Data Sufficiency

[GMAT math practice question]

The product of 4 consecutive odd integers is negative. What is the largest odd integer?

1) The smallest integer is negative.
2) The third smallest integer is negative.

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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 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 their own first.

Let the integers be 2n - 3, 2n - 1, 2n + 1 and 2n +3.
Since (2n-3)(2n-1)(2n+1)(2n+3) < 0, either one of the integers is negative, or three of the integers is negative. There are two possible lists of integers: -1, 1, 3, 5 and -5, -3, -1, 1.

Condition 1)
The largest odd integers in the two possible lists are 5 and 1.
Since we don't have a unique answer, condition 1) is not sufficient.

Condition 2)
If the third smallest integer is negative, then the integers are -5, -3, -1, 1.
The largest integer is 1.
Since we have a unique answer, condition 2) is sufficient.

Therefore, B is the answer.

Answer: B

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.