How to plot the following in coordinate system

Expert replies

goelmohit2002: Legendary Member; Posts: 1799; Joined: Wed Dec 24, 2008 3:03 amFollowed by: 2 members; Thanked: 36 times

by goelmohit2002 » Wed Sep 16, 2009 4:52 am

Hi All,

Can someone please tell how to plot the following equation area in coordinate system and what is the reasoning for the same ?

2x + 3y <= 6

I was able to draw the line that represent 2x + 3y = 6. But how to draw the area that represents 2x + 3y <= 6.

Thanks
Mohit

Like this post

Source: Beat The GMAT — Problem Solving | Wed Sep 16, 2009 4:52 am

kyabe: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Tue Mar 17, 2009 3:03 amFollowed by: 1 member; Thanked: 2 times

by kyabe » Wed Sep 16, 2009 5:10 am

The simplest way is to plug-in values from both the sides of line and whichever satisfies the equation will be ur side.

Tip: If the line is not passing through (0,0) use this co-ordinate to decide.

Like this post

goelmohit2002: Legendary Member; Posts: 1799; Joined: Wed Dec 24, 2008 3:03 amFollowed by: 2 members; Thanked: 36 times

by goelmohit2002 » Wed Sep 16, 2009 5:34 am

kyabe wrote:The simplest way is to plug-in values from both the sides of line and whichever satisfies the equation will be ur side.

Tip: If the line is not passing through (0,0) use this co-ordinate to decide.

Thanks Kyabe.

plugging (0,0)...yields

0 <= 6...which is not true...

Can you please tell does it mean that all the points below the line will not satisfy this inequality....i.e. all the points above the line satisfy this equation ?

Thanks
Mohit

Like this post

kyabe: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Tue Mar 17, 2009 3:03 amFollowed by: 1 member; Thanked: 2 times

by kyabe » Wed Sep 16, 2009 5:36 am

goelmohit2002 wrote:
kyabe wrote:
plugging (0,0)...yields

0 <= 6...which is not true...

Can you please tell does it mean that all the points below the line will not satisfy this inequality....i.e. all the points above the line satisfy this equation ?

Thanks
Mohit
Are u sure its not true???

For me it is true and hence the side containing 0,0 is the side satisfying the equation

Like this post

goelmohit2002: Legendary Member; Posts: 1799; Joined: Wed Dec 24, 2008 3:03 amFollowed by: 2 members; Thanked: 36 times

by goelmohit2002 » Wed Sep 16, 2009 5:41 am

kyabe wrote:
goelmohit2002 wrote:
kyabe wrote:
plugging (0,0)...yields

0 <= 6...which is not true...

Can you please tell does it mean that all the points below the line will not satisfy this inequality....i.e. all the points above the line satisfy this equation ?

Thanks
Mohit
Are u sure its not true???

For me it is true and hence the side containing 0,0 is the side satisfying the equation
sorry sorry my mistake....yes 0 <=6

so in these type of questions....does it mean that all the points on one side of line are less than and all other points on other side are greater than ?

Any mathematical reason for the same ?

Like this post

kyabe: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Tue Mar 17, 2009 3:03 amFollowed by: 1 member; Thanked: 2 times

by kyabe » Wed Sep 16, 2009 5:43 am

Try a few and check urself

.. If u want the proof of it u need to contact a mathematics professor..

Like this post

goelmohit2002: Legendary Member; Posts: 1799; Joined: Wed Dec 24, 2008 3:03 amFollowed by: 2 members; Thanked: 36 times

by goelmohit2002 » Wed Sep 16, 2009 5:48 am

kyabe wrote:Try a few and check urself .. If u want the proof of it u need to contact a mathematics professor..

Thanks Kyabe....

Actually what I meant was not proof....but reason behind this trick ?..so that we can be sure that this trick work all the time and has no dreaded exception.

Like this post

kyabe: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Tue Mar 17, 2009 3:03 amFollowed by: 1 member; Thanked: 2 times

by kyabe » Wed Sep 16, 2009 5:53 am

I dont know how to answer your question.. Only thing I can assure you that this way u'll never get wrong answer..

Like this post

goelmohit2002: Legendary Member; Posts: 1799; Joined: Wed Dec 24, 2008 3:03 amFollowed by: 2 members; Thanked: 36 times

by goelmohit2002 » Wed Sep 16, 2009 5:54 am

kyabe wrote:I dont know how to answer your question.. Only thing I can assure you that this way u'll never get wrong answer..

Thanks a lot Kyabe...that helps !!!

Like this post

goelmohit2002: Legendary Member; Posts: 1799; Joined: Wed Dec 24, 2008 3:03 amFollowed by: 2 members; Thanked: 36 times

by goelmohit2002 » Wed Sep 16, 2009 8:05 am

Hi Kyabe,

Following is the related question from OG-12, Q121. Can you please tell how to solve the same without using number picking....OG has used some random set of numbers to prove the same....but finding those random set is I think very dificult.

In the xy plane, region R consists of all the points (x, y) such that 2x + 3y <= 6. Is the point (r,s) in the Region R ?
1) 3r + 2s = 6
2) r <= 3 and s <= 2

[spoiler]OA = E.[/spoiler]

Like this post

kyabe: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Tue Mar 17, 2009 3:03 amFollowed by: 1 member; Thanked: 2 times

by kyabe » Wed Sep 16, 2009 8:46 am

See the attached document.. Its the most simple way to solve problems like this...

The area marked in RED is not covered by the line 2x + 3y < 6. So the answer is E

Attachments

Like this post

goelmohit2002: Legendary Member; Posts: 1799; Joined: Wed Dec 24, 2008 3:03 amFollowed by: 2 members; Thanked: 36 times

by goelmohit2002 » Wed Sep 16, 2009 8:52 am

Aweome Kyabe ! Fantastic !

You are really ahead of OG....

I guess this is the reason why GMAT gives graph type paper in exam. First question where I have encountered the use of graph....without graph this would have been almost impossible to correctly make.

What do you say ?

Like this post

kyabe: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Tue Mar 17, 2009 3:03 amFollowed by: 1 member; Thanked: 2 times

by kyabe » Wed Sep 16, 2009 8:56 am

I disagree to the statment "You are really ahead of OG.... "

Partially agree to "without graph this would have been almost impossible to correctly make"

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review