Bunuel wrote:

If 2^(x + y) = 4^8, what is the value of y?

(1) x^2 = 81

(2) x − y = 2

Kudos for a correct solution.

Target question: What is the value of y? Given: 2^(x + y) = 4^8 Notice that 4^8 = (2^2)^8 = 2^16

In other words, 2^

(x + y) = 2^

16, which means

x + y = 16 Statement 1: x^2 = 81 This tells us that x = 9 OR x = -9

Let's examine each possible case

Case a: x = 9. If

x + y = 16, then we can conclude that

y = 7Case b: x = -9. If

x + y = 16, then we can conclude that

y = 25Since we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x − y = 2 When we combine this information with

x + y = 16, we see that we have TWO different equations and TWO variables.

So, we COULD solve this system to find one unique value of y (incidentally, we get

y = 7)

Since we can answer the

target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,

Brent

_________________

Brent Hanneson – GMATPrepNow.com

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