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a ) 14 , b ) 15 , c ) 25 , d ) 13 , e ) 42 | a | divide(add(10, 18), const_2) | if x + y = 10 , x - y = 18 , for integers of x and y , x = ? | x + y = 10 x - y = 18 2 x = 28 x = 14 answer is a | a = 10 + 18
b = a / 2
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a ) 4 / 15 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22 | a | multiply(divide(2, 3), subtract(const_1, divide(3, 2))) | wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 2 / 3 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? | "p ( 1 and not 2 ) = 2 / 3 * ( 1 - 3 / 5 ) = 4 / 15 . answer : a ." | a = 2 / 3
b = 3 / 2
c = 1 - b
d = a * c
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a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3 | a | subtract(964807, multiply(floor(divide(964807, 8)), 8)) | find the least number must be subtracted from 964807 so that remaining no . is divisible by 8 ? | "on dividing 964807 by 15 we get the remainder 7 , so 7 should be subtracted a" | a = 964807 / 8
b = math.floor(a)
c = b * 8
d = 964807 - c
|
a ) 15 min , b ) 30 min , c ) 26 min , d ) 28 min , e ) 18 min | b | multiply(divide(8, 16), const_60) | if 8 people take an hour to complete a piece of work , then how long should 16 people will take to complete the same piece of work ? | if 8 people take an hour to complete a piece of work , then 16 people will take 8 * 60 / 16 = 30 mins to complete the same piece of work . answer : b | a = 8 / 16
b = a * const_60
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a ) 295 cm 2 , b ) 385 cm 2 , c ) 275 cm 2 , d ) 375 cm 2 , e ) 285 cm 2 | d | multiply(25, 15) | find the area of a parallelogram with base 25 cm and height 15 cm ? | "area of a parallelogram = base * height = 25 * 15 = 375 cm 2 answer : d" | a = 25 * 15
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a ) [ 12 ] , b ) [ 44 ] , c ) [ 45 ] , d ) [ 88 ] , e ) [ 90 ] | a | multiply(add(divide(6, 2), 1), add(multiply(2, 4), 1)) | when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 6 ] * [ 4 ] = ? | "[ 6 ] * [ 4 ] = ( 6 / 2 + 1 ) ( 4 / 2 + 1 ) = [ 12 ] . ans - a" | a = 6 / 2
b = a + 1
c = 2 * 4
d = c + 1
e = b * d
|
a ) 80 , b ) 95 , c ) 180 , d ) 120 , e ) 210 | c | multiply(divide(120, add(subtract(divide(const_1, const_3), multiply(divide(const_1, const_3), divide(60, const_100))), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))), add(multiply(divide(const_1, const_3), divide(60, const_100)), subtract(subtract(const_1, divide(const_1, const_3)), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100))))) | in a certain company , a third of the workers do not have a retirement plan . 60 % 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 120 of the workers of that company are men , how many of the workers are women ? | "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,4 * 1 / 3 * x 120 = 12 / 30 x x = 300 300 - 120 = 180 answer c" | a = 1 / 3
b = 1 / 3
c = 60 / 100
d = b * c
e = a - d
f = 1 / 3
g = 1 - f
h = 40 / 100
i = g * h
j = e + i
k = 120 / j
l = 1 / 3
m = 60 / 100
n = l * m
o = 1 / 3
p = 1 - o
q = 1 / 3
r = 1 - q
s = 40 / 100
t = r * s
u = p - t
v = n + u
w = k * v
|
a ) 2 hrs , b ) 3 hrs , c ) 1 hrs , d ) 1 1 / 2 hrs , e ) 2 1 / 2 hrs | c | divide(multiply(60, divide(65, 60)), add(60, 5)) | a bus started its journey from mumbai and reached pune in 65 min with its average speed of 60 km / hr . if the average speed of the bus is increased by 5 km / hr , how much time will it take to cover the same distance ? | sol . distance between ramgarh and devgarh = ( 60 * 65 ) / 60 = 60 average speed of the bus is increased by 5 km / hr then the speed of the bus = 60 km / hr required time = 60 / 60 = 1 hr c | a = 65 / 60
b = 60 * a
c = 60 + 5
d = b / c
|
a ) 165 , b ) 185 , c ) 153 , d ) 198 , e ) 199 | c | subtract(200, 47) | the mean of 50 observations is 200 . but later he found that there is decrements of 47 from each observations . what is the the updated mean is ? | "153 answer is c" | a = 200 - 47
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a ) 11 / 144 , b ) 12 / 455 , c ) 10 / 143 , d ) 11 / 125 , e ) 14 / 368 | c | divide(choose(4, const_2.0), choose(add(add(4, 6), const_4.0), const_2.0)) | a bag contains 4 red , 6 blue and 3 green balls . if 3 balls are picked at random , what is the probability that both are blue ? | "p ( both are red ) , = 6 c 3 / 13 c 3 = 10 / 143 c" | a = math.comb(4, 2)
b = 4 + 6
c = b + 4
d = math.comb(c, 2)
e = a / d
|
a ) 52 , b ) 117 , c ) 234 , d ) 312 , e ) 576 | c | divide(multiply(120, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100) | what is 120 % of 13 / 24 of 360 ? | "120 % * 13 / 24 * 360 = 1.2 * 13 * 15 = 234 the answer is c ." | a = 3 + 2
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4
g = 3 + 2
h = f * g
i = 3 + 2
j = i * 2
k = h * j
l = e + k
m = 3 + 3
n = l + m
o = 120 * n
p = o / 100
|
a ) 12 , b ) 24 , c ) 48 , d ) 35 , e ) 60 | d | multiply(add(const_2, 4), multiply(3, 4)) | if a farmer sells 10 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 15 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 - 10 ) * d + 4 = ( n + 15 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 15 d - 3 n = 45 4 n - 10 d = 40 = > n = 35 ans d it is !" | a = 2 + 4
b = 3 * 4
c = a * b
|
a ) 75 , b ) 150 , c ) 300 , d ) 600 , e ) 700 | a | divide(add(37, divide(1, 2)), divide(1, 2)) | how many 1 / 2 s are there in 37 1 / 2 ? | "required number = ( 75 / 2 ) / ( 1 / 2 ) = ( 75 / 2 x 2 / 1 ) = 75 answer : a" | a = 1 / 2
b = 37 + a
c = 1 / 2
d = b / c
|
a ) 23 , b ) 45 , c ) 15 , d ) 28 , e ) 18 | b | multiply(3, 15) | a , b , c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 175 , then how much amount should c pay as his share of rent ? | a : b : c = 10 * 7 : 12 * 5 : 15 * 3 = 2 * 7 : 12 * 1 : 3 * 3 = 14 : 12 : 9 amount that c should pay = 175 * ( 9 / 35 ) = 5 * 9 = 45 answer is b | a = 3 * 15
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a ) 1 / 6 , b ) 5 / 22 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4 | b | multiply(divide(subtract(12, 6), 12), divide(subtract(subtract(12, 6), const_1), subtract(12, const_1))) | in a box of 12 pens , a total of 6 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ? | "method - 1 there are 9 fine pieces of pen and 6 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 6 / 12 ) i . e . probability of second pen not being defective = ( 5 / 11 ) [ 11 pen remaining with 5 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 6 / 12 ) * ( 5 / 11 ) = 5 / 22 answer : option b" | a = 12 - 6
b = a / 12
c = 12 - 6
d = c - 1
e = 12 - 1
f = d / e
g = b * f
|
a ) 4 : 6 , b ) 4 : 9 , c ) 4 : 3 , d ) 5 : 2 , e ) 4 : 2 | d | multiply(divide(15, const_100), 6) | a part of certain sum of money is invested at 6 % per annum and the rest at 15 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ? | "15 : 6 = 5 : 2 answer : d" | a = 15 / 100
b = a * 6
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a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6 | c | divide(const_4, const_10) | if a randomly selected non - negative single digit integer is added to { 2 , 3 , 5 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ? | we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 5 ) / 2 = 4 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c . | a = 4 / 10
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a ) 8 % , b ) 10 % , c ) 12 % , d ) 14 % , e ) 16 % | b | divide(multiply(const_100, subtract(630, 600)), divide(600, 2)) | on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 630 , the rate of interest being the same in both the cases . the rate of interest is ? | "difference in c . i . and s . i for 2 years = $ 630 - $ 600 = $ 30 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 30 rate = ( 100 * 30 ) / ( 300 ) = 10 % the answer is b ." | a = 630 - 600
b = 100 * a
c = 600 / 2
d = b / c
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a ) 165 β cm , b ) 65 β cm , c ) 12 β cm , d ) 14 β cm , e ) 16 β cm | c | add(divide(divide(square_edge_by_area(784), const_2), divide(add(const_3, const_4), const_3)), const_2) | there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle . | "let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 β s = 12 β cm . answer : c" | a = square_edge_by_area / (
b = a / 2
c = 3 + 4
d = c / 3
e = b + d
|
a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | e | divide(const_60, add(divide(divide(const_60, 4), const_10), divide(divide(const_60, 3), const_10))) | y and z walk around a circular track . they start at 5 a . m from the same point in the opposite directions . y and z walk at a speed of 3 rounds per hour and 4 rounds per hour respectively . how many times shall they cross each other before 7 a . m | explanation : relative speed = ( 3 + 4 ) = 9 rounds per hour so , they cross each other 9 times in an hour hence , they cross 18 times before 7 a . m answer : option e | a = const_60 / 4
b = a / 10
c = const_60 / 3
d = c / 10
e = b + d
f = const_60 / e
|
a ) 143 / 969 , b ) 134 / 969 , c ) 120 / 969 , d ) 19 / 969 , e ) 120 / 134 | b | divide(add(add(5, 4), add(const_10, add(5, 3))), multiply(add(const_10, 5), 4)) | a box contains 10 black , 5 red and 4 green marbles . 3 marbles are drawn from the box at random . what is the probability that all the three marbles are of the same color ? | "explanation : total marbles in a box = 10 black + 5 red + 4 green marbles = 19 marbles 3 marbles are drawn from 19 marbles at random . therefore , n ( s ) = 19 c 3 = 969 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 10 c 3 + 5 c 3 + 4 c 3 = 120 + 10 + 4 = 134 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 134 / 969 answer : b" | a = 5 + 4
b = 5 + 3
c = 10 + b
d = a + c
e = 10 + 5
f = e * 4
g = d / f
|
a ) 26 , b ) 28 , c ) 24 , d ) 20 , e ) 22 | b | divide(subtract(multiply(const_100, const_100), multiply(subtract(const_100, 20), subtract(const_100, 10))), const_100) | a towel , when bleached , lost 20 % of its length and 10 % of its breadth . what is the percentage decrease in area ? | "formula for percentage change in area is : = ( β x β y + ( xy ) / 100 ) % = ( β 20 β 10 + ( 20 Γ 10 ) / 100 ) % = β 28 % i . e . , area is decreased by 28 % answer is b ." | a = 100 * 100
b = 100 - 20
c = 100 - 10
d = b * c
e = a - d
f = e / 100
|
a ) 90 % , b ) 47 % , c ) 38 % , d ) 52 % , e ) 83 % | a | subtract(const_100, multiply(divide(add(35, const_100), add(50, const_100)), const_100)) | two numbers are respectively 35 % and 50 % more than a third number . the percentage that is first of the second is ? | "i ii iii 135 150 100 150 - - - - - - - - - - 135 100 - - - - - - - - - - - ? = > 90 % answer : a" | a = 35 + 100
b = 50 + 100
c = a / b
d = c * 100
e = 100 - d
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a ) 400 , b ) 278 , c ) 289 , d ) 500 , e ) 821 | a | divide(272, subtract(const_1, divide(multiply(4, 8), const_100))) | a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 272 less than the sum lent . what was the sum lent ? | "p - 272 = ( p * 4 * 8 ) / 100 p = 400 answer : a" | a = 4 * 8
b = a / 100
c = 1 - b
d = 272 / c
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a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45 | d | add(add(divide(subtract(200, add(80, 60)), add(3, const_1)), divide(subtract(200, add(80, 60)), add(3, const_1))), const_10) | a marketing firm determined that , of 200 households surveyed , 80 used neither brand r nor brand b soap , 60 used only brand r soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ? | solution for soap r and soap b ( d ) 40 | a = 80 + 60
b = 200 - a
c = 3 + 1
d = b / c
e = 80 + 60
f = 200 - e
g = 3 + 1
h = f / g
i = d + h
j = i + 10
|
a ) 0 , b ) 9 , c ) 12 , d ) 16 , e ) 18 | d | power(4, 2) | if x and y are numbers such that ( x + 4 ) ( y - 4 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2 | "from ( x + 4 ) ( y - 4 ) = 0 it follows that either x = - 4 or y = 4 . thus either x ^ 2 = 16 or y ^ 2 = 16 . now , if x ^ 2 = 16 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 16 + 0 = 16 . similarly if y ^ 2 = 16 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 16 = 16 . answer : d ." | a = 4 ** 2
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a ) 180 , b ) 245 , c ) 320 , d ) 405 , e ) 450 | d | divide(multiply(90, multiply(const_3, 5)), 5) | in the set of positive integers from 1 to 90 , what is the sum of all the odd multiples of 5 ? | "reduce 1 - 90 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 - - 85 are valid multiples . add them - - > 405 d" | a = 3 * 5
b = 90 * a
c = b / 5
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a ) 12.9 , b ) 12.8 , c ) 12.6 , d ) 12.2 , e ) 12.1 | b | divide(multiply(18, 1000), add(1000, 400)) | 1000 men have provisions for 18 days . if 400 more men join them , for how many days will the provisions last now ? | 1000 * 18 = 1400 * x x = 12.8 answer : b | a = 18 * 1000
b = 1000 + 400
c = a / b
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a ) 2015 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781 | a | add(1, 2014) | if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2014 ) = ? | "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 β β f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 β β f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 β β f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2014 ) = 2015 ans : a" | a = 1 + 2014
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a ) 12 days , b ) 16 days , c ) 18 days , d ) 11 days , e ) 38 days | a | add(divide(subtract(const_1, multiply(add(divide(const_1, 30), divide(const_1, 30)), 4)), add(divide(const_1, multiply(add(const_2, const_3), multiply(const_2, 4))), add(divide(const_1, 30), divide(const_1, 30)))), 4) | a , b and c can do a piece of work in 30 days , 30 days and 40 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ? | "one day work of a , b and c = 1 / 30 + 1 / 30 + 1 / 40 = 1 / 11 work done by a and b together in the last 4 days = 4 * ( 1 / 30 + 1 / 30 ) = 4 / 15 remaining work = 11 / 15 the number of days required for this initial work = 8 days . the total number of days required = 4 + 8 = 12 days . answer : a" | a = 1 / 30
b = 1 / 30
c = a + b
d = c * 4
e = 1 - d
f = 2 + 3
g = 2 * 4
h = f * g
i = 1 / h
j = 1 / 30
k = 1 / 30
l = j + k
m = i + l
n = e / m
o = n + 4
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a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 % | a | subtract(divide(110, divide(100, const_100)), const_100) | a man buys an article for $ 100 . and sells it for $ 110 . find the gain percent ? | "c . p . = $ 100 s . p . = $ 110 gain = $ 10 gain % = 10 / 100 * 100 = 10 % answer is a" | a = 100 / 100
b = 110 / a
c = b - 100
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a ) rs . 650 , b ) rs . 690 , c ) rs . 698 , d ) rs . 700 , e ) rs . 740 | c | subtract(815, divide(multiply(subtract(854, 815), 3), 4)) | a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 854 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 815 - 117 ) = rs . 698 . answer : option c" | a = 854 - 815
b = a * 3
c = b / 4
d = 815 - c
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a ) β 5 , b ) β 4 , c ) β 2 , d ) β 1 , e ) 0 | a | subtract(multiply(5, const_2), multiply(1, const_2)) | if the average ( arithmetic mean ) of x + 1 , x + 5 , and x + 9 is 0 , then x = | "( x + 1 + x + 5 + x + 9 ) / 3 = 0 = > 3 x + 15 = 0 = > x = - 5 answer a" | a = 5 * 2
b = 1 * 2
c = a - b
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a ) $ 1600 , b ) $ 5333 , c ) $ 6050 , d ) $ 7050 , e ) $ 8000 | b | divide(subtract(1440, multiply(multiply(multiply(const_3, multiply(const_2, const_3)), const_1000), divide(8, const_100))), subtract(divide(14, const_100), divide(8, const_100))) | country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 14 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ? | "let t be the tier price , p be total price = 14000 per the given conditions : 0.14 t + 0.08 ( p - t ) = 1440 - - - - > t = 5333 . b is the correct answer ." | a = 2 * 3
b = 3 * a
c = b * 1000
d = 8 / 100
e = c * d
f = 1440 - e
g = 14 / 100
h = 8 / 100
i = g - h
j = f / i
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a ) 11 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | a | subtract(multiply(add(add(add(add(const_10, const_10), add(const_10, const_10)), add(const_10, const_10)), add(const_4, const_3)), add(add(add(add(const_10, const_10), add(const_10, const_10)), add(const_10, const_10)), add(const_4, const_3))), 4750) | what should be added to 4750 so that it may become a perfect square ? | "69 x 69 = 4761 4761 - 4750 = 11 if added to 11 get perfect square answer = a" | a = 10 + 10
b = 10 + 10
c = a + b
d = 10 + 10
e = c + d
f = 4 + 3
g = e + f
h = 10 + 10
i = 10 + 10
j = h + i
k = 10 + 10
l = j + k
m = 4 + 3
n = l + m
o = g * n
p = o - 4750
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a ) 20 % , b ) 16.66 % , c ) 16.56 % , d ) 17.66 % , e ) 18.1 % | a | multiply(divide(subtract(72, 60), 60), const_100) | john makes $ 60 a week from his job . he earns a raise andnow makes $ 72 a week . what is the % increase ? | "increase = ( 12 / 60 ) * 100 = ( 1 / 5 ) * 100 = 20 % . a" | a = 72 - 60
b = a / 60
c = b * 100
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a ) 23 , b ) 78 , c ) 27 , d ) 51 , e ) 81 | d | add(50, divide(multiply(5, 12), divide(180, 3))) | 50 + 5 * 12 / ( 180 / 3 ) = ? | "explanation : 50 + 5 * 12 / ( 180 / 3 ) = 50 + 5 * 12 / ( 60 ) = 50 + ( 5 * 12 ) / 60 = 50 + 1 = 51 . answer : d" | a = 5 * 12
b = 180 / 3
c = a / b
d = 50 + c
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a ) 18 , b ) 30 , c ) 32 , d ) 26 , e ) 98 | b | divide(multiply(60, 50), const_100) | find number which is 50 % less than 60 . | explanation : 50 % less is 50 % of the given number therefore , 50 % of 60 is 30 . answer : b | a = 60 * 50
b = a / 100
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a ) $ 1.75 , b ) $ 1.93 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30 | b | add(divide(subtract(7.8, multiply(divide(multiply(subtract(6, const_1), 6), const_2), 0.25)), 6), multiply(subtract(6, const_1), 0.25)) | mark bought a set of 6 flower pots of different sizes at a total cost of $ 7.80 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ? | this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 7.80 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.75 the other 5 pots are . . . . 1.75 1.50 1.25 1.00 0.75 total = $ 7.80 so this must be the answer . b | a = 6 - 1
b = a * 6
c = b / 2
d = c * 0
e = 7 - 8
f = e / 6
g = 6 - 1
h = g * 0
i = f + h
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a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3 | c | subtract(multiply(divide(3, 2), add(18, 2)), add(floor(multiply(divide(3, 4), multiply(divide(3, 2), add(18, 2)))), const_1)) | a certain basketball team that has played 2 / 3 of its games has a record of 18 wins and 2 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ? | "18 wins , 2 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 2 games so it can lose another 5 at most . answer ( c )" | a = 3 / 2
b = 18 + 2
c = a * b
d = 3 / 4
e = 3 / 2
f = 18 + 2
g = e * f
h = d * g
i = math.floor(h)
j = i + 1
k = c - j
|
a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8930 | e | divide(divide(multiply(4241.25, const_100), 9), 5) | a sum fetched a total simple interest of $ 4241.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ? | "e 8930 principal = $ 100 x 4241.25 / 9 x 5 = $ 424125 / 45 = $ 8930 ." | a = 4241 * 25
b = a / 9
c = b / 5
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a ) 0 , b ) 8 , c ) 3 , d ) 2 , e ) 1 | a | subtract(multiply(multiply(multiply(635, 767), 984), 489), subtract(multiply(multiply(multiply(635, 767), 984), 489), add(const_4, const_4))) | the unit digit in the product ( 635 * 767 * 984 * 489 ) is : | "explanation : unit digit in the given product = unit digit in ( 5 * 7 * 4 * 9 ) = 0 answer : a" | a = 635 * 767
b = a * 984
c = b * 489
d = 635 * 767
e = d * 984
f = e * 489
g = 4 + 4
h = f - g
i = c - h
|
a ) 10 , b ) 12 , c ) 17 , d ) 22 , e ) 30 | c | add(subtract(subtract(add(subtract(add(50, 30), 5), 20), 5), 78), 5) | in a survey of political preferences , 78 % of those asked were in favour of at least one of the proposals : i , ii and iii . 50 % of those asked favoured proposal i , 30 % favoured proposal ii , and 20 % favoured proposal iii . if 5 % of those asked favoured all 3 of the proposals , what x percentage of those asked favoured more than one of the 3 proposals . | bunuel , my answer for exactly 2 people was 17 and this was my approach : 100 % = ( a + b + c ) - ( anb + anc + bnc ) - 5 % + 22 % which leads me to x = 100 % = ( 50 + 30 + 20 ) - ( at least 2 people ) - 5 % + 22 % . c | a = 50 + 30
b = a - 5
c = b + 20
d = c - 5
e = d - 78
f = e + 5
|
a ) 0.7 , b ) 0.15 , c ) 0.54 , d ) 0.85 , e ) 0.91 | a | divide(add(add(22, 18), 2), 60) | a certain bag contains 60 balls β 22 white , 18 green , 2 yellow , 15 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ? | "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 2 ) / 60 = 42 / 60 = 0.7 . answer : a ." | a = 22 + 18
b = a + 2
c = b / 60
|
a ) $ 1825 , b ) $ 5000 , c ) $ 3150 , d ) $ 7000 , e ) $ 10000 | a | multiply(divide(36500, const_100), subtract(38, 30)) | if the personal income tax rate is lowered from 38 % to 30 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 36500 ? | "saving = ( 38 - 33 ) % of 36500 = 1825 . answer : a" | a = 36500 / 100
b = 38 - 30
c = a * b
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a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 6 , e ) $ 28 | d | subtract(multiply(48, const_2), 90) | elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 48 and elvin ' s total telephone bill for february was 90 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ? | "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 48 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 90 i . e . x + y = 48 and 2 x + y = 90 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 90 - 48 i . e . x = 42 i . e . fixed monthly charge , y = 6 answer : option d" | a = 48 * 2
b = a - 90
|
a ) 59.54 % , b ) 66.25 % , c ) 55.39 % , d ) 63.21 % , e ) 64.22 % | c | multiply(divide(add(add(multiply(500, subtract(const_1, divide(10, const_100))), multiply(300, subtract(const_1, divide(60, const_100)))), multiply(500, subtract(const_1, divide(70, const_100)))), add(add(500, 300), 500)), const_100) | in the recent , climate conference in new york , out of 500 men , 300 women , 500 children present inside the building premises , 10 % of the men , 60 % of the women and 70 % of the children were indians . find the percentage of people who were not indian ? | "solution : number of indians men present there = 500 * 10 / 100 = 50 indian women = 300 * 60 / 100 = 180 indian children = 500 * 70 / 100 = 350 . total member present in climate conference = 500 + 300 + 500 = 1300 total indian = 50 + 180 + 350 = 580 hence , % of indian present there = 580 * 100 / 1300 = 44.61 % % of people who were not indian = 100 - 44.61 = 55.39 % . answer c" | a = 10 / 100
b = 1 - a
c = 500 * b
d = 60 / 100
e = 1 - d
f = 300 * e
g = c + f
h = 70 / 100
i = 1 - h
j = 500 * i
k = g + j
l = 500 + 300
m = l + 500
n = k / m
o = n * 100
|
a ) 122,195 , b ) 121,199 , c ) 120,192 , d ) 102,192 , e ) 126,109 | c | multiply(5, 30) | two numbers are in the ratio of 5 : 8 . if 30 be subtracted from each , they are in the ratio of 5 : 9 . find the numbers ? | "( 5 x - 30 ) : ( 8 x - 30 ) = 5 : 9 x = 24 = > 120,192 answer : c" | a = 5 * 30
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a ) 16 , b ) 17 , c ) 18 , d ) 14 , e ) 13 | d | divide(56, 4) | find k if 56 / k = 4 . | "since 56 / k = 4 and 56 / 14 = 4 , then k = 14 correct answer d" | a = 56 / 4
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a ) 30 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 . | a | inverse(add(inverse(45), divide(inverse(45), const_2))) | a car traveled from san diego to san francisco at an average speed of 45 miles per hour . if the journey back took twice as long , what was the average speed of the trip ? | "let the time taken be = x one way distance = 45 x total distance traveled = 2 * 45 x = 90 x total time taken = x + 2 x = 3 x average speed = 90 x / 3 x = 30 answer : a" | a = 1/(45)
b = 1/(45)
c = b / 2
d = a + c
e = 1/(d)
|
a ) 144 , b ) 108 , c ) 278 , d ) 126 , e ) 112 | a | multiply(divide(400, 10), const_3_6) | a 400 meter long train crosses a man standing on the platform in 10 sec . what is the speed of the train ? | "s = 400 / 10 * 18 / 5 = 144 kmph answer : a" | a = 400 / 10
b = a * const_3_6
|
a ) rs . 2000 , b ) rs . 10,000 , c ) rs . 15,000 , d ) rs . 20,000 , e ) none | d | divide(divide(multiply(5400, const_100), multiply(3, 9)), multiply(divide(const_60, const_4), const_100)) | a man took a loan from a bank at the rate of 9 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was : | "solution principal = rs . ( 100 x 5400 / 9 x 3 ) = rs . 20000 . answer d" | a = 5400 * 100
b = 3 * 9
c = a / b
d = const_60 / 4
e = d * 100
f = c / e
|
a ) 88888883 , b ) 88888884 , c ) 88888885 , d ) 88888886 , e ) 88888873 | a | power(44444445, negate(88888885)) | what is the value of ( 44444445 * 88888885 * 44444442 + 44444438 / 44444444 ^ 2 ) | "let x = 44444444 , then 44444445 = x + 1 88888885 = 2 x - 3 44444442 = x - 2 44444438 = x - 6 44444444 ^ 2 = x ^ 2 then substitute it in equation ( x + 1 ) ( 2 x - 3 ) ( x - 2 ) + ( x - 6 ) / x ^ 2 ans is 2 x - 5 i . e 88888883 answer : a" | a = 44444445 ** negate
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a ) 75 , b ) 90 , c ) 45 , d ) 80 , e ) 84 | e | divide(add(5, 4), subtract(const_1, add(add(add(divide(1, 6), divide(1, 12)), divide(1, 7)), divide(1, 2)))) | jack spent 1 / 6 of his lifetime in adolescence . his facial hair started growing after 1 / 12 more of his life . he successfully married his girlfriend diana after 1 / 7 more of his life . their son was born after 5 years from then . the son lived just 1 / 2 of what jack lived . jack dies 4 years after his son died . how long did jack live ? | e 84 explanation : let us assume that jack lived for p years . p / 6 + p / 12 + p / 7 + 5 + p / 2 + 4 = x = > p = 84 . therefore , jack lived for 84 years . | a = 5 + 4
b = 1 / 6
c = 1 / 12
d = b + c
e = 1 / 7
f = d + e
g = 1 / 2
h = f + g
i = 1 - h
j = a / i
|
a ) - 5 , b ) - 3 , c ) 0 , d ) 3 , e ) 5 | c | divide(const_0_33, const_1000) | if 7 a - 3 b = 10 b + 40 = - 12 b - 2 a , what is the value of 9 a + 9 b ? | ( i ) 7 a - 13 b = 40 ( ii ) 2 a + 22 b = - 40 adding ( i ) and ( ii ) : 9 a + 9 b = 0 the answer is c . | a = const_0_33 / 1000
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a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 % | c | multiply(divide(subtract(420, 300), 300), const_100) | the price of a book is increased from $ 300 to $ 420 . what is the % of increase in its price ? | "explanation : change in the price = rs 420 Γ’ β¬ β rs 300 = rs 120 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 120 300 ) * 100 = 40 % c" | a = 420 - 300
b = a / 300
c = b * 100
|
a ) 40 sec , b ) 50 sec , c ) 44 sec , d ) 49 sec , e ) 28 sec | e | divide(210, multiply(subtract(45, 140), const_0_2778)) | a train 210 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ? | "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 210 + 140 = 350 m required time = 350 * 2 / 25 = 28 sec answer : e" | a = 45 - 140
b = a * const_0_2778
c = 210 / b
|
a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2125 | e | subtract(multiply(multiply(const_0_25, const_1000), const_10), divide(add(500, multiply(multiply(const_0_25, const_1000), const_10)), 8)) | the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 8 of that total . what was the price of the basic computer ? | "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 8 of that new total price : p = 1 / 8 * $ 3,000 = $ 375 . plug this value in the first equation : c + 375 = $ 2,500 - - > c = $ 2,125 . answer : e ." | a = const_0_25 * 1000
b = a * 10
c = const_0_25 * 1000
d = c * 10
e = 500 + d
f = e / 8
g = b - f
|
a ) 401 , b ) 411 , c ) 421 , d ) 431 , e ) 441 | d | add(multiply(divide(add(10, 30), const_2), add(subtract(30, 10), const_1)), add(divide(subtract(30, 10), const_2), const_1)) | if x is equal to the sum of the integers from 10 to 30 , inclusive , and y is the number of even integers from 10 to 30 , inclusive , what is the value of x + y ? | "x = 10 + 11 + . . . + 30 = 21 ( 20 ) = 420 y = 11 x + y = 431 the answer is d ." | a = 10 + 30
b = a / 2
c = 30 - 10
d = c + 1
e = b * d
f = 30 - 10
g = f / 2
h = g + 1
i = e + h
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a ) 101 , b ) 107 , c ) 111 , d ) 117 , e ) 121 | c | multiply(divide(4107, power(37, const_2)), 37) | the product of two numbers is 4107 . if the h . c . f . of these numbers is 37 , then the greater number is : explanation : | let the numbers be 37 a and 37 b . then , 37 a x 37 b = 4107 ab = 3 . now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 x 1 , 37 x 3 ) i . e . , ( 37 , 111 ) . greater number = 111 . answer : option c | a = 37 ** 2
b = 4107 / a
c = b * 37
|
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | d | add(divide(multiply(subtract(const_0_25, divide(const_1, const_100)), 50), divide(subtract(42.36, subtract(const_0_25, divide(const_1, const_100))), 14)), divide(subtract(42.36, subtract(const_0_25, divide(const_1, const_100))), 14)) | if 42.36 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ? | "42.36 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.36 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.36 = km / 50 . . . . . . 36 / 100 = 3 m / 50 . . . . . . m = 6 k + m = 3 + 6 = 9 answer : d" | a = 1 / 100
b = const_0_25 - a
c = b * 50
d = 1 / 100
e = const_0_25 - d
f = 42 - 36
g = f / 14
h = c / g
i = 1 / 100
j = const_0_25 - i
k = 42 - 36
l = k / 14
m = h + l
|
a ) 6 , b ) 16 , c ) 20 , d ) 30 , e ) 174 | c | add(subtract(18, 6), subtract(14, 6)) | if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 14 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ? | the number of integers that belong to set x only is 14 - 6 = 8 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 8 + 12 = 20 . answer : c . | a = 18 - 6
b = 14 - 6
c = a + b
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a ) 287 , b ) 288 , c ) 600 , d ) 277 , e ) 121 | c | multiply(multiply(subtract(divide(700, multiply(subtract(63, 3), const_0_2778)), const_1), const_10), const_2) | how many seconds will a 700 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ? | "let length of tunnel is x meter distance = 700 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 700 + x = ( 65 / 3 ) * 60 700 + x = 20 * 65 = 1300 x = 1300 - 700 = 600 meters answer : c" | a = 63 - 3
b = a * const_0_2778
c = 700 / b
d = c - 1
e = d * 10
f = e * 2
|
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) | 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 = 10 + 10
b = a + 1
c = b + 1
d = c * 3
e = 10 + 10
f = e - 1
g = f * 2
h = d + g
i = 10 + 10
j = i + 1
k = h + j
l = k / 6
|
a ) 1235 , b ) 1456 , c ) 1567 , d ) 1678 , e ) 1631 | e | add(multiply(divide(subtract(1365, 35), subtract(6, const_1)), 6), 35) | find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 35 as remainder | "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 35 5 x = 1330 x = 266 large number = 266 + 1365 = 1631 e" | a = 1365 - 35
b = 6 - 1
c = a / b
d = c * 6
e = d + 35
|
a ) 14 , b ) 17 , c ) 20 , d ) 23 , e ) 26 | b | add(10, const_4) | how many odd numbers between 10 and 1400 are the squares of integers ? | "the numbers are the squares of 5 , 7 , 9 , . . . , 37 which includes 17 numbers . the answer is b ." | a = 10 + 4
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a ) $ 200 , b ) $ 900 , c ) $ 700 , d ) $ 600 , e ) $ 400 | b | multiply(divide(3, add(add(2, 3), 4)), 2700) | a person want to give his money of $ 2700 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ? | "b ' s share = 2700 * 3 / 9 = $ 900 answer is b" | a = 2 + 3
b = a + 4
c = 3 / b
d = c * 2700
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a ) 276 , b ) 414 , c ) 322 , d ) 345 , e ) 355 | b | multiply(23, 18) | the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 18 . the larger of the two numbers is : | "clearly , the numbers are ( 23 x 13 ) and ( 23 x 18 ) . larger number = ( 23 x 18 ) = 414 . answer : option b" | a = 23 * 18
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a ) 2925 , b ) 3456 , c ) 4581 , d ) 3683 , e ) 1308 | b | multiply(power(4, 2), power(6, 3)) | if 6 ^ k = 4 , then 6 ^ ( 2 k + 3 ) = | 6 ^ k = 4 6 ^ 2 k = 4 ^ 2 6 ^ 2 k = 16 6 ^ ( 2 k + 3 ) = 6 ^ 2 k * 6 ^ 3 = 16 * 216 = 3456 answer : b | a = 4 ** 2
b = 6 ** 3
c = a * b
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a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 1 , e ) 1 / 4 | b | add(divide(const_1, divide(18, const_2)), divide(const_1, 18)) | a can finish a work in 18 days and b can do the same work in half the time taken by a . then , working together , what part of the same work they can finish in a day ? | given that b alone can complete the same work in days = half the time taken by a = 9 days a β s one day work = 1 / 18 b β s one day work = 1 / 9 ( a + b ) β s one day work = 1 / 18 + 1 / 9 = 1 / 6 answer : b . | a = 18 / 2
b = 1 / a
c = 1 / 18
d = b + c
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a ) 160 , b ) 98 , c ) 100 , d ) 80 , e ) 50 | b | divide(subtract(multiply(212, divide(16, const_100)), 30), subtract(divide(16, const_100), divide(12, const_100))) | an empty fuel tank with a capacity of 212 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ? | "say there are a gallons of fuel a in the tank , then there would be 212 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 212 - a gallons of fuel b is 0.16 ( 212 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 212 - a ) = 30 - - > a = 98 . answer : b ." | a = 16 / 100
b = 212 * a
c = b - 30
d = 16 / 100
e = 12 / 100
f = d - e
g = c / f
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a ) 16 , b ) r = 32 , c ) r = 64 , d ) 128 , e ) 512 | b | multiply(8, 4) | the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 Ο Β· r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams r ? | "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )" | a = 8 * 4
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a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10 | e | inverse(add(divide(2, multiply(10, 7)), divide(10, multiply(10, 14)))) | 10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 2 women and 10 children take to complete the work ? | "1 women ' s 1 day work = 1 / 70 1 child ' s 1 day work = 1 / 140 ( 2 women + 10 children ) ' s 1 day work = ( 2 / 70 + 10 / 140 ) = 1 / 10 2 women and 10 children will complete the work in 10 days . e" | a = 10 * 7
b = 2 / a
c = 10 * 14
d = 10 / c
e = b + d
f = 1/(e)
|
a ) 8 , b ) 8.5 , c ) 11 , d ) 9.5 , e ) 10 | c | divide(660, add(30, add(10, 20))) | a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops . | a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 8 80 360 9 90 450 10 100 550 11 110 660 it takes a total of nine hours to cover the 660 mile distance . answer : c . 11 | a = 10 + 20
b = 30 + a
c = 660 / b
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a ) 6 , b ) 7 , c ) 21 , d ) 9 , e ) 10 | c | add(divide(20, 2), const_1) | how many integers are divisible by 2 between 10 ! and 10 ! + 20 inclusive ? | "c = 21 10 ! is divisible by 2 there are 20 numbers between 10 ! and 10 ! + 20 that are divisible by 1 . hence 21" | a = 20 / 2
b = a + 1
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a ) 34778 , b ) 26888 , c ) 20350 , d ) 17600 , e ) 12778 | c | divide(multiply(add(const_100, 10), add(divide(multiply(14500, const_100), subtract(const_100, 20)), add(125, 250))), const_100) | ramesh purchased a refrigerator for rs . 14500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ? | "price at which the tv set is bought = rs . 14,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 18125 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 18125 + 375 = rs . 18500 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 18500 * 110 / 100 = rs . 20350 answer : c" | a = 100 + 10
b = 14500 * 100
c = 100 - 20
d = b / c
e = 125 + 250
f = d + e
g = a * f
h = g / 100
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a ) 20 , b ) 50 , c ) 108 , d ) 200 , e ) 400 | c | add(power(multiply(2, 2), 2), power(multiply(2, 2), 2)) | if equation | x / 2 | + | y / 2 | = 4 encloses a certain region on the coordinate plane , what is the area of this region ? | the equation can be reduced to intercept form as | x / 8 | + | y / 8 | = 1 , so these are lines in four quadrants with x and y intercept as 8 , so it is a rhombus with diagonals of 16 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 16 * 16 = 108 . answer c . | a = 2 * 2
b = a ** 2
c = 2 * 2
d = c ** 2
e = b + d
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a ) 120 , b ) 180 , c ) 772 , d ) 720 , e ) 1,440 | c | divide(divide(1, 2), divide(multiply(add(divide(add(divide(add(divide(add(divide(multiply(const_3, 2), const_10), 1), const_10), const_4), const_10), 1), const_10), const_3), 13), multiply(add(add(multiply(add(multiply(add(multiply(multiply(const_3, 2), const_10), const_3), const_10), const_3), const_10), const_3), 2), const_10))) | approximately how many revolutions will be made by a car tire with a 13 - inch diameter if the car travels 1 β 2 mile ? | "diameter of car tire = 13 inches radius of car tire = 6.5 inches = 6.5 * 2.54 cm = 16.51 cm circumference of the car tire = 2 * pi * 16.51 = 2 * 3.14 * 16.51 = 103.68 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 103.68 = 771.60 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c" | a = 1 / 2
b = 3 * 2
c = b / 10
d = c + 1
e = d / 10
f = e + 4
g = f / 10
h = g + 1
i = h / 10
j = i + 3
k = j * 13
l = 3 * 2
m = l * 10
n = m + 3
o = n * 10
p = o + 3
q = p * 10
r = q + 3
s = r + 2
t = s * 10
u = k / t
v = a / u
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a ) 5 , b ) 1 / 5 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 7 / 3 | e | divide(add(2, 5), subtract(2, 5)) | if x / y = 2 / 5 , then ( x + y ) / ( x - y ) = ? | any x and y satisfying x / y = 2 / 5 should give the same value for ( x + y ) / ( x - y ) . say x = 2 and y = 5 , then ( x + y ) / ( x - y ) = ( 2 + 5 ) / ( 2 - 5 ) = - 7 / 3 . answer : e . | a = 2 + 5
b = 2 - 5
c = a / b
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a ) 44 % , b ) 120 % , c ) 156 % , d ) 40 % , e ) none of the above | c | multiply(subtract(divide(const_100, const_100), power(subtract(divide(const_100, const_100), divide(60, const_100)), const_2)), const_100) | if the radius of a circle is increased by 60 % then the area is increased by : | "initially a = pi * r 2 now r 2 = 160 / 100 r then area = pi * ( 160 r / 100 ) 2 area = 256 r / 100 that is area increases from 100 to 256 = increase in area = 156 % answer : c" | a = 100 / 100
b = 100 / 100
c = 60 / 100
d = b - c
e = d ** 2
f = a - e
g = f * 100
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a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24 | b | subtract(divide(factorial(subtract(divide(12, const_2), const_1)), multiply(factorial(const_3), factorial(const_2))), subtract(divide(12, const_2), const_1)) | a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter ) | "back - solving is the best way to solve this problem . you basically need 12 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b" | a = 12 / 2
b = a - 1
c = math.factorial(b)
d = math.factorial(3)
e = math.factorial(2)
f = d * e
g = c / f
h = 12 / 2
i = h - 1
j = g - i
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a ) 87 , b ) 18 , c ) 17 , d ) 16 , e ) 12 | e | divide(divide(1800, 20), divide(1400, multiply(10, 21))) | 10 binders can bind 1400 books in 21 days . how many binders will be required to bind 1800 books in 20 days ? | "binders books days 10 1400 21 x 1600 20 x / 10 = ( 1800 / 1400 ) * ( 21 / 20 ) = > x = 12 answer : e" | a = 1800 / 20
b = 10 * 21
c = 1400 / b
d = a / c
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a ) 211 seconds , b ) 195 seconds , c ) 155 seconds , d ) 115 seconds , e ) 115 seconds | a | divide(27, 0.128) | an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 27 metre of cloth ? | "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 27 : x = > x = { \ color { blue } \ frac { 27 \ times 1 } { 0.128 } } = > x = 210.94 so time will be approx 211 seconds answer : a" | a = 27 / 0
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a ) 19.81 % , b ) 22.38 % , c ) 37.5 % , d ) 25 % , e ) 37.5 % | b | multiply(subtract(add(const_100, 10), add(11, subtract(const_100, 20))), const_2) | a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 11 % below the cost price of the claimed weight . | "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 11 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 89 / 100 = ( 1 + p % ) profit % = 22.38 % b" | a = 100 + 10
b = 100 - 20
c = 11 + b
d = a - c
e = d * 2
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a ) 21.23 , b ) 52.85 , c ) 23.26 , d ) 41.67 , e ) 25.15 | d | divide(divide(multiply(11, const_1000), const_60), multiply(multiply(divide(add(11, const_2), add(const_4, const_3)), const_2), divide(divide(140, const_100), const_2))) | the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 11 kmph ? | "distance covered in 1 min = ( 66 * 1000 ) / 60 = 183.33 cm circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 183.33 / 4.4 = 41.67 answer : d" | a = 11 * 1000
b = a / const_60
c = 11 + 2
d = 4 + 3
e = c / d
f = e * 2
g = 140 / 100
h = g / 2
i = f * h
j = b / i
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a ) 8100312 , b ) 8100313 , c ) 8100412 , d ) 8200312 , e ) 8300312 | a | multiply(multiply(2, add(2012, const_1)), 2012) | 1 * 2 + 2 * 2 ^ 2 + 3 * 2 ^ 3 + 4 * 2 ^ 4 β¦ β¦ β¦ β¦ β¦ β¦ β¦ β¦ + 2012 * 2 ^ 2012 | take 2 outside as common we get 2 ( 1 + 2 * 1 ^ 2 + 3 * 1 ^ 3 + . . . . . . . . . 2012 * 1 ^ 2012 ) then 2 ( 1 + 2 + . . . . . 2012 ) we get 8100312 answer : a | a = 2012 + 1
b = 2 * a
c = b * 2012
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a ) 4 , b ) 6 , c ) 9 , d ) 14 , e ) 20 | d | subtract(subtract(add(94, 23), subtract(56, 20)), subtract(112, 45)) | stock / number of shares v - - - - - - - - - - - - 68 w - - - - - - - - - - 112 x - - - - - - - - - - - - 56 y - - - - - - - - - - - - 94 z - - - - - - - - - - - - 45 the table shows the number of shares of each of the 5 stocks owned by mr sami . if mr . sami was to sell 20 shares of stock x and buy 23 shares of stock y , what would be the increase in the range of the numbers of shares of the 5 stocks owned by mr . sami ? | based on the original number of shares , the range would be : 112 - 45 = 67 however , the prompt tells us that two of the values in the table are going to change . after the changes , the values will be : v 68 w 112 x 36 y 117 z 45 now the range is 117 - 36 = 81 the increase in the range requires us to compare thenewrange to theoldrange : 81 - 67 = 14 d | a = 94 + 23
b = 56 - 20
c = a - b
d = 112 - 45
e = c - d
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a ) 25 % loss , b ) 20 % loss , c ) 25 % profit , d ) 20 % profit , e ) 5 % profit | b | multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 25), 20)), divide(multiply(const_100, 25), 20))) | if the cost price of 20 articles is equal to the selling price of 25 articles , what is the % profit or loss made by the merchant ? | "let the cost price of 1 article be rs . 1 . therefore , cost price of 20 articles = 20 * 1 = rs . 20 the selling price of 25 articles = cost price of 20 articles = rs . 20 . let us find the cost price of 25 articles . cost price of 25 articles = 25 * 1 = rs . 25 . therefore , profit made on sale of 25 articles = selling price of 25 articles - cost price of 25 articles = 20 - 25 = - rs . 5 . because the profit is in the negative , the merchant has made a loss of rs . 5 . therefore , % loss = loss / cost price β 100 % loss = 5 / 25 β 100 = 20 % loss . answer : b" | a = 100 * 25
b = a / 20
c = 100 - b
d = 100 * 25
e = d / 20
f = c / e
g = 100 * f
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a ) 35.2 , b ) 32.5 , c ) 36.5 , d ) 39.1 , e ) none | b | divide(add(multiply(32, 50), subtract(subtract(50, const_2), 23)), 50) | the mean of 50 observations was 32 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is | "sol . therefore correct sum = ( 32 Γ 50 + 48 β 23 ) = 1625 . therefore correct mean = 1625 / 50 = 32.5 . answer b" | a = 32 * 50
b = 50 - 2
c = b - 23
d = a + c
e = d / 50
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a ) 0.00018 , b ) 0.09 , c ) 0.018 , d ) 0.18 , e ) 90 | d | divide(0.009, 0.05) | 0.009 / x = 0.05 . find the value of x | "x = 0.009 / 0.18 = 0.05 answer : d" | a = 0 / 9
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a ) s . 600 , b ) s . 480 , c ) s . 500 , d ) s . 450 , e ) s . 420 | e | subtract(divide(multiply(700, const_100), add(25, const_100)), divide(multiply(divide(multiply(700, const_100), add(25, const_100)), 25), const_100)) | by selling an article at rs . 700 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ? | "sp = 700 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 700 * [ 100 / 125 ] = 560 loss = 25 % = 25 % of 560 = rs . 140 sp = cp - loss = 560 - 140 = rs . 420 answer : e" | a = 700 * 100
b = 25 + 100
c = a / b
d = 700 * 100
e = 25 + 100
f = d / e
g = f * 25
h = g / 100
i = c - h
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a ) 10 % , b ) 14.28 % , c ) 15 % , d ) 16 % , e ) 20 % | e | subtract(divide(multiply(const_100, 6), subtract(6, 1)), const_100) | in a office work is distribute between p persons . if 1 / 6 members are absent then work increased for each person is ? | let total % of work is 100 % total person = p 1 / 6 person are absent of total person . so absent person is 1 / 6 p ie p / 6 . left person is , p - p / 6 = 5 p / 6 . p person do the work 100 % 1 person do the work 100 * p % 5 p / 6 person do the work ( 100 * p * 6 ) / 5 p % = 120.00 % work increased for each person is = ( 120 - 100 ) % = 20 % answer : e | a = 100 * 6
b = 6 - 1
c = a / b
d = c - 100
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a ) 50 hours , b ) 62 hours , c ) 90 hours , d ) 75 hours , e ) 100 hours | c | inverse(subtract(divide(const_1, 9), divide(const_1, const_10))) | a cistern which could be filled in 9 hours takes 1 hour more to be filled owing to a leak in its bottom . if the cistern is full , in what time will the leak empty it ? | "let the leak empty the full cistern in x hours 9 x / x - 9 = 9 + 1 x = 90 hours answer is c" | a = 1 / 9
b = 1 / 10
c = a - b
d = 1/(c)
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a ) 35 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these . | a | divide(add(60, 10), const_2) | the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 10 marks more than that in physics . find the average marks scored in mathamatics and chemistry together . | "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 10 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 10 ) / 2 = 35 . answer : a" | a = 60 + 10
b = a / 2
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a ) 23 , b ) 22 , c ) 21 , d ) 20 , e ) 19 | d | subtract(add(add(25, 20), 20), 50) | mrs . evans gave a test to her freshmen economics class , which has 50 students enrolled and 25 of them answered question 1 correctly . if 20 answered question 2 correctly and 20 did not take the test then how many answered both questions correctly ? | "total number of enrolled students = 50 number of students who did not take test = 20 hence , number of students who took test = 50 - 20 = 30 number of students who answered q 2 correctly = 20 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 20 . number of students who answered both q 1 & q 2 correctly = 20 . answer : d" | a = 25 + 20
b = a + 20
c = b - 50
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a ) 2 , b ) 2 1 / 4 , c ) 3 2 / 2 , d ) 4 1 / 2 , e ) 5 | c | multiply(divide(const_60, add(divide(const_1, 8), divide(const_1, 4))), add(divide(const_1, 8), divide(const_1, 4))) | carl can wash all the windows of his house in 8 hours . his wife maggie can wash all the windows in 4 hours . how many hours will it take for both of them working together to wash all the windows ? | "work hrs = ab / ( a + b ) = 32 / 12 = 3 2 / 2 answer is c" | a = 1 / 8
b = 1 / 4
c = a + b
d = const_60 / c
e = 1 / 8
f = 1 / 4
g = e + f
h = d * g
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a ) 11 , b ) 13 , c ) 15 , d ) 60 , e ) 75 | c | divide(subtract(const_1, divide(80, const_100)), divide(3, const_100)) | in a certain parking lot , 3 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what % of cars in the parking lot are parked illegally . ' | "so total no . of cars parked illegally : 300 total no . of cars : 2000 300 / 2000 * 100 , so 15 % answer : c" | a = 80 / 100
b = 1 - a
c = 3 / 100
d = b / c
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a ) 20 % , b ) 25 % , c ) 18 % , d ) 30 % , e ) none of these | a | multiply(divide(divide(5, const_100), divide(25, const_100)), const_100) | if the given two numbers are respectively 5 % and 25 % of a third number , then what percentage is the first of the second ? | "here , l = 5 and m = 25 therefore , first number = l / m x 100 % of second number = 5 / 25 x 100 % of second number = 20 % of second number answer : a" | a = 5 / 100
b = 25 / 100
c = a / b
d = c * 100
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a ) 8 . , b ) 2 . , c ) 6 . , d ) 4 . , e ) 16 . | e | divide(volume_cylinder(multiply(const_1, const_2), multiply(const_1, const_2)), volume_cylinder(const_1, const_1)) | if the radius of a cylinder is doubled and height 4 times , what is the new volume of the cylinder divided by the old one ? | "let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 2 r ) ^ 2 ( 4 h ) v ' = 16 v e ) 16" | a = 1 * 2
b = 1 * 2
c = volume_cylinder / (
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a ) 1 km , b ) 2 km , c ) 3 km , d ) 4 km , e ) 5 km | b | multiply(multiply(divide(add(10, 10), const_60), 2), add(2, 1)) | starting from his house one day , a student walk at a speed of 2 kmph and reaches his school 10 minutes late . next he increased his speed by 1 kmph and reaches the school 10 minutes early . how far is the school from his house ? | let the distance be x km difference in timings = 20 min = 20 / 60 = 1 / 3 hr x / 2 - x / 3 = 1 / 3 x = 2 km answer is b | a = 10 + 10
b = a / const_60
c = b * 2
d = 2 + 1
e = c * d
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