chetan2u wrote:
Is \(a\) divisible by \(3\)?
(1) \(a+3b\) is divisible by \(3\).
(2) \(b\) is divisible by \(3\).
New Question
Here we are NOT given that a/b are integers, so we cannot assume them to be so.
(1) a+3b is divisible by 3. If b =2/3, this makes 3b = 2. Now we can have a = 1, which makes a+3b divisible by 3, and here 'a' is NOT divisible by 3.
But we can have another case say b = 1, here 3b = 3. Now whichever value a takes will have to be a multiple of 3 (eg, 3, 6,..) in order for a+3b to be a multiple of 3.
So 'a' can or cannot be a multiple of 3.
Not sufficient.
(2) This doesnt tell anything about 'a', so definitely
Not Sufficient.
Combining the two statements, since b is divisible by 3, b has to be an integer. So 3b will also definitely be an integer. Now a+3b is also divisible by 3 and 3b is divisible by 3..this can only happen if 'a' too is divisible by 3. Sufficient.
Hence
C answer