Is \(w+h^4\) positive?

[M7MBA]

Is \(w+h^4\) positive?

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

Answer: B

Source: Official Guide

[Brent@GMATPrepNow]

Is \(w+h^4\) positive?

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

Answer: B

Source: Official Guide

Target question: Is w + h^4 positive?

Statement 1: h is positive
Let's TEST some values.
There are several values of w and h that satisfy statement 1. Here are two:
Case a: w = 1 and h = 1. In this case, w + h^4 = 1 + 1^4 = 2. So, w + h^4 IS positive
Case b: w = -3 and h = 1. In this case, w + h^4= -3 + 1^4 = -2. So, w + h^4 is NOT positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: w is positive
Important concept: (any number)^(even integer) = a value greater than or equal to 0
Statement 2 tells us that w is some positive number
We can write: w + h^4 = (some positive number) + ( a value greater than or equal to 0)
We can see that w + h^4 positive is definitely positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent