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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82
If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 55% (00:58) correct 45% (01:19) wrong based on 105 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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Joined: 31 Jan 2017
Posts: 47
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

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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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Joined: 03 Apr 2016
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GMAT 1: 740 Q49 V42 GPA: 3.58
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

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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?
Intern  B
Joined: 21 Jun 2017
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GMAT 1: 750 Q50 V41 Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

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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 V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

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==> 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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GMAT 1: 730 Q49 V40 Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

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MathRevolution wrote:
==> 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).

I am not following your logic for con 1).
If a=1 and b=3, then ab=3 divisible by 3, however a+b=4 so it would not be true.
I am still not convinced that B is the right answer. Could you please elaborate ?
Manager  B
Joined: 07 May 2016
Posts: 56
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

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krasha wrote:
MathRevolution wrote:
==> 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).

I am not following your logic for con 1).
If a=1 and b=3, then ab=3 divisible by 3, however a+b=4 so it would not be true.
I am still not convinced that B is the right answer. Could you please elaborate ?

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GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

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MathRevolution wrote:
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.

c= 3K, so (a+b)c is definitely divisible by 3.

Now, statement 1,

TU
ab
21
48

All two digit numbers (Any numbers) that are divisible by three their sum is also divisible by 3. This is divisibility rule of three.

So, (a+b) must be divisible by three.

Either statement independently sufficient.
Manager  B
Joined: 07 May 2016
Posts: 56
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

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LeoN88 wrote:
MathRevolution wrote:
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.

c= 3K, so (a+b)c is definitely divisible by 3.

Now, statement 1,

TU
ab
21
48

All two digit numbers (Any numbers) that are divisible by three their sum is also divisible by 3. This is divisibility rule of three.

So, (a+b) must be divisible by three.

Either statement independently sufficient.

I think I know where the confusion comes from. ab doesn’t have a multiplication sign between them. It is not a.b, it is ab without the multiplication.

However, I still think the positioning of the question is a bit confusing

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Intern  B
Joined: 06 Jan 2019
Posts: 4
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

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Sorry, I also don’t get, how ab divisible by 3 get us a+b divisible by 3
3*4 div by 3, but 3+4 is not...
Pls explain and give us several examples.

Posted from my mobile device
Intern  B
Joined: 06 Jan 2019
Posts: 4
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

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nyashka wrote:
Sorry, I also don’t get, how ab divisible by 3 get us a+b divisible by 3
3*4 div by 3, but 3+4 is not...
Pls explain and give us several examples.

Posted from my mobile device

Oh, sorry, I got it...
E.g. 12 is a two-digit number, it is divisible by 3, and the sum of the DIGITS is also divisible
Hence the answer is really D. Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-   [#permalink] 16 May 2019, 08:26
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