Data Sufficiency

[Math Revolution GMAT math practice question]

Is 0 between x and y?

1) x-y>0
2) x^2-y^2>0

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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.

If we modify the question, it asks if xy < 0. Since the two conditions do not give us enough information to determine the sign of xy, both conditions together are not sufficient, and the answer is E.

Since we have 2 variables (x and y) and 1 equation, D is most likely to be the answer. So, we should consider each of the conditions on its own first.

Conditions 1) & 2)
If x = 2 and y = -1, then 0 is between x and y.
If x = 2 and y = 1, then 0 is not between x and y.
Since we don't have a unique solution, both conditions together are not sufficient.

Therefore, E is the answer.

Answer: E

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.