Is w + h^4 positive?

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