rewrite 2x+2x?

[NDroho]

What is the value of 2x + 2x/2y?

1) x - y = 8

2) x/y = -3

Answer here is C, but my question is about re-writing 2x+2x/2y. I dont understand how you can turn 2x+2x into 2^x+1. Explanation said 2x+2x --> 2 (2^x) --> 2^x+1.

I get the jump from 1 to 2, but im confused on step 2 to 3. Any suggestion(s) in how to understand this?

[GMATGuruNY]

I suspect that the question stem should read as follows:

What is the value of (2^x + 2^x)/(2^y)?

1) x - y = 8

2) x/y = -3

2^x + 2^x means that we have TWO values of 2^x:
2 * 2^x.

When we MULTIPLY two values with the same base, we ADD the exponents:
2¹ * 2^x = 2^(1+x).

At this point, the question stem can be rephrased as follows:
What is the value of 2^(1+x) / 2^y?

When we DIVIDE two values with the same base, we SUBTRACT the exponents:
2^(1+x) / 2^y = 2^(1+x-y).

To determine the value of 2^(1+x-y), we need to know the value of x-y.
Final rephrase:
What is the value of x-y?

Statement 1: x-y = 8.
SUFFICIENT.

Statement 2: x/y = -3
x = -3y
x + 3y = 0.
No way to determine the value of x-y.
INSUFFICIENT.

The correct answer is A.