Data Sufficiency

Is xy > 0?

(1) x - y > -2
(2) x - 2y < -6

Is the following approach correct?

First I multiplied the statement (2) with -1:
(2) -x + 2y > 6

Now I added statement (1) and statement (2):
(1) x - y > -2
(2) -x + 2y > 6

results in y > 4

Then I use this expression in combination with statement (1) (I add it):
(1) x - y > -2
y > 4

results in x > 2

Therefore, x > 2 and y > 4 and hence xy = positive

Correct answer: C

I am not sure whether I can do these calculations like this. Could somebody clarify? Or also give a better strategy to solve this question?

Thx a lot

Your method is correct.
1) x > y-2. x=1,y=-2. xy <0 also x=4,y=3,xy>0 insufficient
2) x < 2y-6. y=3, x=-1, xy<0 and y=4,x=1, xy>0 insufficient
1&2) y-2 < x < 2y-6.
thus y>4. and x>y-2 >2
xy>0
Sufficient
IMO C

cans wrote:Your method is correct.
1) x > y-2. x=1,y=-2. xy <0 also x=4,y=3,xy>0 insufficient
2) x < 2y-6. y=3, x=-1, xy<0 and y=4,x=1, xy>0 insufficient
1&2) y-2 < x < 2y-6.
thus y>4. and x>y-2 >2
xy>0
Sufficient
IMO C

Ok thanks! But I am not able to follow your approach! As far as I can see, you just plug in some different number in statement (1) and (2). But then I don't understand, how you combine these two statements? Could you tell me plz? Thx a lot

@Fractal
When you combine both statements u can take an algebraic approach.
x - y > -2
and
-6> x - 2y

Add both

x-y-6 > x-2y-2
y>4
Lets assume y=5 which satisfies the above condition.

Put y=5 in statement 1 and 2

x-5>-2
x>3

x-2(5)<-6
x<4

Combining we get 3<x<4 Meaning x is +ve and we already know that y is +ve. So their product is +ve. Hence C

Fractal wrote:

cans wrote:Your method is correct.
1) x > y-2. x=1,y=-2. xy <0 also x=4,y=3,xy>0 insufficient
2) x < 2y-6. y=3, x=-1, xy<0 and y=4,x=1, xy>0 insufficient
1&2) y-2 < x < 2y-6.
thus y>4. and x>y-2 >2
xy>0
Sufficient
IMO C

Ok thanks! But I am not able to follow your approach! As far as I can see, you just plug in some different number in statement (1) and (2). But then I don't understand, how you combine these two statements? Could you tell me plz? Thx a lot

1 plugged in numbers in 1 and 2, to show they are not sufficient. ant for C),
if x>a and x<b we can say that b>x>a or b>a...

please note the following rules:

you CAN add inequalities with the same direction,
and you can subtract opposite inequalities, but not the other way
around. For example, since we know that:

5 > 4 and
3 > 1

we can add them and know that:

8 > 5

but we can't subtract them and get:

2 > 3 (WRONG!)

However, we can write it as:

5 > 4 and
1 < 3

and then we can subtract them:

4 > 1

but we can't add them:

6 > 7 (WRONG!)

if you prefer adding, just multiply by -1:

5 > 4 and --> 5 > 4
1 < 3 --> -1 > -3
---------
4 > 1