crazy4gmat wrote:Is XY>0?
(1) X-Y > -2
(2) X-2y > -6
Let's start by rephrasing the question.
When will xy be greater than 0? When x and y are the same sign. So, we can ask:
Do x and y have the same sign?
(Note: if either one equals 0, we get an automatic "no" answer to the question.)
Let's look at the statements in general using some basic number properties rules.
If x is positive and y is negative, each statement reduces to:
(positive - negative) > (negative)
Since subtracting a negative is the same as adding a positive, we can rewrite this as:
(positive + positive) > (negative)
which is, of course, always true.
So, we can definitely pick a positive x and a negative y to get a "NO" answer to the original question.
Next we have to see if can get a "YES" answer to the original question, i.e. can we make them both positive or both negative.
Both negative is probably easier, so let's start there.
We're subtracting y from x in both statements, so let's pick a "big" negative y and a "small" negative x.
If x = -1 and y = -100, we get:
1) -1 - (-100) > -2
-1 + 100 > -2
99 > -2.
This inequality is true, so -1 and -100 are permissible numbers. Is (-1)(-100)>0? YES.
2) -1 - 2(-100) > -6
-1 + 200 > -6
199 > -6
This inequality is true, so -1 and -100 are permissible numbers. Is (-1)(-100)>0? YES.
So, even after combining, we can pick two negatives OR a negative and a positive: insufficient, choose (E).
