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Value of k

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Value of k

by apuso » Sun Jan 24, 2010 9:10 am
If x, y, and k are positive numbers such that (x/x+y)*10+(y/x+y)*20 = k and if x < y,
which of the following could be the value of k?
A. 10
B. 12
C. 15
D. 18
E. 30
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by ajith » Sun Jan 24, 2010 10:12 am
apuso wrote:If x, y, and k are positive numbers such that (x/x+y)*10+(y/x+y)*20 = k and if x < y,
which of the following could be the value of k?
A. 10
B. 12
C. 15
D. 18
E. 30
(x/x+y)*10+(y/x+y)*20 = k
=> (x/x+y)*10+(y/x+y)*10 +(y/x+y)*10 = k
=> 10 +(y/x+y)*10 = k

Since x y and k are positive k>10

Now, plugging the answers

A is ruled out
B
12= 10 +(y/x+y)*10
(y/x+y)*10 = 2
(y/x+y) = 2/10

Which is possible when y=2 and x =8

C - (y/x+y) = 5/10

Not possible if x>y

D- (y/x+y) = 8/10

Not possible if x>y

E -(y/x+y) = 2 (Not possible at all)

Hence B
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by sanju09 » Sun Jan 24, 2010 11:34 pm
apuso wrote:If x, y, and k are positive numbers such that (x/x+y)*10+(y/x+y)*20 = k and if x < y,
which of the following could be the value of k?
A. 10
B. 12
C. 15
D. 18
E. 30
We have 10 x + 20 y = k (x + y)

Or (10 - k) x = (k - 20) y

Now, choices say k is a positive integer. No choice is less than 10, and k cannot be 10 as well. (Why?) That means the left hand side of the above equation is negative, and therefore k < 20. (How?) Now give chance to B, C, D, even to E if you are on a holiday, and check which best explains x < y.

B writes -2 x = -8 y or x = 4 y, this doesn't fit when x and y are positive numbers and x < y.

C writes -5 x = -5 y or x = y, which is not the case.

D writes -8x = -2 y or 4 x = y, which fits when x and y are positive numbers and x < y.

E writes -20 x = 10 y, or x and y are not same sign, this contradicts the question's supply.

take [spoiler]D[/spoiler]
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