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

Question

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.

arif24 · Answer

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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blynvaldez · Answer

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?

K_Leon · Answer

Statement 1: ab = 10a+b = (a+b)+9a is divisible by 3 so a+b is divisible by 3
Statement 2: Obvious yes

MathRevolution · Answer

==> 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).

Answer: D

krasha · Answer

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 ?

azoz7 · Answer

I had the same confusion! I agree with your approach

LeoN88 · Answer

Let's start with statement 2,

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.

azoz7 · Answer

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

Posted from my mobile device

nyashka · Answer

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

nyashka · Answer

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.

Capablanca · Answer

1) The 2-digit integer ab is divisible by 3:

By the divisibility rule, we know that for a number to be divisible by 3, the sum of its digits must be divisible by 3. So for the number ab to be divisible by 3 means that (a+b) is divisible by 3, so (a+b)c is divisible by 3.

Sufficient.

2) When c is divided by 3, the remainder is 0.

This means c is divisible by 3.

Sufficient.

Answer (D)

SukhAgam · Answer

yes that was what i was looking for thank for clarifying my doubt

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

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