S is a finite set of numbers. Does S contain more negative

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S is a finite set of numbers. Does S contain more negative numbers than positive numbers?

(1) The product of all the numbers in S is -1,200.
(2) There are 6 numbers in S.

[spoiler]OA=E[/spoiler]

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by Jay@ManhattanReview » Mon Jan 07, 2019 9:33 pm

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VJesus12 wrote:S is a finite set of numbers. Does S contain more negative numbers than positive numbers?

(1) The product of all the numbers in S is -1,200.
(2) There are 6 numbers in S.

[spoiler]OA=E[/spoiler]

Source: GMAT Prep
We have to determine whether set S contains more negative numbers than positive numbers.

Let's take each statement one by one.

(1) The product of all the numbers in S is -1,200.

Case 1: Say Set S has 2 numbers; they are -1200 and 1. The answer is No.
Case 2: Say Set S has 4 numbers; they are -1200, -1, -1 and 1. The answer is Yes.

No unique answer. Insufficient.

(2) There are 6 numbers in S.

Case 1: Say the 6 numbers are -1200, -1, -1, -1, -1 and 1. The answer is Yes.
Case 2: Say the 6 numbers are -1200, 1, 1, 1, 1 and 1. The answer is Yes.

No unique answer. Insufficient.

(1) and (2) together

Both the cases discussed in Statement 2 are applicable here, too. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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