Last visit was: 17 Jul 2025, 08:56 It is currently 17 Jul 2025, 08:56
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
742,198
 [1]
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,198
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
AOD
Joined: 31 Mar 2018
Last visit: 18 Nov 2022
Posts: 9
Own Kudos:
2
 [1]
Given Kudos: 4
WE:Marketing (Telecommunications)
Posts: 9
Kudos: 2
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,198
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
AOD
Joined: 31 Mar 2018
Last visit: 18 Nov 2022
Posts: 9
Own Kudos:
Given Kudos: 4
WE:Marketing (Telecommunications)
Posts: 9
Kudos: 2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
AOD
Bunuel


We got y > 4 not y = 4, so you cannot substitute the way you did. In the solution, x > 2, is derived by adding y > 4 and x > y - 2 (we can add inequalities when their signs are in the same direction): \(y+x>4+(y-2)\) --> \(x>2\).

Hi Bunuel ,

Kindly clarify -

"In the Solution of X>2" : Instead of adding Y>4 and X > Y-2 (from equation 1) , can we not add Y>4 and -X> 6-2y ? (from equation 2 : x-2y <-6)

If we do this , we will arrive at X < 2

y > 4
-x > 6 - 2y

Adding those gives:
y - x > 10 - 2y
3y - x > 10

Sorry Bunuel , I still don't follow. Maybe I'm missing something.

Last step =3y - x > 10

Substituting Y >4 : 12 - X > 10 -> 2 > X -> X < 2 : right?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
742,198
 [1]
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,198
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AOD
Bunuel
AOD

Hi Bunuel ,

Kindly clarify -

"In the Solution of X>2" : Instead of adding Y>4 and X > Y-2 (from equation 1) , can we not add Y>4 and -X> 6-2y ? (from equation 2 : x-2y <-6)

If we do this , we will arrive at X < 2

y > 4
-x > 6 - 2y

Adding those gives:
y - x > 10 - 2y
3y - x > 10

Sorry Bunuel , I still don't follow. Maybe I'm missing something.

Last step =3y - x > 10

Substituting Y >4 : 12 - X > 10 -> 2 > X -> X < 2 : right?

How are you getting 12 - x > 10?

3y - x > 10
3y > 12.

We cannot subtract those two the way you did.

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).
Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).
Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

For more check Manipulating Inequalities.
User avatar
LauraOrion
Joined: 19 Jul 2018
Last visit: 29 Apr 2019
Posts: 97
Own Kudos:
77
 [1]
Given Kudos: 9
Posts: 97
Kudos: 77
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This question is fantastic for bringing up a strategy not enough people think to do with inequalities: as long as you have the inequality signs pointed in the same direction, you can add the inequalities together to eliminate a variable the same way you would for a system of equations.

Here once you've eliminated A, B, and D by quick conceptual number picking**, you can multiply the Statement 2 inequality by -1 so that you have both inequalities with signs in the same direction:

x - y > -2

and

2y - x > 6

If you then add the two inequalities, you eliminate the x term (one is positive and the other is negative), leaving:

y > 4

So you know y is positive, and then when you plug y > 4 in to the first equation (which can be expressed as x > y - 2), you know that x is greater than "something greater than 4, minus 2" so x must also be positive, so you know that the product xy is greater than 0. Together the statements are sufficient and the answer is (C).

Note that when you do have two inequalities this situation presents itself more often than most people think! If you can get the signs facing in the same direction (generally by multiplying one inequality by -1 if they're not already in the same direction) you can add the inequalities together (don't subtract, since "minus" is basically "plus negative" and can screw up the positive/negative inequality logic) and solve like a system of equations.


** Try x = 4 and y = 6 versus x = -2 and y = 0 for statement 1 and x= 0 and y = 3 and x = 1 and y = 12 for statement 2, for example.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 17 Jul 2025
Posts: 11,294
Own Kudos:
41,789
 [2]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,294
Kudos: 41,789
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is xy > 0 ?

This basically asks us .."Are x and y of SAME sign?"

(1) x – y > –2
x>y-2..
y=2, x=4...yes
y=-2, x=4...no
Insufficient

(2) x – 2y < –6
x<2y-6..
y=2, x=-4...no
y=-2, x=-15...yes
Insufficient


Combined
x-y>-2
x-2y<-6 or 2y-x>6
Add the two inequalities
x-y+2y-x>-2+6.......y>4
Multiply first by 2 and add the equations to get x
2(x-y)+2y-x>2*(-2)+6.....2x-2y+2y-x>6-4.....x>2

So both x and y are positive
Ans is always yes
Sufficient

C
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 16 Jul 2025
Posts: 5,703
Own Kudos:
5,228
 [1]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
GMAT 1: 690 Q50 V34
Posts: 5,703
Kudos: 5,228
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Baten80
Is xy > 0?

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

Is xy>0

1) x-y > -2
x>y-2
xy>y(y-2)=y^2-2y
Value of y is unknown
NOT SUFFICIENT

2) x-2y < -6
x<2y-6
xy<y(2y-6)=2y^2-6y
Value of y is unknown
NOT SUFFICIENT

Combining (1) & (2)
1) x-y > -2
x>y-2. (3)
2) x-2y < -6
x<2y-6
-x>-2y+6 (4)
Adding (3) & (4)
0>-y+4
y>4>0 (5)
From equation (3)
x>y-2>4-2=2>0
x>2>0 (6)
xy>0
SUFFICIENT

IMO C
User avatar
avigutman
Joined: 17 Jul 2019
Last visit: 15 Jul 2025
Posts: 1,294
Own Kudos:
1,896
 [19]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
GMAT 3: 770 Q50 V45
Posts: 1,294
Kudos: 1,896
 [19]
14
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
Video solution from Quant Reasoning (starts at 0:00:25):
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
avatar
UserMaple5
Joined: 27 Apr 2021
Last visit: 24 Jul 2022
Posts: 45
Own Kudos:
Given Kudos: 260
Posts: 45
Kudos: 12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EgmatQuantExpert Bunuel JeffTargetTestPrep

Hi experts. I tend to get these types of questions right but they take me WAY TOO LONG to do. I normally test cases and it takes a while. Are there any strategies other than testing cases that I can use for these kind of questions to help improve timing?

Thank you in advance!
User avatar
avigutman
Joined: 17 Jul 2019
Last visit: 15 Jul 2025
Posts: 1,294
Own Kudos:
1,896
 [2]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
GMAT 3: 770 Q50 V45
Posts: 1,294
Kudos: 1,896
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
UserMaple5
EgmatQuantExpert Bunuel JeffTargetTestPrep

Hi experts. I tend to get these types of questions right but they take me WAY TOO LONG to do. I normally test cases and it takes a while. Are there any strategies other than testing cases that I can use for these kind of questions to help improve timing?

Thank you in advance!

UserMaple5 yes, you can use number line reasoning to avoid having to test cases. You can see how I do that in the first part of the video from this post:
https://gmatclub.com/forum/is-xy-0-1-x- ... l#p2686547
avatar
JuliaMaria123
Joined: 13 Jun 2021
Last visit: 22 Jul 2021
Posts: 1
Given Kudos: 2
Posts: 1
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think it should be possible to skip all the calculations and graphical solutions and number line drawings and just think about this for a few moments.

So it is clear by just picking a few numbers that neither (1) nor (2) are sufficient by itself.

So now the big question is - are they sufficient together?

We have: x - y > -2 and x - 2y < -6 from statement (1) and (2).

We can rewrite statement (2): x - y - y < -6 and the red-coloured part much be larger than -2, as it is given by statement (1). But statement (2) must be smaller than -6. We can only achieve that if y is positive (notice the negative sign) and must be great than 4 to make statement (2) smaller than -6).

So now we know that y is positive and greater than 4 and we can go back to (1): x - y > -2. If y is greater than 4, we now know that x must be positive so that (1) is great than -2.
User avatar
Bambi2021
Joined: 13 Mar 2021
Last visit: 23 Dec 2021
Posts: 321
Own Kudos:
Given Kudos: 226
Posts: 321
Kudos: 130
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Taken together:

Subtracting inequalities of different signs -->

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

y > 4

From s1 it is now obvious that x must also be positive.

Posted from my mobile device
User avatar
forrever
Joined: 15 Mar 2023
Last visit: 23 Apr 2025
Posts: 65
Own Kudos:
Given Kudos: 18
Location: India
GMAT 1: 690 Q50 V34
GMAT 1: 690 Q50 V34
Posts: 65
Kudos: 8
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Is xy>0?

Note that question basically asks whether \(x\) and \(y\) have the same sign.

(1) x-y > -2 --> we can have an YES answer, if for example \(x\) and \(y\) are both positive (\(x=10\) and \(y=1\)) as well as a NO answer, if for example \(x\) is positive and \(y\) is negative (\(x=10\) and \(y=-10\)). Not sufficient.

(2) x-2y <-6 --> again it' easy to get an YES answer, if for example \(x\) and \(y\) are both positive (\(x=1\) and \(y=10\)) as well as a NO answer, if for example \(x\) is negative and \(y\) is positive (\(x=-1\) and \(y=10\)). Not sufficient.

You can get that the the two statement individually are not sufficient in another way too: we have (1) \(y<x+2\) and (2) \(y>\frac{x}{2}+3\). We are asked whether \(x\) and \(y\) have the same sign or whether the points (x,y) are in the I or III quadrant ONLY. But all (x,y) points below the line \(y=x+2\) (for 1) and all (x, y) points above the line \(y=\frac{x}{2}+3\) cannot lie only in I or III quadrant: points above or below some line (not parallel to axis) lie at least in 3 quadrants.

(1)+(2) Now, remember that we can subtract inequalities with the signs in opposite direction --> subtract (2) from (1): \(x-y-(x-2y)>-2-(-6)\) --> \(y>4\). As \(y>4\) and (from 1) \(x>y-2\) then \(x>2\) (because we can add inequalities when their signs are in the same direction, so: \(y+x>4+(y-2)\) --> \(x>2\)) --> we have that \(y>4\) and \(x>2\): both \(x\) and \(y\) are positive. Sufficient.

Answer: C.

Hey Bunuel!
I am a bit slow when it comes to thinking of numbers to solve DS Questions like these. I am quite strong in visualising the graphs when it comes to equations. So I started by plotting both the lines after quickly ruling out answer choices (A) and (B). After plotting, I selected the common area i.e the intersection of x - y > -2 and x - 2y < -6 and the common area of these two equations lies completely in the first quadrant, therefore, both x and y will always be positive and we can conclude that (C) is the correct answer. Is there any downside to this approach? I know all the graphs of the basic equations that I have seen on 750, or 700 level questions, what other graphs should I know about if I want to solve problems like these using the graph approach?
avatar
Engineer1
Joined: 01 Jan 2014
Last visit: 15 Jun 2025
Posts: 207
Own Kudos:
Given Kudos: 457
Location: United States (IN)
Concentration: Strategy, Finance
Posts: 207
Kudos: 543
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel


Is xy > 0?

\(xy>0\) means that x and y must have the same sign, so point (x, y) must be either in the first or the third quadrant (green regions).

(1) x-y > -2 --> \(y<x+2\) --> the area below blue line (\(y=x+2\)). (x, y) may or may not be in green region. Not sufficient.

(2) x-2y < -6 --> \(y>\frac{x}{2}+3\) --> the area above red line (\(y>\frac{x}{2}+3\)). (x, y) may or may not be in green region. Not sufficient.

(1)+(2) Below blue line and above red line, is yellow region, which is entirely in I quadrant (where \(y>4\) and \(x>2\)) --> \(xy>0\). Sufficient.

Answer: C.

Hope it helps.

Attachment:
xy.png


Bunuel KarishmaB MartyMurray
Generic question:
I did get it right in my practice exam (1:34) and I plugged in numbers as couple of the solutions show in this discussion. But I typically do not feel confident mostly because I don't want to keep spending time to cross check / revise. What should I do? What is a recommended method to save time and also inadvertently cross check solution for inequality question types? I don't think I have "problem" with the concept and if I have more time, I do these questions well. Thank you.
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 17 Jul 2025
Posts: 16,111
Own Kudos:
74,367
 [1]
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,111
Kudos: 74,367
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Engineer1
Bunuel


Is xy > 0?

\(xy>0\) means that x and y must have the same sign, so point (x, y) must be either in the first or the third quadrant (green regions).

(1) x-y > -2 --> \(y<x+2\) --> the area below blue line (\(y=x+2\)). (x, y) may or may not be in green region. Not sufficient.

(2) x-2y < -6 --> \(y>\frac{x}{2}+3\) --> the area above red line (\(y>\frac{x}{2}+3\)). (x, y) may or may not be in green region. Not sufficient.

(1)+(2) Below blue line and above red line, is yellow region, which is entirely in I quadrant (where \(y>4\) and \(x>2\)) --> \(xy>0\). Sufficient.

Answer: C.

Hope it helps.

Attachment:
xy.png


Bunuel KarishmaB MartyMurray
Generic question:
I did get it right in my practice exam (1:34) and I plugged in numbers as couple of the solutions show in this discussion. But I typically do not feel confident mostly because I don't want to keep spending time to cross check / revise. What should I do? What is a recommended method to save time and also inadvertently cross check solution for inequality question types? I don't think I have "problem" with the concept and if I have more time, I do these questions well. Thank you.

The graphical solution Bunuel has given above is a 1 min solution and that would be my method of choice.
Plugging in numbers is generally not a good strategy for DS questions. At most, it can help you arrive at the pattern in a question.
User avatar
vibhasharma
Joined: 14 Nov 2021
Last visit: 09 May 2025
Posts: 2
Given Kudos: 163
Location: India
GPA: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunuel,

Could you please help with this? Are we missing something here?

Tpral
Hello Bunuel,

I arrive to y>4.

When you replace it in (1) it makes x>2: OK

But

When you replace it in (2) it makes x - 2(4) < -6 ; so x <2 and so can be negative or positive.

Could you advise when replacing in (1) X>2 (answer =C) and when replacing in (2) we have answer (E) as x<2.

Thanks in advance,
User avatar
vibhasharma
Joined: 14 Nov 2021
Last visit: 09 May 2025
Posts: 2
Given Kudos: 163
Location: India
GPA: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunuel,

Could you please help with this? Are we missing something here?

Tpral
Hello Bunuel,

I arrive to y>4.

When you replace it in (1) it makes x>2: OK

But

When you replace it in (2) it makes x - 2(4) < -6 ; so x <2 and so can be negative or positive.

Could you advise when replacing in (1) X>2 (answer =C) and when replacing in (2) we have answer (E) as x<2.

Thanks in advance,
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,601
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,601
Kudos: 742,198
Kudos
Add Kudos
Bookmarks
Bookmark this Post
vibhasharma
Hi Bunuel,

Could you please help with this? Are we missing something here?

Tpral
Hello Bunuel,

I arrive to y>4.

When you replace it in (1) it makes x>2: OK

But

When you replace it in (2) it makes x - 2(4) < -6 ; so x <2 and so can be negative or positive.

Could you advise when replacing in (1) X>2 (answer =C) and when replacing in (2) we have answer (E) as x<2.

Thanks in advance,

That doubt has already been addressed here: https://gmatclub.com/forum/is-xy-0-1-x- ... l#p1989838
   1   2 
Moderators:
Math Expert
102601 posts
453 posts