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If | n + 5 | = 5, what is the value of n? (1) n ^ 2 is not equal to [#permalink]

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02 Sep 2015, 06:30

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If | n + 5 | = 5, what is the value of n?

(1) n ^ 2 is not equal to 0.

(2) n ^ 2 + 10n = 0

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.

*EXPLAIN IN DETAIL
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If |n + 5| = 5, what is the value of n? [#permalink]

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02 Sep 2015, 06:39

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shakticnb wrote:

If | n + 5 | = 5, what is the value of n?

(1) n ^ 2 is not equal to 0.

(2) n ^ 2 + 10n = 0

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.

*EXPLAIN IN DETAIL

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Given |n+5| = 5 , this means that either n=0 or n =-10 and the question asks us what is the value of n?

Per statement 1, \(n^2\) \(\neq\)0 ---> n\(\neq\) 0 ---> n = -10 is the only value possible. Thus this statement is sufficient.

Per statement 2, \(n^2\)+10n=0 --> n(n+10) = 0 ---> either n = 0 or n = -10. This still does not give 1 unique value. This statement is not sufficient.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

If |n + 5| = 5, what is the value of n?

(1) n^2 is not equal to 0. (2) n^2 + 10n = 0.

Transforming the original codntiion we have n+5=-5,5, n=-10,0. Since there is 1 variable (n), we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D is likely the answer.

In case of 1), since n is not 0, n = 10 this is a unique answer and therefore is sufficient. In case of 2), n(n+10)=0, n=0,-10 therefore it is not unique. Thus it is not sufficient. The answer is A.
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