This question is easiest to solve if we know our even/odd properties.
Statement 1
If b = 2c, b must be even. This is because multiplying an even number (like 2) by an even OR an odd number will always give another even number. c can be even or odd. This doesn't tell us anything about a, though. Insufficient.
Statement 2
If a = c + 1, then a must be the opposite of c - so if c is odd, a is even, and if c is even, a is odd. However, we don't know whether c is even or odd, so we can't determine if a is even or odd. Insufficient.
Both
Statement 1 wasn't able to tell us whether c was even or odd, so it doesn't help us determine anything about a in Statement 2. So the correct answer is E - we can't solve the problem, even with both statements.
If you don't have even/odd properties memorized, you can always plug in a couple numbers out to find patterns. For instance, plugging in 2 and 3 for c should lead you to the same conclusion about b - that it will be even whether c is even or odd.
