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Is a^3 > 20?

This topic has 1 expert reply and 0 member replies

Is a^3 > 20?

Post Tue Oct 31, 2017 9:16 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    $$Is\ \ a^3>20?$$

    $$(1)\ \ a^4>80$$
    $$(2)\ \ a^5>200$$

    The OA is B.

    I don't understand it. Please, can any expert help me with this DS question? Thanks.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Fri Nov 10, 2017 12:01 am
    swerve wrote:
    $$Is\ \ a^3>20?$$
    $$(1)\ \ a^4>80$$
    $$(2)\ \ a^5>200$$
    The OA is B.

    I don't understand it. Please, can any expert help me with this DS question? Thanks.
    (1) a^4 > 80

    We can safely assume that a^4 ≥ 81 => a^4 ≥ 3^4 => -3 ≥ a or 3 ≤ a.

    Case 1: If -3 ≥ a, then say at a = -3, we have a^3 > 20 => (-3)^3 > 20 => -27 < 20. The answer is No.
    Case 2: If 3 ≤ a, then say at a = 3, we have a^3 > 20 => (3)^3 > 20 => 27 > 20. The answer is Yes. No unique answer.

    (2) a^5 > 200

    This is a difficult one. We cannot approximate 200 to 243 (= 3^5); This much of approximation is way too much.

    However, since the exponent of a is an odd number, a cannot have a negative value.

    @ a = 3, we have a^5 = 3^5 = 243 > 200. At a = 3, we have a^3 = 3^3 = 27 > 20. The answer is yes. However, if a is closer to 3 but less than 3, it would be interesting to know whether at that value of a, is a^3 > 20?

    Let's devise another tactic.

    Dividing a^5 > 200 by a^3 > 20, we get a^5/a^3 > 200/20 => a^2 > 10 => a > 3. Mind that we already deduced that a is positive. Since at a = 3, we have a^3 = 3^3 = 27 > 20. The answer is yes. We can safely conclude that Statement 2 is sufficient.

    The correct answer: B

    Hope this helps!

    -Jay
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    Thanked by: swerve

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