Is xy 0 ? (1) |xy| + |x|y + x|y| + xy 0 (2) -x

Question

Is xy > 0 ? (1) |xy| + |x|y + x|y| + xy > 0 (2) -x < -y < |y|

rohit8865 · Answer

1. take 4 cases a) y>0 , x<0 then |xy| + |x|y + x|y| + xy =0 but it should be >0 as condition given in option....thus y>0 , x<0 is not the case b) y<0 , x>0 same as above c)y<0 , x<0 same as above d) y>0 , x>0 then |xy| + |x|y + x|y| + xy = 4xy >0 .....thus x>0 and y>0 is only satisfying thus suff 2. givn condition only prevails when y>0 and thus x is also >0 suff Ans D

chetan2u · Answer

Hi, Anything that tells us what are the signs of x and y will be sufficient.. If x and y are SAME sign, ans is YES... If x and y are OPPOSITE, ans is NO.. Let's see the statements.. 1. |xy| + |x|y + x|y| + xy > 0 If only x<0, |xy| and |x|y will be positive and x|y| and xy will be NEGATIVE.. When you add all four terms and will be 0.. Similarly for only y<0.. Thus both are of same sign.. Sufficient 2. -x< -y < |y| In -y<|y|, y will be positive otherwise both would have been EQUAL.. -X<-y means x is positive, which makes -x as negative.. Again xy>0.. Sufficient D

Darkhorse12 · Answer

Hello  chetan2u ,

In statement-1 as you mentioned 
If only x<0, |xy| and |x|y will be positive and x|y| and xy will be NEGATIVE..
When you add all four terms and will be 0..
Similarly for only y<0..

Also if both are x and y are negative then also the result is 0.

Its only true when x and y both are positive.

Hence Sufficient. Right??

pitroncoso · Answer

#1 is equivalent to (|x|+x)*(|y|+y)>0

Now, the terms (|z|+z) can only be positive or zero. As the inequality is stricly greater than zero, the value of zero for any term in the parenthesis is not allowed. Then necessarily (|z|+z)>0 (strictly) for each z=x and z=y. This in turn means that x>0 and y>0 (strictly). Therefore, xy>0 (sufficient)

#2 Can be divided in two: -x<-y and -y<|y|
Restating: (i) x>y and (ii) |y|+y>0
As we have seen (ii) means y>0, and then due to (i), x>0. Therefore, xy>0 (sufficient)

So, the answer is D

HKD1710 · Answer

Yes  Darkhorse12 ,

If both are negative then

|xy| --> +xy

xy --> +xy

x|y| --> -xy

|x|y --> -xy

xy + xy - xy - xy = 0

also x=y=0 is also not valid.

so both x & y has to be +ve.

vishalkumar4mba · Answer

Nice explanation . Thanks !!

musunna · Answer

seems harder. By the way, what is the exact source of this question?

chetan2u · Answer

Yes ...

We are looking for an answer that tells us that x and y are of same sign..
Statement I tells us that both x and y are both POSITIVE hence sufficient..

sobby · Answer

My reasoning:

A- lets take 4 possibility ..
x,y = (+,+) ,(-,+) , (+,-) , (-,-)
1st case (+,+) -- overall we will get positive , so fine 
2nd case -(-,+) -- we will get 0 --discard
3rd case --same as second 
4th case --we will get a negative --discard ...
only viable possibility is x any can be positive..
suff

B--|Y| always be +ve...
-Y < |Y| can be only possible when Y is positive ...
-X < -Y 
RHS is negative (Proved above).
Value of X have to be +ve ..else x < -Y (wrong)
Suff ..

So D...

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is xy > 0 ? (1) |xy| + |x|y + x|y| + xy > 0 (2) -x < -y < |y|

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is xy > 0 ? (1) |xy| + |x|y + x|y| + xy > 0 (2) -x < -y < |y|

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards