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Is x < 5?

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

Is x < 5?

Post Thu Aug 03, 2017 12:07 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Is x < 5?
    (1) x^2 > 5
    (2) x^2 + x < 5

    Official Guide question
    Answer: B

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    Post Thu Aug 03, 2017 1:03 pm
    jjjinapinch wrote:
    Is x < 5?
    (1) x² > 5
    (2) x² + x < 5

    Official Guide question
    Answer: B
    Target question: Is x < 5?

    Statement 1: x² > 5
    This statement doesn't FEEL sufficient, so I'll TEST some values.
    There are several values of x that satisfy statement 1. Here are two:
    Case a: x = 3 is a possible value since 3² > 5. In this case, x < 5
    Case b: x = 6 is a possible value since 6² > 5. In this case, x > 5
    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values

    Statement 2: x² + x < 5
    IMPORTANT: x² is greater than or equal to 0 for ALL values of x.
    So, let's let 0+ represent the value of x². This notation reminds us that x² equals some value that's greater than or equal to 0
    Our inequality becomes: (0+) + x < 5
    In order for the left side to be less than 5, x CANNOT be greater than or equal to 5
    In other words, it MUST be the case that x < 5
    Since we can answer the target question with certainty, statement 2 is SUFFICIENT

    Answer: B

    Cheers,
    Brent

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    Last edited by Brent@GMATPrepNow on Sat Aug 26, 2017 11:47 am; edited 1 time in total

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    Post Thu Aug 03, 2017 9:03 pm
    Hi jjjinapinch,

    We're asked if X is less than 5. This is a YES/NO question. We can answer this question by TESTing VALUES and paying careful attention to the question that is asked. To start, we know that ANY negative value for X and X=0 will lead to a YES answer (as well as any values of X that are less than 5). Answers that are 5 or greater will lead to a NO answer.

    1) X² > 5

    With this inequality, there are clearly multiple values for X (positive and negative).
    IF... X = 5, then the answer to the question is NO.
    IF... X = -5, then the answer to the question is YES.
    Fact 1 is INSUFFICIENT

    2) X² + X < 5

    With this inequality, we know that there are negative solutions and that X=0 is a solution, so there are clearly "NO" answers to this question. However, we now have to think about how big X could get. Thankfully, there's a way to avoid doing that exact math and use a bit of 'brute force' to help us to stop working...

    IF.... X=1, then (X^2 + X) = 1^2 + 1 = 2... which is less than 5
    IF.... X=2, then (X^2 + X) = 2^2 + 2 = 6... which is GREATER than 5
    As X increases, the sum of (X^2 + X) will also increase. Since we're already greater than 5 when X=2, there's no reason to check any larger values. Given this inequality, X MUST be less than 2, so 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 Fri Aug 25, 2017 1:00 am
    jjjinapinch wrote:
    Is x < 5?
    (1) x^2 > 5
    (2) x^2 + x < 5

    Official Guide question
    Answer: B
    Nice solutions by Brent and Rich. Here's one with brute force.

    S1: x^2 > 5

      Plug-in a value of x > 5, say x = 6 such that x^2 > 5. We see that (6^2 = 36) > 5. The answer is No.

      Plug-in a value of x < 5, say x = -6 such that x^2 > 5. We see that (-6)^2 > 5 => 36 > 5. The answer is Yes.

    No unique answer!

    S2: x^2 + x < 5

      Plug-in a value of x > 5, say x = 6 such that x^2 + x > 5. We see that (6^2 + 6 = 42) < 5. It's not a valid value. Let's try with a smaller value.

      Say x = 2 such that x^2 + x > 5. We see that (2^2 + 2 = 6) < 5. It's not a valid value. Let's try with another smaller value.

      Say x = 1 such that x^2 + x > 5. We see that (1^2 + 1 = 6) > 5. It's a valid value. The answer is Yes.

    There is no need to test further as we now know that x < 2, this means that x < 5. Sufficient.

    The correct answer: B

    Hope this helps!

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