Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the 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]

Let’s follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find whether x-y = even – where ‘x’ and ‘y’ are integers.

In order to be x -y = even, (x,y) should be (even, even) or (odd, odd).

Thus, let look at condition (2), it tells us that 3x + 11y = even, from which we get (x,y)=(even,even) since 3 * even + 11 * even = even + even = even, or (x,y) = (odd,odd) since 3 * odd + 11 * odd = odd + odd = even.

So, the answer becomes yes. The answer is unique YES, so the conditions combined are sufficient, according to CMT 1 - there must be a unique YES or a NO.

Condition (1) tells us that x + 4y = odd

=> x = odd [∵ 4y=even]

=> x=y=odd -> x - y=odd-odd=even -> Is x-y=even -> YES

=> x=odd ; y=even -> x-y=odd-even=odd -> Is x-y=even -> NO

The answer is not a unique Yes or a NO, so the condition (1) alone is not sufficient, according to CMT 1 - there must be a unique YES or a NO.

Condition (2) alone is sufficient.

Therefore, B is the correct answer.

Answer: B