starts her journey 20 minutes after stalin , how far from the original destination has heather walked when t...
original distance between s and h = 20 miles . speed of s = 5 + 1 = 6 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 20 / 60 = t + 2 / 6 hours . now , the total distances traveled by s and h = 20 miles - - - > 6 * ( t + 2 / 6 ) + 5 * t = 20 - - - > t = 8 / 11 hours . thus h has...
a ) 4 miles , b ) 6 miles , c ) 9 miles , d ) 10 miles , e ) 12 mile
a
divide(multiply(divide(subtract(20, multiply(divide(add(1, 5), const_60), 20)), add(5, add(1, 5))), 5), const_2)
add(n1,n2)|add(n2,#0)|divide(#0,const_60)|multiply(n0,#2)|subtract(n0,#3)|divide(#4,#1)|multiply(n2,#5)|divide(#6,const_2)
physics
what is the square root of 16 ?
"4 x 4 = 16 answer b"
a ) 8 , b ) 4 , c ) 35 , d ) 42 , e ) 86
b
circle_area(divide(16, multiply(const_2, const_pi)))
multiply(const_2,const_pi)|divide(n0,#0)|circle_area(#1)|
other
a bag marked at $ 240 is sold for $ 120 . the rate of discount is ?
"rate of discount = 120 / 240 * 100 = 50 % answer is d"
a ) 10 % , b ) 25 % , c ) 20 % , d ) 50 % , e ) 45 %
d
multiply(divide(subtract(240, 120), 240), const_100)
subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)|
gain
the average weight of 8 person ' s increases by 2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
"total weight increased = ( 8 x 2 ) kg = 16 kg . weight of new person = ( 65 + 16 ) kg = 81 kg . c )"
a ) 70 kg , b ) 80 kg , c ) 81 kg , d ) 90 kg , e ) 91 kg
c
add(multiply(8, 2), 65)
multiply(n0,n1)|add(n2,#0)|
general
the mean proportional between 4 and 9 is ?
"7 / 20 * 100 = 35 answer : b"
a ) 33 , b ) 77 , c ) 35 , d ) 88 , e ) 29
b
sqrt(multiply(4, 9))
multiply(n0,n1)|sqrt(#0)|
general
a man buy a book in rs 50 & sale it rs 100 . what is the rate of profit ? ? ?
"cp = 50 sp = 100 profit = 100 - 50 = 50 % = 50 / 50 * 100 = 100 % answer : b"
a ) 10 % , b ) 100 % , c ) 30 % , d ) 25 % , e ) 28 %
b
multiply(divide(subtract(100, 50), 50), const_100)
subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)|
gain
a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 6 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
"1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 6 = 720 answer : c"
a ) 480 , b ) 287 , c ) 720 , d ) 270 , e ) 927
c
multiply(24, 20)
multiply(n0,n2)|
physics
a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 20 speak english well , while 60 of them do not speak english . if 60 % of students do not speak french , how many students were surveyed ?
"number of students who speak french are 60 + 20 = 80 of total students , the percentage of students who do not speak french was 60 % - - > percentage of who do is 40 % 80 - - - - - - - 40 % x - - - - - - - 100 % x = 80 * 100 / 40 = 200 = number of all students answer is e"
a ) 250 , b ) 225 , c ) 175 , d ) 195 , e ) 200
e
divide(add(20, 60), divide(subtract(const_100, 60), const_100))
add(n0,n1)|subtract(const_100,n2)|divide(#1,const_100)|divide(#0,#2)|
gain
the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.2 kg . the weight of the new student is
"exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.2 weight of the new student = ( 30 * 27.2 – 29 * 28 ) = 816 - 812 = 4 answer : a"
a ) 4 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) none of these
a
subtract(multiply(add(29, const_1), 27.2), multiply(29, 28))
add(n0,const_1)|multiply(n0,n1)|multiply(n2,#0)|subtract(#2,#1)|
general
the average expenditure of a labourer for 6 months was 80 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i
"income of 6 months = ( 6 × 80 ) – debt = 480 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 750 average monthly income = 750 ÷ 10 = 75 answer c"
a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 80
c
divide(add(add(multiply(80, 6), multiply(60, 4)), 30), add(6, 4))
add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|add(n4,#3)|divide(#4,#0)|
general
the length of a rectangle is halved , whileits breadth is tripled . wat is the % change in area ?
"let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
a ) 40 % , b ) 45 % , c ) 50 % , d ) 65 % , e ) 70 %
c
multiply(divide(subtract(multiply(const_3, divide(const_1, const_2)), const_1), const_1), const_100)
divide(const_1,const_2)|multiply(#0,const_3)|subtract(#1,const_1)|divide(#2,const_1)|multiply(#3,const_100)|
geometry
a man saves 25 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 10 % , he is only able to save rs . 175 per month . what is his monthly salary ?
"income = rs . 100 expenditure = rs . 75 savings = rs . 25 present expenditure 75 + 75 * ( 10 / 100 ) = rs . 82.5 present savings = 100 – 82.50 = rs . 17.50 if savings is rs . 17.50 , salary = rs . 100 if savings is rs . 175 , salary = 100 / 17.5 * 175 = 1000 answer : a"
a ) rs . 1000 , b ) rs . 2000 , c ) rs . 1500 , d ) rs . 3000 , e ) rs . 3100
a
divide(multiply(175, const_100), subtract(const_100, add(subtract(const_100, 25), multiply(subtract(const_100, 25), divide(10, const_100)))))
divide(n1,const_100)|multiply(n2,const_100)|subtract(const_100,n0)|multiply(#0,#2)|add(#3,#2)|subtract(const_100,#4)|divide(#1,#5)|
general
a 15 % stock yielding 12 % is quoted at :
"income of rs 12 on investment of rs 100 income of rs 15 on investment of ? = ( 15 * 100 ) / 12 = 125 answer : d"
a ) s . 83.33 , b ) s . 110 , c ) s . 112 , d ) s . 125 , e ) s . 140
d
multiply(divide(const_100, 12), 15)
divide(const_100,n1)|multiply(n0,#0)|
gain
on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 2 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on september 1 than were in stock on january 1 ?
"jan 1 = c feb 1 = c - 2 march 1 = c - 4 april 1 = c - 8 may 1 = c - 10 june 1 = c - 12 july 1 = c - 14 aug 1 = c - 16 sept 1 = c - 18 difference between stock on september 1 than were in stock on january 1 will be - c - ( c - 18 ) = 18 hence answer will be ( a )"
a ) 18 , b ) 12 , c ) 20 , d ) 32 , e ) 36
a
multiply(subtract(const_10, 1), 2)
subtract(const_10,n0)|multiply(n1,#0)|
gain
having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.92 at the candy store . what is john ’ s weekly allowance ?
"x = 3 x / 5 + 1 / 3 * 2 x / 5 + 92 4 x / 15 = 92 x = 345 = $ 3.45 the answer is d ."
a ) $ 2.55 , b ) $ 2.85 , c ) $ 3.15 , d ) $ 3.45 , e ) $ 3.75
d
divide(0.92, subtract(const_1, add(divide(3, 5), multiply(divide(const_1, 3), subtract(const_1, divide(3, 5))))))
divide(n0,n1)|divide(const_1,n0)|subtract(const_1,#0)|multiply(#1,#2)|add(#0,#3)|subtract(const_1,#4)|divide(n2,#5)|
general
a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1300 plus 2.5 % commission on all sales exceeding rs . 4000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
[ 1300 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 18000 answer : c
a ) 12028 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 18000
c
divide(subtract(subtract(multiply(const_100, const_10), multiply(4000, divide(2.5, const_100))), 600), divide(2.5, const_100))
divide(n2,const_100)|multiply(const_10,const_100)|multiply(n3,#0)|subtract(#1,#2)|subtract(#3,n4)|divide(#4,#0)
general
a sum fetched a total simple interest of 4020.75 at the rate of 9 % . p . a . in 5 years . what is the sum ?
"principal = ( 100 x 4020.75 ) / ( 9 x 5 ) = 402075 / 45 = 8935 . answer e"
a ) 5768 , b ) 8925 , c ) 2345 , d ) 6474 , e ) 8935
e
divide(divide(multiply(4020.75, const_100), 9), 5)
multiply(n0,const_100)|divide(#0,n1)|divide(#1,n2)|
gain
two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 28 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
"1 h - - - - - 5 ? - - - - - - 60 12 h rs = 28 + 21 = 49 t = 12 d = 49 * 12 = 588 answer : d"
a ) 457 km , b ) 444 km , c ) 547 km , d ) 588 km , e ) 653 km
d
add(multiply(divide(60, subtract(21, 28)), 28), multiply(divide(60, subtract(21, 28)), 21))
subtract(n1,n0)|divide(n2,#0)|multiply(n0,#1)|multiply(n1,#1)|add(#2,#3)|
physics
exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 11 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
the total number of the people in the room must be a multiple of both 7 and 11 ( in order 3 / 7 and 5 / 11 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 11 , which is 77 . since , the total number of the people in the room is greater than 50 and less than 100 ...
a ) 21 , b ) 35 , c ) 33 , d ) 60 , e ) 65
c
divide(multiply(multiply(7, 11), 3), 7)
multiply(n1,n4)|multiply(n0,#0)|divide(#1,n1)
general
one night 15 percent of the female officers on a police force were on duty . if 300 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
"let total number of female officers in the police force = f total number of officers on duty on that night = 300 number of female officers on duty on that night = 300 / 2 = 150 ( 15 / 100 ) * f = 150 = > f = 1000 answer e"
a ) 90 , b ) 180 , c ) 270 , d ) 500 , e ) 1,000
e
divide(divide(300, const_2), divide(15, const_100))
divide(n1,const_2)|divide(n0,const_100)|divide(#0,#1)|
gain
with # andeach representing different digits in the problem below , the difference between # and # # is 801 . what is the value of ? # - # # ____ 812
100 x - ( 10 x + x ) - - - - - - - - - - - 89 x = 801 x = 9 c
a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
c
subtract(subtract(812, 801), const_2)
subtract(n1,n0)|subtract(#0,const_2)
general
a cat leaps 5 leaps for every 4 leaps of a dog , but 3 leaps of the dog are equal to 4 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?
"solution : given ; 3 dog = 4 cat ; or , dog / cat = 4 / 3 ; let cat ' s 1 leap = 3 meter and dogs 1 leap = 4 meter . then , ratio of speed of cat and dog = 3 * 5 / 4 * 4 = 15 : 16 . ' ' answer : option d"
a ) 11 : 15 , b ) 15 : 11 , c ) 16 : 15 , d ) 15 : 16 , e ) 11 : 16
d
divide(multiply(divide(3, 4), 5), 4)
divide(n2,n3)|multiply(n0,#0)|divide(#1,n1)|
other
( √ 97 + √ 486 ) / √ 54 = ?
"( √ 96 + √ 486 ) / √ 54 = ( 4 √ 6 + 9 √ 6 ) / 3 √ 6 = 13 √ 6 / 3 √ 6 = 13 / 3 hence , the correct answer is e ."
a ) 2 √ 2 , b ) 2 √ 3 , c ) 3 √ 2 , d ) 3 √ 3 , e ) 13 / 3
e
divide(add(sqrt(97), sqrt(486)), sqrt(54))
sqrt(n0)|sqrt(n1)|sqrt(n2)|add(#0,#1)|divide(#3,#2)|
general
a secret can be told only 2 persons in 5 minutes . the same person tells to 2 more persons and so on . how long will take to tell it to 768 persons ?
at start one person will tell to 2 persons , it will take 5 min , now that 1 + 2 = 3 persons will tell this to next 6 persons , then 1 + 2 + 6 = 9 persons will tell to next 18 persons , then 1 + 2 + 6 + 18 = 27 persons to 54 similarly 1 + 2 + 6 + 18 + 54 = 81 persons will tell this to 162 persons similarly 1 + 2 + 6 + ...
a ) 25 min , b ) 32 min , c ) 33 min , d ) 34 min , e ) 35 min
e
multiply(add(2, 5), 5)
add(n0,n1)|multiply(n1,#0)
physics
in what time will a train 110 m long cross an electric pole , it its speed be 144 km / hr ?
"speed = 144 * 5 / 18 = 40 m / sec time taken = 110 / 40 = 2.75 sec . answer : d"
a ) 2.35 sec , b ) 2.85 sec , c ) 7.5 sec , d ) 2.75 sec , e ) 1.5 sec
d
divide(110, multiply(144, const_0_2778))
multiply(n1,const_0_2778)|divide(n0,#0)|
physics
9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 6 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour faster than the first runner ' s rate . how far apart , to the neares...
"if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 6 m / h - - > 3 m in 1 / 2 hr side 2 = 8 m / h - - > 4 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 3 ^ 2 d ^ 2 = 25 = 5 answer option c"
a ) 6 , b ) 7 , c ) 5 , d ) 12 , e ) 14
c
sqrt(add(power(multiply(6, divide(1, 2)), 2), power(multiply(subtract(6, 2), divide(1, 2)), 2)))
divide(n3,n2)|subtract(n1,n2)|multiply(n1,#0)|multiply(#0,#1)|power(#2,n2)|power(#3,n2)|add(#4,#5)|sqrt(#6)|
physics
find the smallest number which when divided by 13 and 15 leaves respective remainders of 2 and 4
let ' n ' is the smallest number which divided by 13 and 15 leaves respective remainders of 2 and 4 . required number = ( lcm of 13 and 15 ) - ( common difference of divisors and remainders ) = ( 195 ) - ( 11 ) = 184 . answer : c
a ) 187 , b ) 197 , c ) 184 , d ) 219 , e ) 227
c
subtract(multiply(13, 15), add(const_10, const_1))
add(const_1,const_10)|multiply(n0,n1)|subtract(#1,#0)
general
if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to increase by 20 percent , how much would she earn per week ?
"( 406 / 116 ) 120 = 420 in this case long division does not take much time . ( 406 / 116 ) = 3.5 35 * 12 = 420 ( 350 + 70 ) answer a"
a ) $ 420 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 399
a
add(divide(406, add(const_1, divide(16, const_100))), multiply(divide(20, const_100), divide(406, add(const_1, divide(16, const_100)))))
divide(n0,const_100)|divide(n2,const_100)|add(#0,const_1)|divide(n1,#2)|multiply(#1,#3)|add(#3,#4)|
general
two tains are running in opposite directions with the same speed . if the length of each train is 120 metres and they cross each other in 12 seconds , then the speed of each train ( in km / hr ) is :
sol . let the speed of each train be x m / sec . then , relative speed of the two trains = 2 x m / sec . so , 2 x = ( 120 + 120 ) / 12 ⇔ 2 x = 20 ⇔ x = 10 . ∴ speed of each train = 10 m / sec = [ 10 * 18 / 5 ] km / hr = 36 km / hr . answer c
a ) 12 , b ) 24 , c ) 36 , d ) 48 , e ) 38
c
multiply(divide(divide(add(120, 120), 12), const_2), const_3_6)
add(n0,n0)|divide(#0,n1)|divide(#1,const_2)|multiply(#2,const_3_6)
physics
a taxi company charges $ 2.5 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
"if we start out with $ 4.90 and have to spend $ 2.5 for the first quarter - mile , we will have $ 2.40 left to spend on quarter - mile intervals . since $ 2.40 / $ 0.15 = 16 , we can buy 16 more quarter - miles , and will travel 17 quarter miles in all : 17 × 1 / 4 = 4 1 / 4 miles . the correct answer is choice ( b ) ...
a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 2 miles , e ) 6 1 / 4 miles
b
divide(divide(multiply(subtract(4.90, 2.5), const_100), const_3), const_4)
subtract(n1,n0)|multiply(#0,const_100)|divide(#1,const_3)|divide(#2,const_4)|
physics
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
in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .
this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 7 - 2 = 5 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 5 = 216,0...
a ) 215,000 , b ) 216,000 , c ) 217,000 , d ) 218,000 , e ) 219,000
b
multiply(multiply(subtract(7, const_2), const_3600), const_12)
subtract(n0,const_2)|multiply(#0,const_3600)|multiply(#1,const_12)
general
two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36.00001 sec . the length of each train is ?
"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 36 = 25 / 9 = > x = 50 . answer : a"
a ) 50 , b ) 99 , c ) 77 , d ) 26 , e ) 23
a
divide(multiply(36.00001, divide(multiply(subtract(46, 36), const_1000), const_3600)), const_2)
subtract(n0,n1)|multiply(#0,const_1000)|divide(#1,const_3600)|multiply(n2,#2)|divide(#3,const_2)|
general
two numbers n and 14 have lcm = 56 and gcf = 10 . find n .
"the product of two integers is equal to the product of their lcm and gcf . hence . 14 × n = 56 × 10 n = 56 × 10 / 14 = 40 correct answer b"
a ) 24 , b ) 40 , c ) 44 , d ) 54 , e ) 64
b
divide(multiply(56, 10), 14)
multiply(n1,n2)|divide(#0,n0)|
physics
how many liters of water must be evaporated from 50 liters of a 2 percent sugar solution to get a 4 percent sugar solution ?
"let x be the amount that needs to be evaporated . 0.02 ( 50 ) = 0.04 ( 50 - x ) 0.04 x = 2 - 1 x = 1 / 0.04 = 25 liters the answer is b ."
a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
b
subtract(50, multiply(divide(50, const_100), 4))
divide(n0,const_100)|multiply(n2,#0)|subtract(n0,#1)|
gain
a batsman scored 60 runs which included 2 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
"explanation : number of runs made by running = 60 - ( 2 x 4 + 2 x 6 ) = 60 - ( 20 ) = 20 now , we need to calculate 20 is what percent of 60 . = > 20 / 60 * 100 = 33.33 % option b"
a ) 30 % , b ) 33.33 % , c ) 40 % , d ) 60 % , e ) 50 %
b
multiply(divide(subtract(60, add(multiply(2, 2), multiply(2, 2))), 60), const_100)
multiply(n1,n2)|multiply(n1,n2)|add(#0,#1)|subtract(n0,#2)|divide(#3,n0)|multiply(#4,const_100)|
general
if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 5 people to do 5 times of that particular work ?
3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 5 people can do 5 / 3 of the work in one day . 5 people can do 5 times the work in 3 days . the answer is c .
a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
c
multiply(3, divide(5, 5))
divide(n3,n3)|multiply(n0,#0)
physics
what is the value of â ˆ š 64 % ?
"explanation : br > â ˆ š 64 % = â ˆ š 64 / â ˆ š 100 = 8 / 10 = 80 / 100 = 80 % correct answer is a ) 80 %"
a ) 80 % , b ) 20 % , c ) 40 % , d ) 90 % , e ) 26 %
a
circle_area(divide(64, multiply(const_2, const_pi)))
multiply(const_2,const_pi)|divide(n0,#0)|circle_area(#1)|
gain
tom opened a shop investing rs . 500 . jose joined him 2 months later , investing rs . 350 . they earned a profit of rs . 1720 after completion of one year . what will be jose ' s share of profit ?
"sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 1720 = 80 a"
a ) 80 , b ) 20 , c ) 30 , d ) 41 , e ) 15
a
multiply(1720, subtract(const_1, divide(multiply(500, multiply(2, multiply(2, const_3))), add(multiply(350, subtract(multiply(2, multiply(2, const_3)), 2)), multiply(500, multiply(2, multiply(2, const_3)))))))
multiply(n1,const_3)|multiply(#0,n1)|multiply(n0,#1)|subtract(#1,n1)|multiply(n2,#3)|add(#4,#2)|divide(#2,#5)|subtract(const_1,#6)|multiply(n3,#7)|
gain
the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 8748 sq . m , the cost of fencing the field @ 25 paise per metre is
"solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 8748 ⇔ 12 x 2 = 8748 ⇔ x 2 = 729 ⇔ x = 27 . so , length = 81 m and breadth = 108 m . perimeter = [ 2 ( 81 + 108 ) ] m = 378 m . ∴ cost of fencing = rs . ( 0.25 × 378 ) = rs . 94.50 . answer d"
a ) rs . 55.50 , b ) rs . 67.50 , c ) rs . 86.50 , d ) rs . 94.50 , e ) none of these
d
divide(multiply(rectangle_perimeter(multiply(3, sqrt(divide(8748, multiply(3, 4)))), multiply(4, sqrt(divide(8748, multiply(3, 4))))), 25), const_100)
multiply(n0,n1)|divide(n2,#0)|sqrt(#1)|multiply(n0,#2)|multiply(n1,#2)|rectangle_perimeter(#3,#4)|multiply(n3,#5)|divide(#6,const_100)|
physics
the angle between the minute hand and the hour hand of a clock when the time is 4.20 , is :
"angle traced hr 13 / 3 = ( 360 / 12 * 13 / 3 ) = 130 traced by min hand 20 min = ( 360 / 60 * 20 ) = 120 req = ( 130 - 120 ) = 10 d answer a"
a ) 10 d , b ) 0 d , c ) 15 d , d ) 5 d , e ) 20 d
a
divide(multiply(subtract(multiply(divide(multiply(const_3, const_4), subtract(multiply(const_3, const_4), const_1)), multiply(add(const_4, const_1), subtract(multiply(const_3, const_4), const_1))), divide(const_60, const_2)), subtract(multiply(const_3, const_4), const_1)), const_2)
add(const_1,const_4)|divide(const_60,const_2)|multiply(const_3,const_4)|subtract(#2,const_1)|divide(#2,#3)|multiply(#0,#3)|multiply(#4,#5)|subtract(#6,#1)|multiply(#7,#3)|divide(#8,const_2)|
physics
the positive numbers w , x , y , and z are such that x is 40 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
"my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 23.2 - answer d"
a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
d
multiply(const_100, subtract(multiply(multiply(divide(add(40, const_100), const_100), divide(add(40, const_100), const_100)), divide(subtract(const_100, 40), const_100)), const_1))
add(n0,const_100)|subtract(const_100,n0)|divide(#1,const_100)|divide(#0,const_100)|multiply(#3,#3)|multiply(#2,#4)|subtract(#5,const_1)|multiply(#6,const_100)|
general
if 10 men do a work in 80 days , in how many days will 20 men do it ?
"10 * 80 = 20 * x x = 40 days answer : c"
a ) 18 days , b ) 38 days , c ) 40 days , d ) 48 days , e ) 50 days
c
divide(multiply(10, 80), 20)
multiply(n0,n1)|divide(#0,n2)|
physics
a trader sells 60 meters of cloth for rs . 8400 at the profit of rs . 12 per metre of cloth . what is the cost price of one metre of cloth ?
"sp of 1 m of cloth = 8400 / 60 = rs . 140 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 140 - rs . 12 = rs . 128 . answer : a"
a ) 128 , b ) 140 , c ) 123 , d ) 110 , e ) 150
a
subtract(divide(8400, 60), 12)
divide(n1,n0)|subtract(#0,n2)|
physics
48 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
"x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 48 = 21 answer : e"
a ) 66 , b ) 26 , c ) 42 , d ) 27 , e ) 21
e
divide(multiply(divide(add(const_4, const_3), add(add(const_4, const_3), const_2)), 48), const_2)
add(const_3,const_4)|add(#0,const_2)|divide(#0,#1)|multiply(n0,#2)|divide(#3,const_2)|
general
a car covers a distance of 624 km in 6 â ½ hours . find its speed ?
explanation : 624 / 6 = 104 kmph answer : c
a ) 104 , b ) 190 , c ) 109 , d ) 278 , e ) 211
c
divide(624, 6)
divide(n0,n1)
physics
when average age of 23 members are 0 , how many members greater than 0 ?
"average of 23 numbers = 0 . sum of 23 numbers ( 0 x 23 ) = 0 . it is quite possible that 22 of these numbers may be positive and if their sum is a then 23 rd number is ( - a ) answer is 22 ( b )"
a ) 17 , b ) 22 , c ) 21 , d ) 24 , e ) 25
b
subtract(23, const_1)
subtract(n0,const_1)|
general
if 2 : 9 : : x : 18 , then find the value of x
"explanation : treat 2 : 9 as 2 / 9 and x : 18 as x / 18 , treat : : as = so we get 2 / 9 = x / 18 = > 9 x = 36 = > x = 4 option c"
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
c
divide(add(multiply(9, 2), 9), 18)
multiply(n0,n1)|add(n1,#0)|divide(#1,n2)|
general
during the first two weeks of january , the total rainfall in springdale was 35 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?
total rainfall in 2 weeks = 35 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 35 inches x = 14 and 1.5 x = 21 rainfall during second week = 21 inches option e
a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 21 inches
e
multiply(35, divide(1.5, add(const_1, 1.5)))
add(n1,const_1)|divide(n1,#0)|multiply(n0,#1)
general
if you roll one fair 6 - sided die , what is the probability that the number is even or less than 3 ?
the numbers which satisfy the conditions are 1 , 2 , 4 , and 6 . the probability is 4 / 6 = 2 / 3 the answer is a .
a ) 2 / 3 , b ) 1 / 2 , c ) 3 / 4 , d ) 5 / 6 , e ) 1 / 3
a
add(divide(const_3, 6), divide(const_1, 6))
divide(const_3,n0)|divide(const_1,n0)|add(#0,#1)
probability
a fifth of arun â € ™ s marks in mathematics exceed a third of his marks in english by 20 . if he got 260 marks in two subjects together how many marks did he got in english ?
let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 5 ) x - ( 1 / 3 ) y = 20 3 x - 5 y = 300 â € ¦ â € ¦ > ( 1 ) x + y = 260 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 200 and y = 60 answer is c .
a ) 12080 , b ) 18060 , c ) 20060 , d ) 20040 , e ) none of them
c
multiply(multiply(multiply(260, 20), const_2), const_2)
multiply(n0,n1)|multiply(#0,const_2)|multiply(#1,const_2)
general
in a colony of 70 residents , the ratio of the number of men and women is 4 : 3 . among the women , the ratio of the educated to the uneducated is 1 : 4 . if the ratio of the number of education to uneducated persons is 8 : 27 , then find the ratio of the number of educated and uneducated men in the colony ?
"number of men in the colony = 4 / 7 ( 70 ) = 40 number of women in the colony = 3 / 7 ( 70 ) = 30 number of educated women in the colony = 1 / 5 ( 30 ) = 6 number of uneducated women in the colony = 4 / 5 ( 30 ) = 24 number of educated persons in the colony = 8 / 35 ( 70 ) = 16 as 6 females are educated , remaining 10...
a ) 1 : 7 , b ) 1 : 1 , c ) 1 : 2 , d ) 1 : 9 , e ) 1 : 3
e
divide(subtract(multiply(divide(70, add(8, 27)), 8), divide(multiply(divide(70, add(4, 3)), 3), add(1, 4))), subtract(multiply(divide(70, add(8, 27)), 27), multiply(divide(multiply(divide(70, add(4, 3)), 3), add(1, 4)), 4)))
add(n5,n6)|add(n1,n2)|add(n1,n3)|divide(n0,#0)|divide(n0,#1)|multiply(n5,#3)|multiply(n2,#4)|multiply(n6,#3)|divide(#6,#2)|multiply(n1,#8)|subtract(#5,#8)|subtract(#7,#9)|divide(#10,#11)|
other
40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 4 like all . how many people like apple ?
"orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 4 40 + 10 + 4 - 7 = 47 like apple answer : a"
a ) 47 , b ) 46 , c ) 54 , d ) 58 , e ) 62
a
add(add(subtract(40, const_3), 7), subtract(10, 7))
subtract(n0,const_3)|subtract(n2,n1)|add(n1,#0)|add(#2,#1)|
general
one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 50,000 as total savings , how much has he saved in public provident fund ?
"let savings in n . s . c and p . p . f . be rs . x and rs . ( 150000 - x ) respectively . then , ( 1 / 3 ) x = ( 1 / 2 ) ( 150000 - x ) ( x / 3 ) + ( x / 2 ) = 75000 5 x / 6 = 75000 x = 75000 x 6 / 5 = 90000 savings in public provident fund = rs . ( 150000 - 90000 ) = rs . 60000 answer is b ."
a ) 30000 , b ) 60000 , c ) 50000 , d ) 90000 , e ) 70000
b
multiply(add(multiply(multiply(const_100, const_10), const_100), subtract(multiply(multiply(const_100, const_10), const_100), multiply(multiply(const_2, const_100), const_100))), divide(1, add(divide(const_3, const_2), 1)))
divide(const_3,const_2)|multiply(const_10,const_100)|multiply(const_100,const_2)|add(n0,#0)|multiply(#1,const_100)|multiply(#2,const_100)|divide(n0,#3)|subtract(#4,#5)|add(#4,#7)|multiply(#8,#6)|
general
a girl goes to her school from her house at a speed of 6 km / hr and returns at a speed of 4 km / hr . if she takes 10 hours in going and coming back , the distance between her school and house is
let distance be d 10 = d / 4 + d / 6 answer : d
a ) 12 kms , b ) 16 kms , c ) 20 kms , d ) 24 kms , e ) none of above
d
divide(multiply(10, multiply(6, 4)), add(6, 4))
add(n0,n1)|multiply(n0,n1)|multiply(n2,#1)|divide(#2,#0)
physics
if x = - 6 and y = - 3 , what is the value of 4 ( x - y ) ^ 2 - xy ?
x = - 6 and y = - 3 x - y = - 6 - ( - 3 ) = - 6 + 3 = - 3 x * y = - 6 * - 3 = 18 now we apply it in the equation 4 ( x - y ) ^ 2 - xy = 4 ( - 3 ) ^ 2 - 18 = = > 4 * 9 - 18 = 36 - 18 = 18 answer : b
a ) 20 , b ) 18 , c ) 17 , d ) 22 , e ) 23
b
subtract(multiply(power(subtract(negate(6), negate(3)), 2), 4), multiply(negate(6), negate(3)))
negate(n0)|negate(n1)|multiply(#0,#1)|subtract(#0,#1)|power(#3,n3)|multiply(n2,#4)|subtract(#5,#2)
general
if the sum of the 4 th term and the 12 th term of an arithmetic progression is 12 , what is the sum of the first 15 terms of the progression ?
"4 th term + 12 th term = 12 i . e . , ( a + 3 d ) + ( a + 11 d ) = 12 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 12 - - - - - - - - - - - - - - - from ( 1 ) = 90 answer : a"
a ) 90 , b ) 80 , c ) 70 , d ) 60 , e ) 50
a
multiply(divide(15, const_2), 12)
divide(n3,const_2)|multiply(n2,#0)|
general
( 51 + 52 + 53 + . . . + 100 ) = ?
"explanation : this is an a . p . in which a = 51 , l = 100 and n = 50 . sum = n ( a + l ) = 50 x ( 51 + 100 ) = ( 25 x 151 ) = 3775 . 2 2 answer : d"
a ) 2525 , b ) 2975 , c ) 3225 , d ) 3775 , e ) 2753
d
divide(add(51, 52), 53)
add(n0,n1)|divide(#0,n2)|
general
the edges of a cuboid are 2 cm , 5 cm and 8 cm . find the volume of the cuboid ?
"2 * 5 * 8 = 80 answer : b"
a ) 90 , b ) 80 , c ) 40 , d ) 120 , e ) 70
b
volume_rectangular_prism(2, 5, 8)
volume_rectangular_prism(n0,n1,n2)|
physics
a car was driving at 50 km / h for 30 minutes , and then at 40 km / h for another 30 minutes . what was its average speed ?
"driving at 50 km / h for 30 minutes , distance covered = 50 * 1 / 2 = 25 km driving at 40 km / h for 30 minutes , distance covered = 40 * 1 / 2 = 20 km average speed = total distance / total time = 45 / 1 = 45 km / h answer : a"
a ) 80 . , b ) 75 . , c ) 70 . , d ) 65 . , e ) 54 .
a
divide(add(multiply(divide(30, add(30, 30)), 50), multiply(divide(30, add(30, 30)), 40)), divide(add(30, 30), const_60))
add(n1,n3)|divide(n1,#0)|divide(n3,#0)|divide(#0,const_60)|multiply(n0,#1)|multiply(n2,#2)|add(#4,#5)|divide(#6,#3)|
general
a and b walk around a circular track . they start at 9 a . m . from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 11 : 00 a . m . ?
"sol . relative speed = ( 2 + 3 ) = 5 rounds per hour . so , they cross each other 5 times in an hour . hence , they cross each other 15 times before 11 : 00 a . m . answer d"
a ) 8 , b ) 7 , c ) 6 , d ) 15 , e ) 3
d
add(add(2, 3), add(2, 3))
add(n1,n2)|add(#0,#0)|
physics
a can do a work in 21 days and b alone can do it 28 days , they begin the work together , but a left after some days . b completed the remaining work in 21 days . after how many days did a leave ?
explanation : ( a + b ) 1 day work = { 1 / 21 + 1 / 28 } = 1 / 12 = 12 days is required for a & b b ’ s 1 day work = 1 / 28 b ’ s 21 days work = 21 / 28 1 - 21 / 28 = 7 / 28 - 1 / 4 1 / 4 * 12 = 3 days answer : option c
a ) 10 , b ) 8 , c ) 3 , d ) 15 , e ) 16
c
divide(subtract(const_1, multiply(speed(const_1, 28), 21)), add(speed(const_1, 21), speed(const_1, 28)))
speed(const_1,n1)|speed(const_1,n0)|add(#1,#0)|multiply(n0,#0)|subtract(const_1,#3)|divide(#4,#2)
physics
a started a business with an investment of rs . 10000 and after 7 months b joined him investing rs . 12000 . if the profit at the end of a year is rs . 24000 , then the share of b is ?
"ratio of investments of a and b is ( 10000 * 12 ) : ( 12000 * 5 ) = 2 : 1 total profit = rs . 24000 share of b = 1 / 3 ( 24000 ) = rs . 8000 answer : b"
a ) 10000 , b ) 8000 , c ) 12000 , d ) 6000 , e ) 14000
b
subtract(24000, multiply(const_60, const_100))
multiply(const_100,const_60)|subtract(n3,#0)|
gain