Question

If $2^{x+y}=4^8$, what is the value of y?
(1) $x^2=81$
(2) $x-y=2$

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Since , the equation becomes , which is equivalent to $x+y=16$.

1. Given that , then both $x=9$ and $x=-9$ are possible. Therefore, $y=7$ is possible (choose $x=9$) and $y=25$ is possible (choose $x=-9$); NOT sufficient.
2. Given that $x-y=2$, it follows that $-x+y=-2$. Adding the last equation to $x+y=16$ gives $2y=14$, or $y=7$; SUFFICIENT.

• The correct answer is B; statement 2 alone is sufficient.