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don't understand the explanation in OG to this problem

This topic has 1 expert reply and 2 member replies
isisalaska Community Manager Default Avatar
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don't understand the explanation in OG to this problem

Post Sun Jan 07, 2007 10:37 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Hi, could anyone give me a better explanation to this problem?:
    If a is a positive and if the unit digit of a^2 is 9 and (a+1)^2 is 4, what is (a+2)^2

    Thanks!

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    rajs.kumar Senior | Next Rank: 100 Posts Default Avatar
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    Post Sun Jan 07, 2007 1:20 pm
    I assume the question asks for the unit digit of (a+2) ^ 2.

    if unit digit of a ^ 2 is 9 then unit place a should be 3 or 7

    if unit digit of (a+1) ^ 2 is 4 then unit place can only be 8

    => unit digit of (a+2) ^ 2 is 1

    Hope this helps.

    axefx Newbie | Next Rank: 10 Posts Default Avatar
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    Post Thu Jan 25, 2007 11:57 am
    rajs.kumar wrote:
    I assume the question asks for the unit digit of (a+2) ^ 2.

    if unit digit of a ^ 2 is 9 then unit place a should be 3 or 7

    if unit digit of (a+1) ^ 2 is 4 then unit place can only be 8

    => unit digit of (a+2) ^ 2 is 1

    Hope this helps.
    can you please elaborate... your analysis seems to have a ton of holes... how do the first two statements conclude into the third one!?

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    Stacey Koprince GMAT Instructor
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    Post Fri Jan 26, 2007 11:47 pm
    Raj is right. If the units digit of a^2 is 9, only two numbers will square to give a units digit of 9: 3 or 7. See below.

    Units digit when squaring:
    0^2 = 0
    1^2 = 1
    2^2 = 4
    3^2 = 9
    4^2 = 6
    5^2 = 5
    6^2 = 6
    7^2 = 9
    8^2 = 4
    9^2 = 1

    So, a is either 3 or 7. If (a+1)^2 units digit is 4, then a must be 7, because (7+1)^2 = 8^2 = units digit of 4. a can't be 3, b/c (3+1)^2 = 4^2 = units digit of 6.

    So if a is 7, then (a+2) = 9. 9^2 = units digit of 1.

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