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Is w + h^4 positive?

This topic has 3 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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24 Jul 2017
Posted:
83 messages

Is w + h^4 positive?

Post Thu Jul 27, 2017 12:12 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Is w + h^4 positive?

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

    Official Guide question
    Answer: B

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    Post Thu Jul 27, 2017 12:34 pm
    jjjinapinch wrote:
    Is w + h^4 positive?
    (1) h is positive
    (2) w is positive

    Official Guide question
    Answer: B
    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

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    Post Thu Jul 27, 2017 12:38 pm
    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

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    Post Thu Jul 27, 2017 10:40 pm
    jjjinapinch wrote:
    Is w + h^4 positive?

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

    Official Guide question
    Answer: B
    We need to ensure whether (w + h^4) positive.

    Since the exponent of h is 4, an even number, whether h is positive or negative, h^4 is positive.

    Thus, (w + h^4) is positive, if

    1. w is positive, or
    2. w is negative, but |w| < h^4

    (w + h^4) is NOT positive, if

    w is negative, and |w| ≥ h^4

    Statement 1: h is positive.

    We already know the nature of h^4, we are not interested in the nature of h. Insufficient.

    Statement 2: w is positive.

    We already deduced that if w is positive, (w + h^4) is positive. Sufficient.

    The correct answer: B

    Hope this helps!

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