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What is the units digit of 248^20?

This topic has 2 expert replies and 1 member reply

What is the units digit of 248^20?

Post Fri Sep 22, 2017 10:34 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    What is the units digit of 248^20?

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

    The OA is D.

    How can I find the units digit without making the whole calculus?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Fri Sep 22, 2017 1:23 pm
    Vincen wrote:
    What is the units digit of 248^20?

    A) 0
    B) 2
    C) 4
    D) 6
    E) 8
    Look for a pattern

    248^1 = 248
    248^2 = (248)(248) = ---4 [aside: we need not determine the other digits. All we care about is the units digit]
    248^3 = (248)(248^2) = (248)(---4) = ----2
    248^4 = (248)(248^3) = (248)(---2) = ----6
    248^5 = (248)(248^4) = (248)(---6) = ----8

    NOTICE that we're back to where we started.
    248^5 has units digit 8, and 248^1 has units digit 8
    So, at this point, our pattern of units digits keep repeating 8, 4, 2, 6, 8, 4, 2, 6, 8,...
    We say that we have a "cycle" of 4, which means the digits repeat every 4 powers.

    So, we get:
    248^1 = --8
    248^2 = ---4
    248^3 = ----2
    248^4 = ----6
    248^5 = ----8
    248^6 = ---4
    248^7 = ----2
    248^8 = ----6
    248^9 = ----8
    248^10 = ----4
    etc.

    Notice that when the exponent is a MULTIPLE of 4 (4, 8, 12, 16, ...), the units digit will be 6
    Since 20 is a MULTIPLE of 4, we know that the units digit of 248^20 will be 6
    Answer: D

    Here's an article I wrote on this topic (with additional practice questions): https://www.gmatprepnow.com/articles/units-digits-big-powers

    Cheers,
    Brent

    _________________
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    mbouayad14 Newbie | Next Rank: 10 Posts
    Joined
    02 Aug 2017
    Posted:
    1 messages
    Post Sat Sep 23, 2017 7:13 am
    20 is a multiple of 2....so why couldnt rhe answer be 4???

    Post Sat Sep 23, 2017 7:33 am
    mbouayad14 wrote:
    20 is a multiple of 2....so why couldnt rhe answer be 4???
    That would be true if it were the case that ALL exponents that are multiples of 2 yielded units digit 4

    Cheers,
    Brent

    _________________
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