math problem?

If m=121-5k, and m is divisible by 3, which of the following could be true?

I. m is odd

II. m is even

III. k is divisible by 3

I only

II only

I and II only

II and III only

I, II, and III

Comments

  • if m is divisible by 3, m = 3n for some integer n. then

    3n = 121 - 5k

    n = 40 1/3 - 5/3 k

    40 1/3 - 5/3 (0) = 40 1/3

    40 1/3 - 5/3 (1) = 38 2/3

    40 1/3 - 5/3 (2) = 37

    and

    40 1/3 - 5/3 (5) = 32

    when k = 2 mod 3, m = 0 mod 3, but m can be either odd or even, so I and II only.

  • I and II only

    take k = 2 or 5 for I and II

    if k can't be divisible by 3, because 5k = 121-m, which is not divisible by 3.

  • I and II only...if k were divisible by three, it would lead to a decimal for m and then wouldnt be divisible by 3.

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