Saturday, August 8, 2009

Problem 52 - GMAT Number Properties


11 comments:

  1. try n=3, then r=1, i guess neither are correct.

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  2. I think answer is C (Both answer together)
    (1) n is even-> r might be 6 or 0
    (2) n is not divisible by 5 -> n cannot be 5 0R 10; then r might be 1,6
    (1)+(2) --> r = 6

    trial:
    1 r=1
    2 r=6
    3 r=1
    4 r=6
    5 r=5
    6 r=6
    7 r=1
    8 r=6
    9 r=1
    10 r=0
    n>10 repeat

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  3. Answer is (C),
    If n=even then remainder will be 6 & 0.
    taking the II statement into account 0 is eliminated.
    r=6 answer.

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  4. Vivek is right, statement 2 eliminates the 0 option, and so the answer is C.

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  5. In my opinion, E.

    If, for example, n=2 or n=4, we know that both are not divisible by 5. And their remainders when n^4/10 are not the same. Thus, NS.

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  6. Hey Anonymous, sorry but you are wrong, 2^4 and 4^4 will both end in a 6, so answer is C. Sorry!

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  7. This comment has been removed by the author.

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  8. Find n^4 (mod 10)

    (1) n = 0 (2), n^4 = 0 (2), but we need to know n^4 (mod 5) to get the exact figure

    (2) n = 1, 2, 3, 4 (mod 5)
    n^4 = 1^4, 2^4, 3^4, 4^4 = 1 (mod 5) (power up the remainders)
    We need to know n^4 (mod 2) to get the exact figure.

    Combing both gives: n^4 = 1 (mod 5) and n^4 = 0 (mod 2).

    n^4 = 1 (mod 5) {1,6,11,16,...}
    n^4 = 0 (mod 2) {0,2,4,6,8,...}

    Intersection {6,16,26...}

    Hence n^4 = 6 (mod 10)

    Well, we don't need to get the exact remainder.

    If x = p (mod a), x = q (mod b) and gcd(a,b) =1, x has a unique value modulo ab.

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  9. Typical GMAT trap

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  10. answer C:
    from 1: n can be 2,4,6,8,10 for n=2,4,..will work but for n=10 it will not, since we do not have unique r hence not suff.
    2nd, clearly not suff, as n can be 1,2, 3....
    from 1 &2, n can be 2,4,6,8, or number ending with these numbers. in any case n^4 will give 6 as unit digit and hence when divided by 10, we will get unique remainder 6. suff... answer C

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