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Thread: Q55. GMAT Math DS - Powers and units digit

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    The Keeper of Grounds Hagrid's Avatar
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    Q55. GMAT Math DS - Powers and units digit

    Q. If a is an integer. What is the units digit of a^36?
    a) a^2 has 9 as the units digit
    b) a^3 has 3 has the units digit

    PLEASE PROVIDE YOUR REASONING AND NOT JUST THE ANSWER CHOICES.

    Difficulty Level : Moderate
    Time to Solve : <70 secs


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    Just starting GMAT Prep Sekhar's Avatar
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    B
    As Statement 2 is sufficient to get the number as 7
    Time 90 Secs

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    Begining to Crack GMAT mickey's Avatar
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    IMO D

    Statemenet 1 gives units place as 1

    Statement 2 gives units place as 1

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    Just starting GMAT Prep Jilany's Avatar
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    D .. guessing a number 7, 7*7=49 and 7*7*7=343. Statement 1 and 2 both sufficient separately ..
    Nurul Hai

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    Just starting GMAT Prep anks22's Avatar
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    B

    statement 1 can be true for 3 & 7

    statement 2 can be true for 7 only

    Hence B

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    Ready to Crack GMAT clerk's Avatar
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    1) a^36=(a^2)^18=(...9)^18, from this we can find the units digit
    2) a^36=(a^3)^12=(...3)^12, from here we can find the units digit.
    As mentioned by Mickey, both times the units digit equals to 1

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    Serious about GMAT Prep rkandell's Avatar
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    D – 90 secs

    From a: Since a^2 has 9 as the units digit, “a” has either 3 or 7 as the ones digit.

    · Number 3: The number 3 has a repeating series of the ones digit every 4th power. e.g. 3^1 = 3, 3^2 = 9, 3^3 = 27, 3^4 à 1 is the one digit of this number (= 7*3), 3^5 à 3 is the ones digit of this number (= 1*3). Since there is a repeating pattern every 4th power, the one digit of a^36 can be deduced to be 1 since 36 is divisible by 4.

    · Number 7: The number 7 also has repeating series of the ones digit every 4th power. e.g. 7^1 = 7, 7^2 = 49, 7^3 à 3 is the ones digit of this number (=9*7), 7^4 à 1 is the ones digit of this number (=3*7), 7^5 à 7 is the ones digit of this number (=1*7). Since there is a repeating pattern every 4th power, the one digit of a^36 can be deduced to be 1 since 36 is divisible by 4.

    Either number 3 or 7 will produce 1 as the ones digit of a^36th. Sufficient.

    From b: Since a^3 has a 3 in the units digit, “a” has to have 7 as the ones digit. Since we know the ones digit of a^36 is equal to 1 from the analysis shown above, this is Sufficient also.

    Hence D. à Either statement by itself is sufficient to answer the question.

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    Just starting GMAT Prep gaurav85's Avatar
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    D............
    agree with rkandell

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    Probably, if it were indicated that "a" is integer, the conditions would be a little bit more correct. Whatever, even if it's not integer (let's say (19)^0,5 in the first case and 3^(1/3) in the second), the answer is D. Both will end with 1

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    Serious about GMAT Prep rkandell's Avatar
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    Clerk,
    Good point about "a" being an integer. I didn't think about the possibilities of "a" not being an integer.

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    Ready to Crack GMAT clerk's Avatar
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    Still no OA and OE

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    GMAT Druid Guardian's Avatar
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    Good point clerk, a should have been given as an integer ...

    What is the units digit of a^36?
    a) a^2 has 9 as the units digit
    b) a^3 has 3 has the units digit

    OA: D

    a) a^2 has 9 => (a^2)^18 will have 9^18 ... which gives 1 as units digit. suff

    b) a^3 has 3 => (a^3)^12 will have 3^13 .. which gives 1 as units digit. suff
    ~|Guardian|

    I am an instructor on ScoreChase GMAT Crash Course . I also provide GMAT Private Tutoring sessions.

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    Really wants to crack GMAT ! GMAT_Dreamer's Avatar
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    D

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