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Units digit?

This topic has 2 expert replies and 0 member replies
oquiella Master | Next Rank: 500 Posts Default Avatar
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Units digit?

Post Mon Sep 28, 2015 2:27 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If N=(33)^43 + (43)^33, what is the units digit of n?

    A. 0
    B. 2
    C. 4
    D. 6
    E. 8

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    Post Mon Sep 28, 2015 2:35 pm
    oquiella wrote:
    If N=(33)^43 + (43)^33, what is the units digit of n?

    A. 0
    B. 2
    C. 4
    D. 6
    E. 8
    3¹ --> units digit of 3.
    3² --> units digit of 9. (Since the product of the preceding units digit and 3 = 3*3 = 9.)
    3³ --> units digit of 7. (Since the product of the preceding units digit and 3 = 9*3 = 27.)
    3⁴ --> units digit of 1. (Since the product of the preceding units digit and 3 = 7*3 = 21.)
    From here, the units digits will repeat in the same pattern: 3, 9, 7, 1.
    The units digit repeat in a CYCLE OF 4.
    Implication:
    When an integer with a units digit of 3 is raised to a power that is a multiple of 4, the units digit will be 1.

    Thus:
    33⁴⁰ and 43³² each have a units digit of 1.
    From here, the cycle of units digits will repeat: 3, 9, 7, 1...
    Thus:
    33⁴¹ and 43³³ each have a units digit of 3.
    33⁴² has a units digit of 9.
    33⁴³ has a units digit of 7.

    Result:
    Since n = 33⁴³ + 43³³, n ---> (units digit of 3) + (units digit of 7) = units digit of 0.

    The correct answer is A.

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    Post Mon Sep 28, 2015 3:17 pm
    FYI - we have a free video on finding the Units Digit of Large Powers -http://www.gmatprepnow.com/module/gmat-powers-and-roots/video/1031

    Then you can practice with this question - http://www.gmatprepnow.com/module/gmat-powers-and-roots/video/1032

    Cheers,
    Brent

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