Data Sufficiency

BTGmoderatorDC wrote:If x and y are positive, what is the value of x+y?

(1) (2^x)(3^y) = 72
(2) (2^x)(2^y) = 32

-------------ASIDE--------------------------------
IMPORTANT: We are not told that x and y are integers. So, they need not be integers!

ALSO IMPORTANT: There exists a value of y so that 3^y = 36.
How do we know this?
Well, 3^3 = 27 and 3^4 = 81
Since 36 is BETWEEN 27 and 81, there must be a y-value BETWEEN 3 and 4 such that 3^y = 36.
Let's say that, when y = 3.something, 3^y = 36.
------ONTO THE QUESTION!!-----------------------------

Target question: What is the value of x+y?

Statement 1: (2^x)(3^y) = 72
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 3 and y = 2. In this case, x + y = 3 + 2 = 5. So, the answer to the target question is x + y = 5
Case b: x = 1 and y = 3.something. In this case, x + y = 1 + 3.something = 4.something. So, the answer to the target question is x + y = 4.something
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (2^x)(2^y) = 32
Since we have the SAME BASE, we can rewrite this as: 2^(x + y) = 32
Replace 32 with 2^5 to get: 2^(x + y) = 2^5
So, it must be the case that x + y = 5
So, the answer to the target question is x + y = 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent