Data Sufficiency

Hi jjjinapinch,

This question is built around some Number Property Rules, so you can either TEST VALUES or use those NP rules to get to the correct answer.

We're asked if (W + H^4) is positive. This is a YES/NO question.

Before we get to the two Facts, it's worth noting that H^4 can NEVER be negative (it can be 0 when H=0, but in all other situations, H^4 will be POSITIVE). Thus, this question really comes down to the value of W....

1) H is positive

Fact 1 tells us that H is POSITIVE, so H^4 will be POSITIVE. However, it does NOT tell us anything about the value of W.

IF... H=1, W=1, then (H+W^4) = 2 and the answer to the question is YES.
IF... H=1, W= -2, then (H+W^4) = -1 and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) W is positive

Since W is POSITIVE, and we know that H^4 is >= to 0, then we know that (W+H^4) MUST be POSITIVE and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

jjjinapinch wrote:Is w + h^4 positive?

(1) h is positive
(2) w is positive

We need to determine whether w+h^4 is positive. First, we know that h^4 is always non-negative.

Let's look at the 2 possibilities for the value of w+h^4:

1) If w is positive, then (w + h^4) will be positive.

2) If w is negative, then h^4 must be greater than |w| in order for (w + h^4) to be positive. For example if w = -4, then h^4 must be greater than 4 in order for (w + h^4) to be positive.

Statement One Alone:

h is positive

Since we already know that h^4 is positive and do not have any information about w, we do not have enough information to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

w is positive

Since we know that h^4 is non-negative, also knowing that w is positive is enough information to determine that w + h^4 is positive. Statement two is sufficient to answer the question.

Answer: B