I'll try to make it more clear.
Is xy > 0?
1) x-y > -2
2) x-2y < -6
When we have two variables, there is essentially an infinite number of possibilities. If X = 10, then Y must be less than 12 because 10 - 12 = -2, which is equal to, not less than 12. The key to answer the question Is xy > 0 is to find any values for x & y that have different signs.
Since we are not told x and y are integers, fractions are possible. This is as simple as x = -1 and y = \(\frac{1}{2}\). That would be \(-1\frac{1}{2}\) which is greater than -2. -1 * 1/2 = - 1/2, and xy is NOT greater than 0, but at the same time, some values for X and Y that satisfy #1 have a product greater than zero. This means the information is insufficient because greater than 0 and less than 0 is possible. We cannot difinitively answer either way.
Is xy > 0?
1) x-y > -2
2) x-2y < -6
Same idea for #2. Easiest way to start is X = 1. Then y < 3.5. If y is 3.5, then 1 - 2 * 3.5 = 1 - 7 < -6 = -6<-6 which isn't true. We need to find some way that either x or y is negative when the other is positive. If X is a negative, such as -1, then
-1 - 2y < -6
-2y < -5
{switch the sign because we're dividing by a negative number}
y > 5/2
This means we have x = -1 and y > \(\frac{5}{2}\) then x * y = a number less than zero.
If you take the equations together, we must find some values for x and y that satisfy both equations. Then we must determine if there is any possible way x or y can be negative, but not both.
I take some of the numbers I've already come up with. Like #1, x = 10 and y =13. 10 - 13 = 3 (i.e., greater than -2). Works for #1, check for #2.
x-2y < -6
10 - 2 (13) < -6
10 - 26 < -6
-16 < -6 TRUE
We need to check answers for #2 that had 1 pos and 1 neg to see if they work in #1. So x = -1, and y = 5/2
-1 - 5/2 > -2
-3.5 > -2 FALSE!
In statement #2, if x is negative and the value of y is such that the statement is true, then y must be between 2.5>y>0.
I used the following possibilities:
x= -1, y>2.5
x= -2, y>2
x= -3, y>1.5
x= -4, y>1
x= -5, y>0.5
x= -6, y>0
x = -7, y = -0.5 ( At this point we have 2 negative numbers, which would always make xy>0 true. we're looking to disprove this in some manner in order to answer the question.
Not one of these possible combinations makes #1 true.
-1 - 2.5 > -2 Nope
-2 - 2 > -2 Nope
-6 - 0 > -2 Nope
etc...
The only values that satisfy both equations will always lead to x * y being a positive number (i.e., greater than zero).
I'm sorry this is so long. I tried to explain each step of my analysis in greater detail than I would actually use on the GMAT simple for the sake of time.
utgirl826 wrote:
The OA is C but I am having trouble understanding jallenmorris's explanation. Can someone help me? or explain?? Thank you!
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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.
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