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Problem in the Problem

by smagish » Sun Jul 29, 2012 1:58 am
If x, y, and k are positive numbers such that (x)10/(x+y) + (y)20/(x+y) = 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

I doubt the question to be erroneous....any thoughts

Thanks in advance:)
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by niketdoshi123 » Sun Jul 29, 2012 3:07 am
smagish wrote:If x, y, and k are positive numbers such that (x)10/(x+y) + (y)20/(x+y) = 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, y, & k are positive numbers
x < y
Simplifying the given equation
(10x + 20y) = k(x+y)

Let plug in the value of k
We will start with option C as the options are in increasing order
Substituting k=15 in the equation

10x + 20y = 15x + 15y
=>5y = 5x => y = x but we know that x<y so eliminate option C. Also the value of k<15 will give us the inequality x>y, therefore eliminate options A and B.

Check for option E
k= 30

10x + 20y = 30x + 30y
=> -10y = 20x => y = -2x but we know that x and y both are positive. Hence eliminate option E

We are left with option D, which is the correct answer.
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by Anurag@Gurome » Sun Jul 29, 2012 8:18 pm
smagish wrote:If x, y, and k are positive numbers such that (x)10/(x+y) + (y)20/(x+y) = 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

I doubt the question to be erroneous....any thoughts

Thanks in advance:)
(x/(x + y))(10) + (y/(x + y))(20) = k and x < y
10x + 20y = k(x + y)
x(10 - k) = y(k - 20)
y/x = (10 - k)/(k - 20) and we know y > x or y/x > 0

So, 15 < k < 20 implies k = 18

The correct answer is D.
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by sanrisenew » Tue Jul 31, 2012 2:39 am
10x/(x+y) + 20y/(x+y) = K


(10x+20y)/(x+y) =K

(10(x+y) + 10y)/(x+y) = k

10 + 10*y/(x+y) = K

Now, second term on LHS is less than 10 therefore , 30 is out
y/(x+y) can't be less than 1/2 as x<y therefore only option left is 18.
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