If a, b, and c are integers, is the number 3(a + b) + c divisible by 3

Solution -

We have to verify that (3(a + b) + c)/3 = (a + b) + c/3, is c a multiple of 3?

Stmt1 - a + b is not divisible by 3. -> No information about c. Not Sufficient.
Stmt2 - c is divisible by 3. -> Clearly Sufficient.

Ans B.

3(a+b) i a multiple of 3, so if c is a multiple of 3 the answer will be Yes
(1) no info about c - not suff
(2) bingo... Ans (B)

Question : is the number 3(a + b) + c divisible by 3?

Statement 1: a + b is not divisible by 3.
No information about C hence,
NOT SUFFICIENT

Statement 2: c is divisible by 3.
In the expression 3(a + b) + c, 3(a+b) is already divisible by 3an if c is a multiple of 3 as well then 3(a + b) + c must be a sum of two multiples of 3 which must be a multiple of 3. Hence
SUFFICIENT

Answer: option B

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No Is the number 3(a + b) + c divisible by 3?

Given information: a, b and c are integers. You can Use Conceptual Knowledge here. Given that each of these numbers is an integer, 3(a + b) will be a multiple of 3 regardless of the values of a and b. Therefore you are simply focused on the question “Is c a multiple of 3?” If c is a multiple of 3 then the whole thing is divisible by 3. If c is not a multiple of 3 then the whole thing is not divisible by 3.

Statement 1: a + b is not divisible by 3. As mentioned above the value of a + b does not matter. So this statement is not sufficient alone. This is the advantage of doing your work early. When you truly understand the question you can work through the statements very efficiently. This statement is not sufficient. The correct answer is B, C, or E.

Statement 2: c is divisible by 3. This is an exact answer to the question that you developed by manipulating the question stem. If c is a multiple of 3 and since we know from algebra that 3(a + b) will also be a multiple of 3 then we also know that adding two multiples of 3 gives a result that is a multiple of 3. Try it. Make c = any multiple of 3. Then make a and b any integers at all. 3(a + b) will also be a multiple of 3 and “3(a + b) + c = a multiple of 3.” The answer is always “yes.” It is consistent and sufficient.

The correct answer is B.

This is really just an algebra question- we need to find out whether we can prove "3(a +b) + c / 3 = x where x must be an integer" - true or false

St 1

3(a +b) + c / 3 = x
(a+b) + (c/3) = x ... a + b doesn't actually have to be divisible 3 only "C" has to in order for "3(a + b) + c [to be] divisible by 3"

insufficient

St 2

If c is divisible by 3 then yes

suff

b