Question

# What is the value of integer n?(1) n(n+1)=6(2) 22n=16

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

## 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 $n^{2}+n= 6$. If 6 is subtracted from both sides, the equation becomes $n^{2}+n-6= 0$. 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 $2^{2n}= 16$, $2^{2n}$ must equal $2^{4}$. Therefore, 2n=4 and n=2; SUFFICIENT. The correct answer is B; statement 2 alone is sufficient.

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