Max@Math Revolution wrote:Is |x+y|<|x|+|y|?
1) xy<0
2) x+y<0

*An answer will be posted in 2 days.

Dear Max

The answer is A as this question tests basic property of absolute value: |x+y|is always less than equal to |x| +|y| i.e. |x+y|<= |x| +|y|

The question stem can actually be rephrased. From above we know that it will always be : |x+y|<= |x| +|y|

The less than criteria will come when X & Y are opposite in signs. Hence the question can be rephrased: Are X and Y are opposite in sign?

Statement 1: SUFFICIENT

As per above explanation

Statement 2: INSUFFICIENT

As both X & Y can be negative or X negative but Greater than Y or Y negative but Greater than X, no conclusion can be drawn from this statement.

No need to check if both combined can solve. Hence answer is A

We can modify the original condition and the question. Even if we square the both sides, the sign of the inequality dos not change. Hence, the question becomes, |x+y|<|x|+|y|? |x+y|^2<(|x|+|y|)^2?, x^2+y^2+2xy< x^2+y^2+2|x||y|?, 2xy<2|xy|?, xy<|xy|?. Hence, the question becomes xy<0. The correct answer, thus, is A.
- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.