Question

What is the value of $W^{-2}$?
(1) $W^{-1}=\frac{1}{2}$
(2) $W^8=8$

• 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

Answer: (D)

Each statement alone is sufficient.

Algebra Exponents

(1) Since $w^{-1}=\frac{1}{2}$, then $(w^{-1}{)}^2=(\frac{1}{2}{)}^2=\frac{1}{4}$ or $w^{-2}=\frac{1}{4}$; SUFFICIENT.

(2) Since $w^3=8$, then $w=\sqrt[3]{38}=2$ and $w^{-2}=2^{-2}=\frac{1}{4}$; SUFFICIENT.

The correct answer is D; each statement alone is sufficient.