Data Sufficiency

[GMAT math practice question]

If a, b, and c are consecutive integers and a<b<c, is a an even number?

1) ac is a multiple of 8.
2) abc is a multiple of 8.

Max@Math Revolution wrote:[GMAT math practice question]

If a, b, and c are consecutive integers and a<b<c, is a an even number?

1) ac is a multiple of 8.
2) abc is a multiple of 8.

Case 1: a, b and c are EVEN-ODD-EVEN
Case 2: a, b and c are ODD-EVEN-ODD

Statement 1:
Here, Case 2 is not possible: if a and c are both odd, then ac will be odd and thus not a multiple of 8.
Since only Case 1 is possible, a must be even.
SUFFICIENT.

Statement 2:
Case 1 is possible if a, b and c are 2, 3, and 4.
Case 2 is possible if a, b and c are 7, 8, and 9.
Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT.

The correct answer is A.

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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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The statement that a is an even integer is equivalent to the statement that ac is a multiple of 8: if a and c are two consecutive even integers, then one of them is a multiple of 4.
Thus, condition 1) is sufficient.

Condition 2)
If a = 2, b = 3, c = 4, then ac = 8, and the answer is "yes".
If a = 7, b = 8, c = 9, then ac = 7*9, and the answer is "no".
Since we don't have a unique answer, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A