Data Sufficiency

[GMAT math practice question]

What is the median of 3 consecutive integers?

1) The product of the integers is 0
2) The sum of the integers is equal to their product

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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.

Let the 3 consecutive integers be n - 1, n and n + 1.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on its own first.

Condition 1)
Since the product of the three integers is 0, one of the integers must be 0. There are three possible lists of consecutive integers:
( -2, -1, 0 ), ( -1, 0, 1) and ( 0, 1, 2 ).
The medians of these lists are -1, 0 and 1.
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
Since the sum of the integers is equal to their product, there are three possible lists of consecutive integers:
(-3, -2, -1), ( -1, 0, 1) and ( 1, 2, 3).
The medians of these lists are -2, 0 and 2.
Since we don't have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
(-1, 0, 1) is the unique list of three consecutive integers that satisfies both conditions 1) & 2).
Both conditions together are sufficient.

Therefore, C is the answer.

Answer: C

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.