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Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2- [#permalink]

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03 Aug 2017, 02:44

Statement 1: let a=3 and b=2 then ab=6 which is divisble by 3 then putting the value in the eq we get 5c which is not divisible by 3 so no put a=3 and b=3 then ab is divisible by 3 and also 6c which is divisible by 3 so yes Insufficient

Statement 2: since c is divisible by 3 therefore (a+b)c is also divisible by 3 Sufficient

==> If you modify the original condition and the question, in order to have (a+b)c to be divided by 3, a+b or c has to be divided by 3. However, if you look at con 2), c is divisible by 3, hence it is yes and sufficient. For con 1), ab is also divisible by 3, and thus a+b is also divisible by 3, hence it is yes and sufficient. Therefore, the answer is D. This type of question is a 5051-level question which applies CMT 4 (B: if you get A or B too easily, consider D).

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