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Is n<0? (1) -n=|-n| (2) n^2=16

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Mar 29, 2017 12:25 am
ziyuenlau wrote:Is n<0?

(1) -n=|-n|
(2) n^2=16

OFFICIAL ANSWER : C
Hi ziyuenlau,

The question asks whether n is negative.

Let's take each statement one by one.

S1: -n = |-n|

Case 1: If n = 0, the answer is NO.

Case 2: Since RHS (|-n|) is positive, LHS (-n) must also be positive, thus n must be negative. The answer is YES.

No unique answer. Insufficient.

S2: n^2=16

=> n = 4 or n = -4

n may be positive or negative. No unique answer. Insufficient.

S1 and S2:

From both the statements, we get that n = -4 or n < 0. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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by [email protected] » Wed Mar 29, 2017 10:16 am
Hi ziyuenlau,

This question can be solved by TESTing VALUES or Number Properties.

We're asked if N is less than 0. This is a YES/NO question.

1) -N = |-N|

Since the 'result' of an absolute value CANNOT be negative, the possible solutions are limited to 0 and anything NEGATIVE.

IF....
N = 0, then the answer to the question is NO.
N = Negative, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) N^2 = 16

This question has 2 solutions: +4 and -4

IF....
N = +4, then the answer to the question is NO.
N = -4, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, there's only one solution that fits BOTH Facts: -4 ... and the answer to the question is YES.
Combined, SUFFICIENT

Final Answer: C

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by Jeff@TargetTestPrep » Tue Apr 04, 2017 2:56 pm
ziyuenlau wrote:Is n<0?

(1) -n=|-n|
(2) n^2=16
We need to determine whether n is less than 0.

Statement One Alone:

-n = |-n|

Since - n = |-n|, n must be a negative number or 0. For example:

-(-2) = |-2|

2 = 2

and

-0 = |-0|

0 = 0

If n = -2 (or any negative number), then n < 0. However, if n = 0, then n is not less than 0.

Statement one is not sufficient to answer the question.

Statement Two Alone:

n^2 = 16

Since n^2 = 16, n = 4 or n = -4.

Statement two is not sufficient to answer the question.

Statements One and Two Together:

From statement two, we know that n is either 4 or -4. From statement one, we know n is nonpositive. Therefore, n must be -4, and thus it's less than 0. The two statements together are sufficient.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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