If a, b, c, d and k are positive integers, is (ac - bd) divisible by k

Question

If a, b, c, d and k are positive integers, is (ac - bd) divisible by k ?

(1) (a - b) is divisible by k
(2) (c - d) is divisible by k

gmatophobia · Answer

The statements are individually not sufficient as we don't have information on the nature of the other variable.

However, if we combine the two statements - we would be able to determine that given term is divisible.

The working is shown in the attached figure.

IMO C

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