Is XY>0?

[hunkysden]

Is XY>0?

(1) X-Y > -2
(2) X-2y > -6
[editor: this question is transcribed incorrectly. see below.]

Got this question GMATprep 2.

I tried plugging in different values but that didn't lead me to a correct answer. Request you guys to help.

Thanks.






The OA is C.

[dsprashanth]

but both the equations satisy X=1, Y= -2, ?? so XY is negative...I think it should be E..
[editor: a non-positive value for XY, by itself, doesn't prove insufficiency. to prove insufficiency, you must prove that XY can be EITHER positive OR non-positive.]

[Ben Ku]

Is XY>0?

(1) X-Y > -2
(2) X-2y > -6

The question can be rephrased as: Do both x and y have the same signs?

Statement (1): This statement provides no information about x and y. We don't know which is larger. Nor do we know if they're positive or negative. (1) is insufficient.

Statement (2) basically provides the same information as (1), and is insufficient.

Looking at the statements together:
We can add or subtract the two inequalities if the direction of the inequalities are the same.
(x - y) - (x - 2y) > (-2) - (-6)
y > 4, so y must be positive.
[editor: this is incorrect. you can only ADD inequalities that face the same way.]

Using statement (1), we know that x - y > -4, so x > y - 4. If y > 4, then x will always be > 0. So x is also positive. (C) is correct.

[nitin_prakash_khanna]

Ben,

Are we allowed to Subtract Inequalities?
I think MGMAT Guide 3 (Equations, Ineq...) clearly explains that Addition of Inequality is allowed but subtraction is not.
[editor: this is correct; the above post was erroneous.
also, the question was transcribed incorrectly; see below.]

Even in this question if you see
X= 4, y=5/2
x-y = -3/2 >-2 Satisfy St 1
x-2y = -1> -6 Satisy St 2

And XY > 0

Now lets keep X=4 , y= -5/2
x-y = 13/2 >-2 Satisfy St 1
x-2y = 9 >-6 Satisfy St 2
And XY <0

So Answer Should E not C.
What did i miss?

[nitin_prakash_khanna]

Actually after doing a google search, i found the correct Question.

Is XY >0
1. X-Y >-2
2. X-2Y <-6

The sign of second inequality which was posted originally is wrong and with this Answer will be C

x-y >-2
-X + 2y >6

Now if you add the two y > 4 and it goes on as Ben explained. So Answer is C.

[anoo.anand]

can we subtract the inequalities if the sign is same in 2 equations ?

[RonPurewal]

can we subtract the inequalities if the sign is same in 2 equations ?

no!
YOU CANNOT SUBTRACT INEQUALITIES THAT FACE THE SAME WAY.

proof:
say x > 0 and y > 0.
if you could subtract these, then you'd have a comparison between x - y and 0. but, since x and y are arbitrary positive numbers, it's clear that x - y could be ... anything at all.

let's re-iterate that for everybody:
YOU CANNOT SUBTRACT INEQUALITIES THAT FACE THE SAME WAY.

[lh.abhishek]

Can anyone explain to me ..the following...as Y>4

now lets us take the 1st statement

X-Y>-2 then X-4>-2 then X>2 so X is positve..

however, it is not the case with the equation 2...

X-2Y<-6 then X-8<-6.. X<-6+8 .... X<2..

this means X can take negative values as wel?? then how can it be C!?

[lalitkc]

Abhishek ,

Addressing your doubt here :

Y > 4 means you cannot substitue Y = 4 in any of the two equations. Instead subsitiute a value greater than 4 for Y. Lets put Y = 4.1

St 1 ==> X - 4.1 > -2 ==> X > 2.1
St 2 ==> X - 2(4.1) < -6 ==> X < 2.2
From above two, we can conclude that if Y = 4.1 , X is between 2.1 and 2.2 which obviously be positive.

Hope above clears your doubts.

Lalit

[RonPurewal]

Abhishek ,

Addressing your doubt here :

Y > 4 means you cannot substitue Y = 4 in any of the two equations. Instead subsitiute a value greater than 4 for Y. Lets put Y = 4.1

St 1 ==> X - 4.1 > -2 ==> X > 2.1
St 2 ==> X - 2(4.1) < -6 ==> X < 2.2
From above two, we can conclude that if Y = 4.1 , X is between 2.1 and 2.2 which obviously be positive.

Hope above clears your doubts.

Lalit

nice.

by the way, it's extremely important that you learn to manipulate inequalities. if you have to "plug in", you'll have to plug in all extreme values in order to see the entire spectrum of the inequality's behavior.

you can't plug in just one number into an inequality and think you've pegged the behavior of the whole inequality.

[vicksikand]

Is xy >0
1: x-y > -2
2: x-2y <-6
Rewrite 1: y-2<x
Rewrite 2: x<2y-6
combine 1 &2
y-2 < x < 2y-6
y-2 < 2y-6
or y>4
Say y=4.1
4.1 -2 < x < 2*4.1 -6
2.1 < x < 2.2
x could be 2.15,2.16 etc. hence x is +ive
xy > 0
Answer is C.

[mschwrtz]

very nice to this point:

combine 1 &2
y-2 < x < 2y-6
y-2 < 2y-6
or y>4

but rather than plugging values, just note that

y-2 < x

means

y<x+2

so
4<y<x+2

4<x+2

2<x

both x and y are positive

[shaji]

"both x and y are positive"-NOT NECESSARY!!!

x=80 & y=-10 does satisfy both statements.

[RonPurewal]

"both x and y are positive"-NOT NECESSARY!!!

x=80 & y=-10 does satisfy both statements.

are you responding to the incorrectly transcribed version of the problem (the one in the original post)?
if so, go back and read the boldfaced editor's note in that post -- the original post contains an incorrect transcription of the problem.

the correct version is in a post a little bit further down the thread (the fifth post on the thread, if you count from the beginning). if you look at that version, you will note that these values do not work.

[shaji]

Ron;
Thanks indeed!
I was referring to the original transcription.