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If n=(-72)^(1/3), then the value of n is:

This topic has 1 expert reply and 0 member replies

If n=(-72)^(1/3), then the value of n is:

Post Fri Sep 29, 2017 6:02 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If n=(-72)^(1/3), then the value of n is:

    A. -9 < n < -8
    B. -8 < n < -7
    C. -7 < n < -6
    D. -6 < n < -5
    E. -5 < n < -4

    The OA is E.

    How can I know the answer without using the calculator?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sat Sep 30, 2017 4:05 pm
    Hi Vincen,

    While you will almost certainly have to deal with a square-root a couple of times on Test Day (in both Arithmetic and Geometry questions), cube-roots are relatively rare (you probably won't see them at all on Test Day). That having been said, cube-roots are based on the same general math concepts as square-roots.

    For example...
    The square-root of 4 is +2 ... since (2)(2) = 4
    The cube-root of 27 is +3 ... since (3)(3)(3) = 27
    The cube-root of -27 is -3 ... since (-3)(-3)(-3) = -27

    In this question, we're asked for the cube-root of -72, but the solution will NOT be an integer (notice how the answer choices are all RANGES - that's a hint that N is not an integer AND that we don't actually have to find the exact value of N; we just have to figure out what numbers it is between). Thus, we have to look for cubes of negative integers:

    (-3)^3 = -27
    (-4)^3 = -64
    (-5)^3 = -125

    Since -72 is between -64 and -125, the cube-root of -72 has to be between -4 and -5

    Final Answer: E

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

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