Data Sufficiency

[GMAT math practice question]

$$Is\ 2x+y>0?$$

$$1)\ x+y>0$$
$$2)\ xy<0$$

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

$$Is\ 2x+y>0?$$

$$1)\ x+y>0$$
$$2)\ xy<0$$

Both statements are satisfied by the following:
Case 1: x=-1 and y=3
Case 2: x=-2 and y=3
In Case 1, 2x+y = 2(-1)+3 = 1, so the answer to the question stem is YES.
In Case 2, 2x+y = 2(-2) + 3 = -1, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.

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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.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2) together:
If x = 2, and y = -1, then the answer is 'yes'.
If x = -1, and y = 2, then the answer is 'no'.

Since we don't have a unique solution, both conditions together are not sufficient.

Therefore, the answer is E.

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.