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Let us suppose:
m = a.k
n = b.k
Then

A. 2n+m = 2ak+bk = K * certain value

B. mn - m = (ak bk) - ak = K^2 * Certain value - k *certain value [may not be a multiple of k]

C. Likewise others will be multiple of K
APram
If A can be multiple of k then D can also be multiple of k.
Is it that if k = 2, the answer is considering this assumption?

Kindly explain!
Aabhash777
If n and m are both multiples of k, which of the following may NOT be a multiple of k?

A. 2n+m

B. mn − n

C. m + n +3k

D. 0.5*(m + n)

E. 3n + km + m^2
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Aabhash777
If n and m are both multiples of k, which of the following may NOT be a multiple of k?

A. 2n+m

B. mn − n

C. m + n +3k

D. 0.5*(m + n)

E. 3n + km + m^2
Assume k = 3, n = 6 and m = 9

All options except D would turn out to be multiples of 3.
Option D = 0.5 * (6+9) = 7.5 which is not a multiple of 3.
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