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

Hi Bunuel - can you provide an explanation for this question? I got (B) because I reduced the equation to 2(2^(x/y)) and I'd like to know what I'm doing wrong. Thanks.

Hi revul,

You bring up an interesting point (that X and Y could be a variety of different values), but then you stopped working and immediately called Fact 1 INSUFFICIENT. If you do a bit more work, you'll find that that is NOT the case (the answer to the question stays the same....it's always 512).

Hi cg0588,

Here's how you can 'rewrite' the question:

First, it's important to realize that when you add two of the 'same thing' together, you can write the result as 2 "times"....

A + A = 2A
10 + 10 = 2(10)
Etc.

The question asks us for the value of (2^X + 2^X)/(2^Y)

Let's start with the numerator...
2^X + 2^X = 2(2^X)

2(2^X) = (2^1)(2^X) = 2^(X+1)

Now, using exponent rules...since the numerator and denominator have the SAME BASE (2), we can SUBTRACT the exponents...

2^(X+1)/(2^Y) = 2^(X+1-Y)

So we're really asked for the value of 2^(X+1-Y).

From this, can you get to the question answer?

GMAT assassins aren't born, they're made,
Rich

My approach:

Factor out 2^x --> 2^x (1+1)/2^y --> 2^x(2)/2^y

Then reorganize to 2^(x-y) * 2 = 2^(x-y+1)

Essentially you just need to solve for x-y and A gives us that answer directly.

Simplifying the given: (2^x + 2^x)/2^y

2^x(1+1)/2^y
2^x+1/2^y
2^x+1-y

We can clearly see A is sufficient but B is not.
Hence A

Also 2^2+2^2 = 2^3 or 2^4+2^4 = 2^5