Solution: To save time and improve accuracy on DS questions in GMAT, learn, and apply Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find ‘Is a – b – c is odd’ – where a, b, and c are integers.

For a - b - c = odd, (a,b,c) = (even,odd,even), (even,even,odd), or (odd, even, even).

Thus, look at condition (1), it tells us that 'a' and 'b' are 'even' and 'c' is 'odd', from which a - b - c = even - even - odd = odd.

So we get YES as an answer. The answer is unique, yes, so condition (1) alone is sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.

Condition (2) tells us that a, b and c are consecutive integers, from which we cannot determine whether a - b - c = odd.

For example, if (a,b,c) = (2,3,4), then a - b - c = 2 - 3 - 4 = -5 = odd we get YES as answer.

However if (a,b,c) = (1,2,3), then a - b - c = 1 - 2 - 3 = -4 = even we get NO as answer.

The answer is not unique, both yes and no, so condition (2) alone is sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.

Condition (1) alone is sufficient.

Therefore, A is the correct answer.

Answer: A