Data Sufficiency

[GMAT math practice question]

Is xy<0?

1) |x+y| < |x| + |y|
2) |x| - |y| < | x - y |

=>

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.
In order to solve this type of question within a limited time, we should memorize the property that | x + y | < |x| + |y| is equivalent to xy < 0.
So, condition 1) is sufficient.

Condition 2)
|x| - |y| < | x - y |
=> |x| < | x - y | + |y|
=> | x - y + y | < | x - y | + |y|
=> ( x - y )y < 0

because of the above property.
If x = 1 and y = -1, then we have xy < 0 and the answer is 'yes'.
If x = 1 and y = 2, then we have xy > 0 and the answer is 'no'.
Since we don't have a unique answer, condition 2) is not sufficient.

Therefore, A is the answer.

Answer: A