Question

What is the value of integer $n$?
(1) $n(n+1)=6$
(2) $2^{2n}=16$

• 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.

• If $n+1$ is multiplied by $n$, the result is . If 6 is subtracted from both sides, the equation becomes . This in turn can be factored as $(n+3)(n-2)=0$. Therefore, n could be either $-3$ or $2$, but there is no further information for deciding between these two values; NOT sufficient.
• From , must equal . Therefore, $2n=4$ and $n=2$; SUFFICIENT. The correct answer is B; statement 2 alone is sufficient.