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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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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, 01:26
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45% (medium)

Question Stats:

59% (01:05) correct 41% (01:30) wrong based on 77 sessions

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If a, b, and c are positive integers, is (a+b)c divisible by 3?

1) 2-digit integer ab is divisible by 3.
2) When c is divided by 3, the remainder is 0.

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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

Ans: B

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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, 09:09
Is "two digit integer ab" supposed to reflect a number where a is the tens digit, and b the ones digit? Or does it mean the product of a and b?
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Joined: 21 Jun 2017
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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, 10:49
Statement 1: ab = 10a+b = (a+b)+9a is divisible by 3 so a+b is divisible by 3
Statement 2: Obvious yes
Math Revolution GMAT Instructor
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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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06 Aug 2017, 18:13
==> 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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Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-   [#permalink] 06 Aug 2017, 18:13
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