If A and B denote the digits of a three-digit number BAB, is BAB divis

Breaking Down the Info:

In order for BAB to be divisible by 4, we need AB (the two-digit number) to be a multiple of 4.

Statement 1 Alone:

We may have A = 2 and B = 2, then 22 is not divisible by 4 so 222 is not either.

We could also have A and B both be multiples of 4, making BAB a multiple of 4. Insufficient.

Statement 2 Alone:

2B + A is a multiple of 4. Since 2B has to be even, we know that A must be even. However, B can still be odd so this is insufficient.

Both Statements Combined:

Combining the statements, if we let B be an odd number, then A must be a multiple of 4 plus 2 (\(4i+2\)) since 2B + A must be a multiple of 4. In this case, A*B would not be a multiple of 4 since \(A*B = Odd * (4i + 2)\) is only a multiple of 2.

Then we can conclude that B cannot be odd, thus B must be even. Then both B and A must be even. From statement 2, we can conclude A must be a multiple of 4 if B must be even. Finally, this still does not guarantee that BA is a multiple of 4, as we can still have A = 4 and B = 2. Insufficient.

Answer: E