BTGmoderatorDC wrote:The values of x and y vary with the value of z so that each additive increase of 2 in the value of z corresponds to the value of x increasing by a factor of 2 and the value of y increasing by a factor of 3. If x and y are positive for each z > 0, what is the value of x/(x + y) when z = 12?

(1) When z = 6, x = 5y
(2) z = 0, x = y + 1

OA A

Source: GMAT Prep

Let's take each statement one by one.

(1) When z = 6, x = 5y

Say at z = 0, x = p and y = q; thus,
at z = 0 + 2 = 2, we have x = 2p and y = 3q;
at z = 2 + 2 = 4, we have x = 2^2p and y = 3^2q;
at z = 4 + 2 = 6, we have x = 2^3p and y = 3^3q;
at z = 6 + 2 = 8, we have x = 2^4p and y = 3^4q;
at z = 8 + 2 = 10, we have x = 2^5p and y = 3^5q;
at z = 10 + 2 = 12, we have x = 2^6p and y = 3^6q

Thus, at z = 12, the value of x / (x + y) = (2^6p) / (2^6p + 3^6q)

Since at x = 6, we have x = 5y; thus 2^3p = 5*3^3q => p = 5*(3/2)^3*q

Plugging-in the value of p in x / (x + y) = (2^6p) / (2^6p + 3^6q) , we get

x / (x + y) = (2^6p) / (2^6p + 3^6q) = (5*2^3*3^3) / (5*2^3*3^3 + 3^6) = 40/67. Sufficient.

(2) z = 0, x = y + 1

=> p = q + 1

Thus, at z = 12, the value of x / (x + y) = (2^6p) / (2^6p + 3^6q) =(2^6*(q + 1)) / (2^6*(q + 1) + 3^6q) = 64(p + 1) / (793 p + 64)

The correct answer: A

Hope this helps!

-Jay
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