Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 15 Nov 2010
Posts: 18

Re: xy>0 ?
[#permalink]
Show Tags
26 Jan 2011, 01:47
VeritasPrepKarishma wrote: 0987654312 wrote: Is xy>0? 1) xy> 2 2) x2y<6 Help!!?? ) As pointed out above, using graphs is extremely quick and efficient in such questions. The only region where xy> 2 and x2y<6 intersect is the first quadrant (as shown in the graph below). If you are uncomfortable with drawing accurate lines quickly, check out 'Bagging the graphs  Parts I, II and III' at http://www.veritasprep.com/blog/category/gmat/quarterwitquarterwisdom/Part III discusses a question exactly like this. Attachment: Ques1.jpg Dear Karishma, thank you very much for the link provided:very helpful! the approach with the graphs is very efficient! However, just one more comment as a clarification: I understand why the the lines are drawn in this way and i see that they intersect in Q1. However, how can i relate this to the question directily, i .e. what would the right logic be in order to answer the question (is xy>0?)?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8281
Location: Pune, India

Re: xy>0 ?
[#permalink]
Show Tags
26 Jan 2011, 05:29
0987654312 wrote: VeritasPrepKarishma wrote: 0987654312 wrote: Is xy>0? 1) xy> 2 2) x2y<6 Help!!?? ) As pointed out above, using graphs is extremely quick and efficient in such questions. The only region where xy> 2 and x2y<6 intersect is the first quadrant (as shown in the graph below). If you are uncomfortable with drawing accurate lines quickly, check out 'Bagging the graphs  Parts I, II and III' at http://www.veritasprep.com/blog/category/gmat/quarterwitquarterwisdom/Part III discusses a question exactly like this. Attachment: Ques1.jpg Dear Karishma, thank you very much for the link provided:very helpful! the approach with the graphs is very efficient! However, just one more comment as a clarification: I understand why the the lines are drawn in this way and i see that they intersect in Q1. However, how can i relate this to the question directily, i .e. what would the right logic be in order to answer the question (is xy>0?)? Question: Is xy > 0 xy > 0 when either both x and y are positive or both are negative. If the intersection lies in only first quadrant, both x and y are positive (In I Quadrant, x > 0 and y > 0) If the intersection lies in only third quadrant then both x and y are negative because in III quadrant, x < 0 and y < 0. As long as your points lie in I and III quadrants only, xy will be > 0. If your points lie in II or IV quadrant too, xy can be negative too because either x or y (both not both) is negative in II and IV quadrant. Since in the graph above, the intersection lies only in I quadrant, it means x and y are both +ve and hence xy > 0.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8281
Location: Pune, India

Re: xy>0 ?
[#permalink]
Show Tags
26 Jan 2011, 05:35
0987654312 wrote: "In part I of Graphs, I had also mentioned “Learn how to draw a line from its equation in under ten seconds and you shall solve the related question in under a minute" http://www.veritasprep.com/blog/2011/01 ... partiii/Thank you!!!! This post is a part of three post series where I have discussed how to draw graphs and how to use them in GMAT questions. The link to all 3 parts: http://www.veritasprep.com/blog/2010/12/quarterwitquarterwisdombaggingthegraphs/http://www.veritasprep.com/blog/2010/12/quarterwitquarterwisdombaggingthegraphspartii/http://www.veritasprep.com/blog/2011/01/quarterwitquarterwisdombaggingthegraphspartiii/The link to all my posts related to graphs (and some other topics) is: http://www.veritasprep.com/blog/category/gmat/quarterwitquarterwisdom/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 14 Sep 2010
Posts: 20

Is xy > 0 ? 1) x  y > 2 2) x  2y < 6
[#permalink]
Show Tags
01 Feb 2011, 02:05
Is xy > 0 ?
1) x  y > 2 2) x  2y < 6



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: GMAT prep Inequality, positive negative
[#permalink]
Show Tags
01 Feb 2011, 02:58
tradinggenius wrote: Is xy > 0 ?
1) x  y > 2 2) x  2y < 6 Is xy>0?Note that question basically asks whether \(x\) and \(y\) have the same sign. (1) xy > 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) x2y <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 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): \(xy(x2y)>2(6)\) > \(y>4\). As \(y>4\) and (from 1) \(x>y2\) then \(x>2\) (because we can add inequalities when their signs are in the same direction, so: \(y+x>4+(y2)\) > \(x>2\)) > we have that \(y>4\) and \(x>2\): both \(x\) and \(y\) are positive. Sufficient. Answer: C. Also discussed here: gprepdsisxyo87751.html
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 30 Mar 2011
Posts: 18

Q: Is xy > 0 (1) XY > 2 (2) X2Y < 6 I received
[#permalink]
Show Tags
01 May 2011, 01:30
Q: Is xy > 0
(1) XY > 2 (2) X2Y < 6
I received the following answer in a different post and cannot follow the logic  can anyone help?
together a and b , As the inequality signs are different, we have to subtract the equations. XY  (X2Y) > 2 + 6 Y > 4 meaning X > y 2 that is X>2 and Y >4 implies XY >0. Hence C.



Senior Manager
Joined: 03 Mar 2010
Posts: 394

Re: Inequalities data sufficiency question
[#permalink]
Show Tags
01 May 2011, 01:59
chloeholding wrote: Q: Is xy > 0
(1) XY > 2 (2) X2Y < 6 Basically question is asking if x > 0 AND y >0 OR x < 0 AND y <0. Stmt1: x>y2. Now take y such that y>0. y=3, Check if x > 0 or not, x>1. Hence x >0. Hence xy >0. Take y =1, x >1. Hence x can be 0.5. Hence xy <0. Yes and No. Insufficient. Stmt2: x2y < 6. x<2(y3). Take y=2. x<2. Hence xy < 0. Take y=4, x<2. Hence xy>0 if x=1 and xy<0 if x=1. Yes and No. Insufficient. Combining, Multiplying (2) by 1 and change sign: x+2y > 6 Adding, xy+(x+2y) > 2+6 y > 4. and x>y2, hence x>2. On the number line, both x and y are to the right of 0. Hence both positive. x>0, y>0. xy>0 OA. C
_________________
My dad once said to me: Son, nothing succeeds like success.



Retired Moderator
Joined: 20 Dec 2010
Posts: 1868

Re: Inequalities data sufficiency question
[#permalink]
Show Tags
01 May 2011, 02:07
Chloeholding: You are repeatedly making the same mistake. You must not post a PS problem in DS forum or viceversa. Please let me know if you have trouble following my instruction.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 544

Re: Inequalities data sufficiency question
[#permalink]
Show Tags
01 May 2011, 02:31
chloeholding wrote: Q: Is xy > 0
(1) XY > 2 (2) X2Y < 6
I received the following answer in a different post and cannot follow the logic  can anyone help?
together a and b , As the inequality signs are different, we have to subtract the equations. XY  (X2Y) > 2 + 6 Y > 4 meaning X > y 2 that is X>2 and Y >4 implies XY >0. Hence C. doing same as jamifahad for both options as: Stmt1: x>y2. Now take y such that y>0. y=3, Check if x > 0 or not, x>1. Hence x >0. Hence xy >0. Take y =1, x >1. Hence x can be 0.5. Hence xy <0. Yes and No. Insufficient. Stmt2: x2y < 6. x<2(y3). Take y=2. x<2. Hence xy < 0. Take y=4, x<2. Hence xy>0 if x=1 and xy<0 if x=1. Yes and No. Insufficient. But for c xyx+2y>2(6) = y>8 so from 1 x > y2 x > 92 x > 7 so xy>0
_________________
Collections: PSof OG solved by GC members: http://gmatclub.com/forum/collectionpswithsolutionfromgmatclub110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collectiondswithsolutionfromgmatclub110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmatprepproblemcollections114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collectionsofworkrateproblemwithsolutions118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixtureproblemswithbestandeasysolutionsalltogether124644.html



Director
Status: Up again.
Joined: 31 Oct 2010
Posts: 508
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42

Re: Inequalities data sufficiency question
[#permalink]
Show Tags
02 May 2011, 10:16
chloeholding wrote: Q: Is xy > 0
(1) XY > 2 (2) X2Y < 6
I received the following answer in a different post and cannot follow the logic  can anyone help?
together a and b , As the inequality signs are different, we have to subtract the equations. XY  (X2Y) > 2 + 6 Y > 4 meaning X > y 2 that is X>2 and Y >4 implies XY >0. Hence C. 1. X+2>Y. Plug X=0 and Y=1. Answer is NO. Put X=1 and Y=2. Answer is YES. 2 answers. insufficient. 2. X+6<2Y. Plug different values and you can get 2 different answers. Insufficient 1 and 2 combined: Subtract eqn 1 from 2. Use the "GT/ LT"(GREATER THAN/ LESS THAN) terminology: 4<Y or Y= GT 4Put this value in eqn 1: X=GT42. This implies that X=GT2. Therefore both X and Y are positive. Hence XY>0. Answer C.
_________________
My GMAT debrief: http://gmatclub.com/forum/from620to710mygmatjourney114437.html



Retired Moderator
Joined: 16 Nov 2010
Posts: 1452
Location: United States (IN)
Concentration: Strategy, Technology

Re: Inequalities data sufficiency question
[#permalink]
Show Tags
04 May 2011, 20:22
(1) x = 0, y = 0 xy = 0 > 2, but xy = 0 x = 1, y = 2, but xy > 0 Insufficient (2) x = 1, y = 5, xy > 0 (x  y = 1  10 = 9 < 6) x = 1, y = 3, xy < 0 (x  y = 7 < 6) (1) + (2) xy > 2 2y x > 6 (multiplying by 1) Adding both, y > 4 => x > y  2 => x is also positive xy > 0 Answer  C
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Director
Joined: 14 Dec 2012
Posts: 795
Location: India
Concentration: General Management, Operations
GPA: 3.6

Re: Is xy > 0 ? 1) x  y > 2 2) x  2y < 6
[#permalink]
Show Tags
12 Jul 2013, 11:44
tradinggenius wrote: Is xy > 0 ?
1) x  y > 2 2) x  2y < 6 Hi, statement 1: y<x+2===>this is straight line in coordinate system==>and all values below line(includes coordinates of all 4 coordinate ) will satisfy this condition==>hence xy can be positive or negative or zero==>not sufficient. statement 2: y>x/2+3===>again straight line==>and all values above line(includes coordinates of 1/2/3 coordinate ) will satisfy this condition==>hence xy can be positive or negative ==>not sufficient. combining 2 we can get the unique value for x/y==>hence we can say xy is positive/negative defenetely.....hence sufficient C
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....
GIVE VALUE TO OFFICIAL QUESTIONS...
GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabularylistforgmatreadingcomprehension155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmatanalyticalwritingassessment : http://www.youtube.com/watch?v=APt9ITygGss



Intern
Joined: 20 Feb 2013
Posts: 20

Re: Is xy > 0 ? 1) x  y > 2 2) x  2y < 6
[#permalink]
Show Tags
13 Jul 2013, 06:35
tradinggenius wrote: Is xy > 0 ?
1) x  y > 2 2) x  2y < 6 Is xy > 0 ? 1) x  y > 2 2) x  2y < 6 1) X = 2 and Y = 3 XY > 0 X =  0.5 and Y = 1 XY < 0 2) X = 2 and Y = 3 XY > 0 X = 0.5 and Y = 3 XY < 0 Now combine both X> Y  2 X < 6 + 2y The only values that suffice are values greater than 4 for y and greater than 2 for x. Hence C is the answer.
_________________
Pushpinder Gill



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: Is xy > 0? (1) x  y > 2 (2) x  2y < 6
[#permalink]
Show Tags
14 Sep 2014, 17:36
Is xy>0?Note that question basically asks whether \(x\) and \(y\) have the same sign. (1) xy > 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) x2y <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): \(xy(x2y)>2(6)\) > \(y>4\). As \(y>4\) and (from 1) \(x>y2\) then \(x>2\) (because we can add inequalities when their signs are in the same direction, so: \(y+x>4+(y2)\) > \(x>2\)) > we have that \(y>4\) and \(x>2\): both \(x\) and \(y\) are positive. Sufficient. Answer: C. OPEN DISCUSSION OF THIS QUESTION IS HERE: isxy01xy22x2y114731.html
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6213
GPA: 3.82

Re: Is xy>0? (1) xy>2 (2) x2y<6
[#permalink]
Show Tags
01 Nov 2017, 22:52
4test1 wrote: Is xy>0?
(1) xy>2 (2) x2y<6 Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. Since we have 2 variables and 0 equation, C could be the answer most likely. 1) & 2) x  y > 2 x  2y < 6 <=> x + 2y > 6 When we add two inequalities, y > 4. And we have x > y  2 > 2. Both x and y are positive and xy > 0. 1) x = 3, y = 1 => xy > 0 : Yes x = 0, y = 1 => xy = 0 : No This is not sufficient. 2) x = 0, y = 4 => xy = 0 : No x = 1, y = 4 => xy > 0 : Yes Therefore, the answer is C. Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: Is xy>0? (1) xy>2 (2) x2y<6
[#permalink]
Show Tags
28 Nov 2017, 23:17




Re: Is xy>0? (1) xy>2 (2) x2y<6 &nbs
[#permalink]
28 Nov 2017, 23:17



Go to page
Previous
1 2
[ 37 posts ]



