It is currently 13 Dec 2017, 05:12

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

5 KUDOS received
Director
Director
User avatar
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 603

Kudos [?]: 1168 [5], given: 39

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

Show Tags

New post 05 Jun 2011, 04:06
5
This post received
KUDOS
39
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (01:00) correct 37% (01:10) wrong based on 931 sessions

HideShow timer Statistics

Is xy > 0?

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

_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html


Last edited by Bunuel on 09 Jul 2014, 09:49, edited 2 times in total.
Edited the question.

Kudos [?]: 1168 [5], given: 39

3 KUDOS received
TOEFL Forum Moderator
avatar
Joined: 16 Nov 2010
Posts: 1586

Kudos [?]: 607 [3], given: 40

Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: Is xy > 0? (1) x - y > -2 (2) x - 2y < -6 [#permalink]

Show Tags

New post 05 Jun 2011, 04:20
3
This post received
KUDOS
2
This post was
BOOKMARKED
(1)

x = 1, y = 0

xy = 0 although x-y = 1 > -2

x = -3, y = -2

xy = 6 > 0 and x-y = -1 > -2

Insufficient

(2)

x - 2y < -6

x = 1, y = 4

x - 2y = 1 - 8 = -7 < -6 and xy > 0

x = 0, y = 4

x - 2y = 0 - 8 = -8 < -6 and xy = 0

Insufficient

(1) + (2)

x - y > -2

2y - x > 6

y > 4

Now x has to be such that x > y - 2

So x is positive, because y is 4.1, 5 etc.
and x is > 2.1, 3 etc.


So xy = positive

Answer - C
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 607 [3], given: 40

Expert Post
9 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42577

Kudos [?]: 135466 [9], given: 12695

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

Show Tags

New post 26 May 2012, 02:09
9
This post received
KUDOS
Expert's post
17
This post was
BOOKMARKED
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135466 [9], given: 12695

4 KUDOS received
Manager
Manager
avatar
Status: How easy it is?
Joined: 09 Nov 2012
Posts: 119

Kudos [?]: 104 [4], given: 174

Location: India
Concentration: Operations, General Management
GMAT 1: 650 Q50 V27
GMAT 2: 710 Q49 V37
GPA: 3.5
WE: Operations (Other)
GMAT ToolKit User Reviews Badge
Re: Is xy > 0? (1) x - y > -2 (2) x - 2y < -6 [#permalink]

Show Tags

New post 17 Jul 2013, 10:24
4
This post received
KUDOS
1
This post was
BOOKMARKED
Please find attached graphical solution. I think its easier and simpler to solve such inequality problem using co-ordinate geometry.

I made this graph in a hurry in paint, so please don't mind the poorly drawn lines.

Consider pressing on Kudos if my post helped you in any way!
Attachments

Solution.JPG
Solution.JPG [ 39.4 KiB | Viewed 44290 times ]

Kudos [?]: 104 [4], given: 174

Expert Post
9 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42577

Kudos [?]: 135466 [9], given: 12695

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

Show Tags

New post 17 Jul 2013, 22:34
9
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
Image

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.

[Reveal] Spoiler:
Attachment:
xy.png
xy.png [ 8.35 KiB | Viewed 50590 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135466 [9], given: 12695

Intern
Intern
avatar
Joined: 23 Jul 2013
Posts: 9

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

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

Show Tags

New post 31 Jul 2014, 06:19
Bunuel wrote:

Graphic approach:

Attachment:
xy.png


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.



Hi Bunuel,

I have doubts on graphical method -->

why is line y<x+2 passing through x = -2 ?
the value of x should be greater than -2 (the line may pass through x = -1, 0, 1, 2, ...)
Similarly, why is line y > (x/2) + 3 passing through x = -6
the value of x should be less than -6 (the line may pass through x = -7, -8, -9,...)

With the graphical method, can you illustrate solution of following example ?

Is x + y > 0 ?

1) x - y > 0
2) x^2 - y^2 > 0

Regards,
Akshay

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42577

Kudos [?]: 135466 [0], given: 12695

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

Show Tags

New post 31 Jul 2014, 06:40
AkshayDavid wrote:
Bunuel wrote:

Graphic approach:


Image

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.



Hi Bunuel,

I have doubts on graphical method -->

why is line y<x+2 passing through x = -2 ?
the value of x should be greater than -2 (the line may pass through x = -1, 0, 1, 2, ...)
Similarly, why is line y > (x/2) + 3 passing through x = -6
the value of x should be less than -6 (the line may pass through x = -7, -8, -9,...)

With the graphical method, can you illustrate solution of following example ?

Is x + y > 0 ?

1) x - y > 0
2) x^2 - y^2 > 0

Regards,
Akshay


y < x + 2 is the region which lies BELOW (because of < sign) line y = x + 2.

y > x/2 + 3 is the region which lies ABOVE (because of > sign) line y = x/2 + 3.

Check here for more: graphic-approach-to-problems-with-inequalities-68037.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135466 [0], given: 12695

Current Student
avatar
Joined: 14 Oct 2013
Posts: 47

Kudos [?]: 8 [0], given: 120

GMAT ToolKit User
Re: Is xy > 0? (1) x - y > -2 (2) x - 2y < -6 [#permalink]

Show Tags

New post 13 May 2015, 19:37
Hi,

I approached the 1&2 decision the same way as Bunuel but just had a clarifying question. When we subtract the two inequalities from eachother..how do we know that the sign stays as greater than (i.e. how do we know that it's y>4 instead of y<4). I assumed it was y>4 and got the question correct because i was subtracting a less than equation from a greater than equation but I have a feeling that's not the right logic. Thanks!

Kudos [?]: 8 [0], given: 120

Expert Post
5 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 755

Kudos [?]: 2240 [5], given: 123

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

Show Tags

New post 14 May 2015, 00:32
5
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
healthjunkie wrote:
Hi,

I approached the 1&2 decision the same way as Bunuel but just had a clarifying question. When we subtract the two inequalities from eachother..how do we know that the sign stays as greater than (i.e. how do we know that it's y>4 instead of y<4). I assumed it was y>4 and got the question correct because i was subtracting a less than equation from a greater than equation but I have a feeling that's not the right logic. Thanks!



Hi healthjunkie,

Let me help you out with such operations on inequalities.

Assume two inequalities x + y > 10......(1)
& x - y < 2........(2)

We see here that both the inequalities have opposite signs.

The basic concept of the inequality says to convert the inequalities into same sign before adding or subtracting them.

We can change the sign of the inequality by multiplying -1 on both sides of the inequality. Let's do it on inequality (2)

x - y < 2, multiplying -1 on both sides we get
-x + y > -2.

Since we have inequality (1) & (2) with the same signs we can add them now

x + y -x + y > 10 -2 i.e. y > 4.

Note here that adding inequality (1) to inequality (2) after multiplying inequality (2) by -1 is similar to subtracting inequality (2) from inequality (1). This concept is used when we say that we can subtract two inequalities with opposite signs.

In this question you asked we subtracted inequality in st-II from inequality in st-I which incidentally meant that st-II was multiplied by -1 and then added to st-I. So, the sign of inequality in st-II flipped.

x - 2y < -6, multiplying it with -1 gave the inequality -x + 2y > 6 which was then added to inequality in st-I

Hope its clear :-D

Regards
Harsh
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2240 [5], given: 123

Manager
Manager
avatar
B
Joined: 26 Jan 2015
Posts: 94

Kudos [?]: 15 [0], given: 112

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

Show Tags

New post 01 Apr 2016, 04:40
Bunuel wrote:

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 \(y=\frac{x}{2}+3\) can not lie only 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.


Dear Bunuel,

Please find my attached process.

However, the combined solving of eqns gave me, x<-4 or x>-1, a case in which we cannot comment on sign of x. Can you please help me understand where I have gone wrong?
Attachments

IMG_20160401_163125.jpg
IMG_20160401_163125.jpg [ 2.2 MiB | Viewed 23411 times ]


_________________

Kudos is the best way to say Thank you! Please give me a kudos if you like my post

Kudos [?]: 15 [0], given: 112

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5345

Kudos [?]: 6111 [0], given: 121

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

Show Tags

New post 01 Apr 2016, 06:30
Alok322 wrote:
Bunuel wrote:

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 \(y=\frac{x}{2}+3\) can not lie only 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.


Dear Bunuel,

Please find my attached process.

However, the combined solving of eqns gave me, x<-4 or x>-1, a case in which we cannot comment on sign of x. Can you please help me understand where I have gone wrong?


Hi,
your Equations are further to be simplified..

you got
2y-6 > x> y-2
we can infer 2y-6>y-2...
or 2y-y>6-2 that is y>4..
if y>4 and x+2>y, x will be >2..
thus both x and y are +ive and our answer is YES for xy>0..

Do not substitute value in 2y-6 > x> y-2 and find the signs of x and y..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6111 [0], given: 121

Manager
Manager
avatar
Joined: 20 Mar 2015
Posts: 63

Kudos [?]: 32 [0], given: 9

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

Show Tags

New post 06 May 2016, 02:52
chetan2u Looks like how I came with the solution is wrong. Since statement 1 and 2 are not sufficient I tried to combine the two statements.

1. X- Y>-2 2. X-2Y <-6

FROM 1: X>Y-2-------(WE HAVE A VALUE FOR X) substituting this value in statement 2 yields;

Y-2 -2Y<-6
OR, -Y < -4
OR, Y> 4 (MUTLIPLYING BOTH SIDES WITH A NEGATIVE SIGN.)

SINCE Y> 4, FROM STATEMETN ONE

X-Y>-2 OR, X- 4.1> -2, SOLVING FOR THIS WOULD GIVE X>2.1.

Is my process correct?

Kudos [?]: 32 [0], given: 9

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5345

Kudos [?]: 6111 [0], given: 121

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

Show Tags

New post 07 May 2016, 07:22
bimalr9 wrote:
chetan2u Looks like how I came with the solution is wrong. Since statement 1 and 2 are not sufficient I tried to combine the two statements.

1. X- Y>-2 2. X-2Y <-6

FROM 1: X>Y-2-------(WE HAVE A VALUE FOR X) substituting this value in statement 2 yields;

Y-2 -2Y<-6
OR, -Y < -4
OR, Y> 4 (MUTLIPLYING BOTH SIDES WITH A NEGATIVE SIGN.)

SINCE Y> 4, FROM STATEMETN ONE

X-Y>-2 OR, X- 4.1> -2, SOLVING FOR THIS WOULD GIVE X>2.1.

Is my process correct?


HI,
In this Q it is ok..
But a lot depends on '>' and '<' signs.. you cannot substitute without knowing these..
1. X- Y>-2 ...... x>y-2
2. X-2Y <-6..... x<2y-6..
so y-2<x<2y-6....
so here clearly y-2<2y-6 .... or y>4...
so form equations then substitute...
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6111 [0], given: 121

Manager
Manager
User avatar
Joined: 13 Jun 2016
Posts: 134

Kudos [?]: 135 [0], given: 424

Location: United States
Concentration: Finance, Technology
Re: Is xy > 0? (1) x - y > -2 (2) x - 2y < -6 [#permalink]

Show Tags

New post 05 Aug 2016, 09:42
I didn't know that you can subtract opposite sign equations and actually I feel that many will still get the sign mixed up as to whether it would be < or >. Instead you can flip one of the equations and then you will end up with one sign and then just add from there. That way, there is less chance for a mistake to occur.

Kudos [?]: 135 [0], given: 424

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1796

Kudos [?]: 980 [0], given: 5

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

Show Tags

New post 07 Dec 2017, 07:43
Baten80 wrote:
Is xy > 0?

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


We need to determine whether the product of x and y is positive. We should recall that the product of two numbers is positive only if both the numbers are positive or if both are negative.

Statement One Alone:

x - y > -2

Statement one tells us that the difference between x and y is -2; it does not tell us anything about the signs of x and y. For instance, if x = 2 and y = 1, we have x - y = 1 > -2, and xy is positive. However, if x = 3 and y = -2, 3 - (-2) = 5 > -2, but xy is negative. Statement one alone is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone:

x - 2y < -6

Again, we have a statement that tells us nothing about the signs of x and y. For instance, if x = 3 and y = 5, then x - 2y = 3 - 2(5) = 3 - 10 = -7 < -6, and xy is positive. However, if x = -1 and y = 5, then x - 2y = -1 - 2(5) = -11 < -6, and xy is negative. Statement two alone is not sufficient. We can eliminate answer choice B.

Statements One and Two Together:

Let’s manipulate the first inequality to read: y < x + 2. Similarly, we can manipulate the second inequality to read: y > (1/2)x + 3.

Thus, we can say the following:

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

(1/2)x + 3 < x + 2

x + 6 < 2x + 4

2 < x

Thus, x is positive.

We also know the following:

y > (1/2)x + 3

Since x is greater than two, let’s see what we can determine about y, if we substitute 2 for x.

y > (1/2)(2) + 3

y > 4

So y is positive as well. Both statements together are sufficient.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 980 [0], given: 5

Re: Is xy > 0? (1) x - y > -2 (2) x - 2y < -6   [#permalink] 07 Dec 2017, 07:43
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.