If x, y, and z are integers, is xyz a multiple of 6?

[Max@Math Revolution]

[GMAT math practice question]

If x, y, and z are integers, is xyz a multiple of 6?

1) x+y+z is a multiple of 6
2) x, y, and z are consecutive

[Max@Math Revolution]

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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.

Since the product of three consecutive integers is a multiple of 6, condition 2) is sufficient. Without loss of generality, since condition 2) tells us that x, y and z are consecutive, we can write y = x + 1 and z = x + 2. Then xyz = x(x+1)(x+2) is a multiple of 6 since x(x+1) is a multiple of 2 and x(x+1)(x+2) is a multiple of 3.

Condition 1)
If x = 1, y = 2 and z = 3, then xyz = 6 and the answer is 'yes'.
If x = 2, y = 2 and z = 2, then xyz = 8 and the answer is 'no'.
Condition 1) is not sufficient, since it doesn't yield a unique answer.

Therefore, B is the answer.
Answer: B