-
iwillsurvive101
- Senior | Next Rank: 100 Posts
- Posts: 58
- Joined: Mon Nov 07, 2011 7:44 pm
- Location: Washington DC
- Thanked: 1 times
Hi!iwillsurvive101 wrote:Is x + y > 0?
(1) x - y > 0
(2) x2 - y2 > 0
We want to know if the sum of x and y is positive. So, we either need the individual values of x and y or information about the expression "x+y".
(1) x - y > 0
We know nothing about x and y individually, so (1) is insufficient.
If the concepts don't jump out at you, then pick numbers to see if you can get both a YES and a NO answer.
if x = 5 and y = 3, then x-y>0. Is 5+3>0? YES
if x = 5 and y = -6, then x-y>0. Is 5 + (-6) > 0? NO
Since we can get both a yes and no answer, (1) is insufficient: eliminate A and D.
(2) x^2 - y^2 > 0
The GMAT loves to test us on special quadratics - here we have a difference of squares. We can rewrite (2) as:
(x+y)(x-y) > 0
For any product of two terms to be positive, the signs of the two terms must be the same (i.e. both + or both -). So, (2) tells us that:
x+y and x-y are both positive;
OR
x+y and x-y are both negative.
So, do we know if x+y is positive? NO - it could be positive or negative. Insufficient: eliminate B.
Since neither statement was sufficient alone, we have to combine them. So, now we know that:
x+y and x-y are both the same sign;
AND
x-y is positive.
Accordingly, x+y must be positive as well. Together sufficient: choose C!
