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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] New post 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] New post 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] New post 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] New post 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
Ques1.jpg [ 15.35 KiB | Viewed 472 times ]

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Re: xy>0 ? [#permalink] New post 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?)?
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Re: xy>0 ? [#permalink] New post 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!!!!
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Re: xy>0 ? [#permalink] New post 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.
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Re: xy>0 ? [#permalink] New post 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] New post 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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