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Is k^2 + k - 2 > 0?

This topic has 3 expert replies and 0 member replies

Is k^2 + k - 2 > 0?

Post Fri Nov 10, 2017 6:27 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Is k^2 + k - 2 > 0?

    (1) k is an integer greater than zero.
    (2) k divided by 2 is an integer.

    The OA is C .

    Why is C? I don't know how to use both statements together to get a solution.

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    Post Fri Nov 10, 2017 7:00 am
    Vincen wrote:
    Is k^2 + k - 2 > 0?

    (1) k is an integer greater than zero.
    (2) k divided by 2 is an integer.

    The OA is C .

    Why is C? I don't know how to use both statements together to get a solution.
    Statement 1: k > 0
    Pick easy numbers. Case 1: k = 1. $$ k^2 + k -2$$ becomes $$1^2 + 1 - 2 = 0$$. So the expression is not greater than 0, and we have a NO.

    Case 2: k = 2; $$ k^2 + k -2$$ becomes $$2^2 + 2 - 2 = 4$$ The expression is greater than 0, and we have a YES. Statement 1 alone is not sufficient.

    Statement 2: We can reuse Case 2. If k = 2; $$ k^2 + k -2$$ becomes $$2^2 + 2 - 2 = 4$$ The expression is greater than 0, and we have a YES.
    Case 3: k = -2. $$ k^2 + k -2$$ becomes $$(-2)^2 - 2 - 2 = 0$$. 0 is not greater than 0, we have a NO. Not sufficient.

    Together. We know that k is a positive integer divisible by 2, so k = 2, 4, 6, et. No matter what we pick $$k^2 + k - 2$$ will be positive, and the answer will always be YES. The statements together are sufficient and the answer is C

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    Post Fri Nov 10, 2017 10:11 am
    Vincen wrote:
    Is k² + k - 2 positive?

    (1) k is an integer greater than zero.
    (2) k divided by 2 is an integer.
    Target question: Is k² + k - 2 > 0?
    This is a good candidate for rephrasing the target question.
    What needs to happen in order for k² + k - 2 to be positive?
    Factor to get: k² + k - 2 = (k + 2)(k - 1)
    For (k + 2)(k - 1) to be positive, we need one of two scenarios:

    Scenario A: (k + 2) and (k - 1) are both POSITIVE
    For this to occur, k must be greater than 1

    Scenario B: (k + 2) and (k - 1) are both NEGATIVE
    For this to occur, k must be less than -2

    In other words, for k² + k - 2 to be positive, it must be the case that EITHER k is greater than 1 OR k is less than -2
    REPHRASED target question: Is it true that EITHER k is greater than 1, OR k is less than -2?

    Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100
    Once we've rephrased the target question, we can head to the two statements....

    Statement 1: k is an integer greater than zero.
    There are several values of k that satisfy statement 1. Here are two:
    Case a: k = 2, in which case the answer to the REPHRASED target question is YES
    Case b: k = 1, in which case the answer to the REPHRASED target question is NO
    Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: k divided by 2 is an integer
    There are several values of k that satisfy statement 2. Here are two:
    Case a: k = 2, in which case the answer to the REPHRASED target question is YES
    Case b: k = 0, in which case the answer to the REPHRASED target question is NO
    Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined
    Statement 1 tells us that k is positive
    Statement 2 tells us that k divided by 2 is an integer.
    In other words, k/2 must be a positive integer
    Some possible values of k: 2, 4, 6, 8, . . .
    In all of these cases, the answer to the REPHRASED target question is YES
    Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

    Answer: C

    Cheers,
    Brent

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    GMAT/MBA Expert

    Post Fri Nov 10, 2017 1:14 pm
    k² + k - 2 > 0 becomes

    (k + 2) * (k - 1) > 0

    That'll be greater than 0 if either:

    (i) the smaller of the two terms, k - 1, is positive
    (ii) the larger of the two terms, k + 2, is negative

    So our question can be rephrased as "Is either k > 1 or -2 > k?" and from there the statements are a snap! Smile

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