Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 23 Aug 2016, 22:19

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is xy>0? (1) x-y>-2 (2) x-2y<-6

Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Nov 2009
Posts: 64
WE 1: Research
WE 2: Corporate Strat
Followers: 1

Kudos [?]: 29 [0], given: 1

Is xy>0? (1) x-y>-2 (2) x-2y<-6 [#permalink]

### Show Tags

08 Dec 2009, 09:07
6
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

65% (02:33) correct 35% (02:04) wrong based on 246 sessions

### HideShow timer Statistics

Is xy>0?

(1) x-y>-2
(2) x-2y<-6
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 May 2012, 03:08, edited 1 time in total.
Edited the question and added the OA
VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 253 [1] , given: 31

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

08 Dec 2009, 09:43
1
KUDOS
1
This post was
BOOKMARKED
4test1 wrote:
Can't seem to find this in the forum. From the Gprep test:

Is xy>0?
1. x-y > -2
2. x-2y <-6

Can't seem to get my head around this. Appreciate any help.

Statement 1:
x = 5 and y = 4 answer is yes
x = -1 and y = 0 answer is no

Statement 2:
x = -7 and y = 0 answer is no
x = -10 and y = -1 answer is yes

Combined:
x - y > -2
x - 2y < -6

or
-x + y < 2
x - 2y < - 6
-y < -4
y > 4 so you know y is positive

What about x..plug a value of y > 4 in the equation and you'll get x > 0
VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 253 [0], given: 31

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

18 Dec 2009, 14:14
burnttwinky wrote:
How did you get X > 0? I got X< 2. Can you please show me the math when you plug y > 4 back in to get x?

I just meant that x is positive if you plug in y>4 in equation 1 and 2
Intern
Joined: 22 Dec 2009
Posts: 28
Followers: 0

Kudos [?]: 14 [0], given: 6

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

25 Dec 2009, 05:03
lagomez wrote:
4test1 wrote:
Can't seem to find this in the forum. From the Gprep test:

Is xy>0?
1. x-y > -2
2. x-2y <-6

Can't seem to get my head around this. Appreciate any help.

Statement 1:
x = 5 and y = 4 answer is yes
x = -1 and y = 0 answer is no

Statement 2:
x = -7 and y = 0 answer is no
x = -10 and y = -1 answer is yes

Combined:
x - y > -2
x - 2y < -6

or
-x + y < 2
x - 2y < - 6
-y < -4
y > 4 so you know y is positive

What about x..plug a value of y > 4 in the equation and you'll get x > 0

hi lagomez,

nice method, but i m afraid there is some mistake in ur explanation.

if y>4. say y=5
now plugging this value in eq2, i.e. option 2

x-2y < -6 ===> x-10<-6 ===> x<4 ===> so x can also be -ve... in this case xy<0

plugging the value of y=5 in eq1, i.e. option 1

x-y > -2 ===> x>y+2 ===> x>7 ===> x=+ve.... in this case xy>0

here is my method..
as u know, 1 & 2 are individually insuff..
taking 1&2 together

x-y>-2 ===> x>y+2
x-2y<-6 ===> x<2y-6

so combining both the above equations (y+2)< x < (2y-6)

by plugging values, if y= 2 ==> 4<x<-2 ==> x<-2 & x>4
two cases arise. so, data insuff.
_________________

Deserve before you Desire

Math Expert
Joined: 02 Sep 2009
Posts: 34393
Followers: 6245

Kudos [?]: 79323 [2] , given: 10016

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

25 Dec 2009, 06:22
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
logan wrote:
hi lagomez,

nice method, but i m afraid there is some mistake in ur explanation.

if y>4. say y=5
now plugging this value in eq2, i.e. option 2

x-2y < -6 ===> x-10<-6 ===> x<4 ===> so x can also be -ve... in this case xy<0

plugging the value of y=5 in eq1, i.e. option 1

x-y > -2 ===> x>y+2 ===> x>7 ===> x=+ve.... in this case xy>0

here is my method..
as u know, 1 & 2 are individually insuff..
taking 1&2 together

x-y>-2 ===> x>y+2
x-2y<-6 ===> x<2y-6

so combining both the above equations (y+2)< x < (2y-6)

by plugging values, if y= 2 ==> 4<x<-2 ==> x<-2 & x>4
two cases arise. so, data insuff.

Not so. Lagomez's answer is correct.

Is xy>0?

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

Note that question basically asks whether $$x$$ and $$y$$ have the same sign.

Statements alone are not sufficient as was shown above.

Now, remember we can subtract inequalities with the signs in opposite direction.

$$x-y-(x-2y)>-2-(-6)$$ --> $$y>4$$. As $$y>4$$ and (from 1) $$x>y-2$$, hence $$x>2$$ (we can add inequalities when their signs are in the same direction, so $$y+x>4+y-2$$ --> $$x>2$$) --> both $$x$$ and $$y$$ are positive. Sufficient.

When you got that for y=5 --> x<4, it's correct, but it doesn't mean that x can be negative, as this is not ALL information you have. If you plug the same value y=5 in (1) you'll get --> x>3, which is also correct.

Basically when y=5 --> 3<x<4.

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 34393
Followers: 6245

Kudos [?]: 79323 [0], given: 10016

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

25 Dec 2009, 06:51
chetan2u wrote:
i think ans should be E...
agreed y>4..
substitute in eq 1...x>2...
substitute in eq 2... x<2y-6...x<8-6...x<2..... combining the two , can we get a value of x, which is both < 2 and>2,, i dont think

When you substitute in equation 2, you take the value of y=4 (which can not be as y>4).

C is correct.
_________________
Manager
Status: Applying Now
Joined: 21 Nov 2009
Posts: 63
WE: Project Management (Manufacturing)
Followers: 3

Kudos [?]: 137 [0], given: 3

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

25 Dec 2009, 06:51
This question is best seen graphically. It is a very quick method.

See the graphs below. They only meeting in 1st Quadrant. So both equations together tell us that x>0 y>0.

Attachment:

x-ygr-2.GIF [ 3.63 KiB | Viewed 4536 times ]

Attachment:

eqn2.GIF [ 2.88 KiB | Viewed 4531 times ]

_________________

If you like my post, consider giving me a kudos. THANKS!

Intern
Joined: 22 Dec 2009
Posts: 28
Followers: 0

Kudos [?]: 14 [0], given: 6

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

25 Dec 2009, 11:34
Bunuel wrote:
Not so. Lagomez's answer is correct.

Is xy>0?
(1) x-y > -2
(2) x-2y <-6

Statements alone are not sufficient as was shown above.

Now, remember we can subtract inequalities with the signs in opposite direction.

x-y-(x-2y)>-2-(-6) --> y>4. As y>4 and (from 1) x>y-2, hence x>2. Sufficient.

When you got that for y=5 --> x<4, it's correct, but it doesn't mean that x can be negative, as this is not ALL information you have. If you plug the same value y=5 in (1) you'll get --> x>3, which is also correct.

Basically when y=5 --> 3<x<4.

Hope it's clear.

oh yeah... too bad that i forgot to plug the value of y=5 in both the equations...
thanx a ton Bunuel...
kudos..
_________________

Deserve before you Desire

Senior Manager
Joined: 25 Jun 2009
Posts: 293
Followers: 1

Kudos [?]: 126 [0], given: 4

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

25 Dec 2009, 16:25
I am still having some confusion about this problem. Let me show you my steps. I solved for X first. First I aligned the inequalities:

y < x + 2
1/2x + 3 < y

so by combining the equations, we get:

1/2x + 3+ y < x+y+2

the y's cancel on both sides, and we have 1/2x > 1

so x>2

My question is, how do you plug in greater than 2 into an inequality? y < (Greater than 2) + 2

we get y < Greater than 4, so doesn't that mean y can still be negative while X is greater than 2 (always positive)?
Intern
Joined: 25 Apr 2009
Posts: 10
Followers: 0

Kudos [?]: 1 [0], given: 2

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

31 Dec 2009, 22:59
Draw the X,Y graph like what msunny did.

Senior Manager
Joined: 25 Jun 2009
Posts: 293
Followers: 1

Kudos [?]: 126 [0], given: 4

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

01 Jan 2010, 12:28
Bunuel wrote:
chetan2u wrote:
i think ans should be E...
agreed y>4..
substitute in eq 1...x>2...
substitute in eq 2... x<2y-6...x<8-6...x<2..... combining the two , can we get a value of x, which is both < 2 and>2,, i dont think

When you substitute in equation 2, you take the value of y=4 (which can not be as y>4).

C is correct.

If I substituted x=2 into each of the equations to solve for Y, i got two different answers. Y>4 and Y<4, depending on which equation you substitute it into.
Senior Manager
Joined: 22 Dec 2009
Posts: 362
Followers: 11

Kudos [?]: 333 [0], given: 47

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

01 Jan 2010, 17:04
lagomez wrote:
4test1 wrote:
Can't seem to find this in the forum. From the Gprep test:

Is xy>0?
1. x-y > -2
2. x-2y <-6

Can't seem to get my head around this. Appreciate any help.

Statement 1:
x = 5 and y = 4 answer is yes
x = -1 and y = 0 answer is no

Statement 2:
x = -7 and y = 0 answer is no
x = -10 and y = -1 answer is yes

Combined:
x - y > -2
x - 2y < -6

or
-x + y < 2
x - 2y < - 6
-y < -4
y > 4 so you know y is positive

What about x..plug a value of y > 4 in the equation and you'll get x > 0

As pointed by Bunuel, when u plug in y > 4 in both the above equations, you get x range as 3<x<4.... Therefore xy > 0!

You shouldn't consider only x - 2y < -6 for determining the value of x. Both the equations should be considered!

Cheers!
JT
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!!

|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

Math Expert
Joined: 02 Sep 2009
Posts: 34393
Followers: 6245

Kudos [?]: 79323 [0], given: 10016

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

01 Jan 2010, 17:08
burnttwinky wrote:
Bunuel wrote:
chetan2u wrote:
i think ans should be E...
agreed y>4..
substitute in eq 1...x>2...
substitute in eq 2... x<2y-6...x<8-6...x<2..... combining the two , can we get a value of x, which is both < 2 and>2,, i dont think

When you substitute in equation 2, you take the value of y=4 (which can not be as y>4).

C is correct.

If I substituted x=2 into each of the equations to solve for Y, i got two different answers. Y>4 and Y<4, depending on which equation you substitute it into.

I don't quite understand what's your point. Answer to the original question is C.

xy>0 means that the point (x,y) is either in I quadrant or in III.

(1) x-y > -2 the points satisfying this inequality can be in ALL four quadrants, refer to the first graph msunny provided (blue area). Hence insufficient.

(2) x-2y <-6 the points satisfying this inequality can be in I, II or in III quadrants, refer to the second graph msunny provided (blue area). Hence insufficient.

(1)+(2) Points satisfying BOTH inequalities are only in I quadrant: intersection of blue areas. Hence sufficient.

Hope it's clear.
_________________
Senior Manager
Joined: 25 Jun 2009
Posts: 293
Followers: 1

Kudos [?]: 126 [0], given: 4

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

01 Jan 2010, 17:49
I apologize if my point is unclear, but my question is that, after I calculated X>2 (I solved for X first), I plugged in X=2 into the first equation, and I got Y<4. What I am confused about is that if Y<4, that means Y can be negative; however, x>2, so if Y is negative and X is always positive, then you would be in quadrant IV.

If plugged in X=2 into the second equation, then you get y>4, which is sufficient since X>2 and Y>4, so you will always be in quadrant I.
Senior Manager
Joined: 22 Dec 2009
Posts: 362
Followers: 11

Kudos [?]: 333 [0], given: 47

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

01 Jan 2010, 18:01
burnttwinky wrote:
I apologize if my point is unclear, but my question is that, after I calculated X>2 (I solved for X first), I plugged in X=2 into the first equation, and I got Y<4. What I am confused about is that if Y<4, that means Y can be negative; however, x>2, so if Y is negative and X is always positive, then you would be in quadrant IV.

If plugged in X=2 into the second equation, then you get y>4, which is sufficient since X>2 and Y>4, so you will always be in quadrant I.

Your X value is > 2, do not substitute 2 as X in the equation. Substituting X = 3 would be a right approach. On doing that for first eq, you get:
3-y>-2 i.e. y < 5 --- [1]
Substituting X = 3 in equation 2, you get:

3-2y<-6 i.e. y > 4.5....

Therefore if X = 3, then y range is from 4.5 to 5 which means both X and Y are positive. Hence XY > 0.

Hope this is clear..

Thanks,
JT
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!!

|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

Math Expert
Joined: 02 Sep 2009
Posts: 34393
Followers: 6245

Kudos [?]: 79323 [0], given: 10016

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

01 Jan 2010, 18:16
burnttwinky wrote:
I apologize if my point is unclear, but my question is that, after I calculated X>2 (I solved for X first), I plugged in X=2 into the first equation, and I got Y<4. What I am confused about is that if Y<4, that means Y can be negative; however, x>2, so if Y is negative and X is always positive, then you would be in quadrant IV.

If plugged in X=2 into the second equation, then you get y>4, which is sufficient since X>2 and Y>4, so you will always be in quadrant I.

First of all when you solved system of inequalities and got x>2 and you want to continue by number plugging you should plug correct numbers. You got x>2, hence you should plug x more than 2. Any value more than 2 for x will give you the RANGE for y which is positive.

x=3:
x-y > -2 --> 3-y>-2 --> y<5
and
x-2y <-6 --> 3-2y<-6 --> y>4.5

So, for x=3, y is in the range {4.5, 5}.

You'll get only positive range for y, when you test ANY value of x>2, as the solution of this system of inequalities is x>2 and y>4 (refer to the solution in my first post in this topic). And vise-versa: if you try values of y>4 you'll get only positive range for x.

Hope it's clear.
_________________
Senior Manager
Joined: 25 Jun 2009
Posts: 293
Followers: 1

Kudos [?]: 126 [0], given: 4

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

01 Jan 2010, 18:25
That makes much more sense. Thanks for the explanation.
VP
Joined: 09 Jun 2010
Posts: 1331
Followers: 3

Kudos [?]: 96 [0], given: 768

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

20 Dec 2010, 02:54
you are wrong.

a>b and c>d

we can not have a+c>b+d . because there is some redundant

we use this method

y-2<x<2y-6
y-2<2y-6
4<y
that means x>2, C is correct.
Math Expert
Joined: 02 Sep 2009
Posts: 34393
Followers: 6245

Kudos [?]: 79323 [1] , given: 10016

Re: Gprep DS: Is xy>o? [#permalink]

### Show Tags

20 Dec 2010, 03:01
1
KUDOS
Expert's post
thangvietnam wrote:
you are wrong.

a>b and c>d

we can not have a+c>b+d . because there is some redundant

we use this method

y-2<x<2y-6
y-2<2y-6
4<y
that means x>2, C is correct.

The red part is not correct.

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 $$2<5$$ --> $$3+2<4+5$$.

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 $$5>1$$ --> $$3-5<4-1$$.

Hope it's clear.
_________________
Intern
Joined: 15 Nov 2010
Posts: 20
Followers: 0

Kudos [?]: 0 [0], given: 0

### Show Tags

25 Jan 2011, 14:28
Is xy>0?

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

Help!!?? )
xy>0 ?   [#permalink] 25 Jan 2011, 14:28

Go to page    1   2    Next  [ 30 posts ]

Similar topics Replies Last post
Similar
Topics:
Is X^2Y^3Z^2>0 ? (1) XY>0 (2) YZ<0 3 17 Aug 2015, 14:59
69 Is xy > 0? (1) x - y > -2 (2) x - 2y < -6 28 05 Jun 2011, 05:06
2 Q: Is xy > 0 (1) X-Y > -2 (2) X-2Y < -6 I received 5 01 May 2011, 01:30
Is xy > 0 ? 1) x - y > -2 2) x - 2y < -6 4 01 Feb 2011, 02:05
11 Is xy > 0? (1) x - y > -2 (2) x - 2y < -6 7 03 Aug 2009, 04:11
Display posts from previous: Sort by