psm12se wrote:Is xy > 0 ?
1. x - y > -2
2. x - 2y < -6
Is xy>0?
i. x-y>-2
ii. x-2y<-6
[/quote]
Target question:
Is xy>0?
Statement 1: x-y > -2
There are several pairs of numbers that meet this condition. Here are two:
Case a: x = 5 and y = 1, in which case
xy is greater than 0
Case b: x = 5 and y = -1, in which case
xy is not greater than 0
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x - 2y < -6
There are several pairs of numbers that meet this condition. Here are two:
Case a: x = 1 and y = 5, in which case
xy is greater than 0
Case b: x = -1 and y = 5, in which case
xy is not greater than 0
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Here's what we know:
x-y > -2
x-2y < -6
Since both inequalities have an x, let's isolate x in both of them to get:
y-2 < x
x < 2y-6
Aside: Notice that I rewrote them so that the 2 inequality symbols are pointing in the same direction.
Now we can combine these inequalities to get: y-2 <
x < 2y-6
Next, remove the x to get: y-2 < 2y-6
Then subtract y from both sides and add 6 to both sides to get: 4 < y
Great, we now know that
y is positive.
Also, if y-2 < x (and y>4), then we know that
x must also be positive
Since we now know that x and y are positive, we can be
certain that
xy is greater than 0
So, the answer is
C
Cheers,
Brent
