Let r = the remainder when k is divided by 7.
So we can write: k = 7n + r (for some integer n)
In other words, k equals r greater than some multiple of 7

This means k + 21 = 7n + r + 21 (for some integer n)
Rewrite as: k + 21 = 7n + 21 + r
Factor: k + 21 = 7(n + 3) + r
This tells us that k+21 is r greater than some multiple of 7

Since k and k+21 are both r greater than some multiple of 7, they will both leave the same remainder when divided by 7.

Answer: C

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let k=8
quant A: remainder will be 1 when 8 divided by 7
quant B: remainder will be 1 when (8+21) divide by 7

taking another example k=4
quant A: remainder will be 4 when 4 divided by 7
quant B: remainder will be 4 when (4+21) divide by 7

so option C is correct