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
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.
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.
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.