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

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Re: Gprep DS: Is xy>o? [#permalink]  25 Jan 2011, 14:34
Dear Bunuel,

cold you please explain this " Now, remember we can subtract inequalities with the signs in opposite direction."
I seem to have forgotten basic arithmetic operations... ((

Thank youuu
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Re: Gprep DS: Is xy>o? [#permalink]  25 Jan 2011, 14:43
Expert's post
0987654312 wrote:
Dear Bunuel,

cold you please explain this " Now, remember we can subtract inequalities with the signs in opposite direction."
I seem to have forgotten basic arithmetic operations... ((

Thank youuu

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.
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Re: Gprep DS: Is xy>o? [#permalink]  25 Jan 2011, 14:53
Bunuel wrote:
0987654312 wrote:
Dear Bunuel,

cold you please explain this " Now, remember we can subtract inequalities with the signs in opposite direction."
I seem to have forgotten basic arithmetic operations... ((

Thank youuu

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.

Thank you so much!!!
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Re: xy>0 ? [#permalink]  25 Jan 2011, 19:08
Expert's post
0987654312 wrote:
Is xy>0?

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

Help!!?? )

As pointed out above, using graphs is extremely quick and efficient in such questions. The only region where x-y> -2 and x-2y<-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/quarter-wit-quarter-wisdom/
Part III discusses a question exactly like this.
Attachment:

Ques1.jpg [ 15.35 KiB | Viewed 601 times ]

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 15 Nov 2010 Posts: 20 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: xy>0 ? [#permalink] 26 Jan 2011, 00:47 VeritasPrepKarishma wrote: 0987654312 wrote: Is xy>0? 1) x-y> -2 2) x-2y<-6 Help!!?? ) As pointed out above, using graphs is extremely quick and efficient in such questions. The only region where x-y> -2 and x-2y<-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/quarter-wit-quarter-wisdom/ 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?)? Intern Joined: 15 Nov 2010 Posts: 20 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: xy>0 ? [#permalink] 26 Jan 2011, 01:01 0987654312 wrote: VeritasPrepKarishma wrote: 0987654312 wrote: Is xy>0? 1) x-y> -2 2) x-2y<-6 Help!!?? ) As pointed out above, using graphs is extremely quick and efficient in such questions. The only region where x-y> -2 and x-2y<-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/quarter-wit-quarter-wisdom/ 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?)? Dear Karishma, one more question for you. I read the link you suggested and the explanations are brilliant ! I was wandering, can you provide me with a link to this: ( it is taken from the link posted below) "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 ... -part-iii/ Thank you!!!! Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5584 Location: Pune, India Followers: 1381 Kudos [?]: 7040 [0], given: 182 Re: xy>0 ? [#permalink] 26 Jan 2011, 04:29 Expert's post 0987654312 wrote: VeritasPrepKarishma wrote: 0987654312 wrote: Is xy>0? 1) x-y> -2 2) x-2y<-6 Help!!?? ) As pointed out above, using graphs is extremely quick and efficient in such questions. The only region where x-y> -2 and x-2y<-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/quarter-wit-quarter-wisdom/ 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 My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: xy>0 ? [#permalink]  26 Jan 2011, 04:35
Expert's post
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 ... -part-iii/

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/quarter-wit-quarter-wisdom-bagging-the-graphs/
http://www.veritasprep.com/blog/2010/12/quarter-wit-quarter-wisdom-bagging-the-graphs-part-ii/
http://www.veritasprep.com/blog/2011/01/quarter-wit-quarter-wisdom-bagging-the-graphs-part-iii/

The link to all my posts related to graphs (and some other topics) is:
http://www.veritasprep.com/blog/category/gmat/quarter-wit-quarter-wisdom/
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Re: Is xy>0? (1) x-y>-2 (2) x-2y<-6 [#permalink]  17 Jun 2014, 09:08
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Re: Is xy>0? (1) x-y>-2 (2) x-2y<-6   [#permalink] 17 Jun 2014, 09:08

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

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