Graph Question

Expert replies

winnerhere: Master | Next Rank: 500 Posts; Posts: 231; Joined: Thu Apr 12, 2007 2:45 amFollowed by: 1 member; Thanked: 5 times

by winnerhere » Sat Jun 26, 2010 11:09 am

Which of the following is true of the areas represented by the inequalities 3x+2y >12 and y+x<3 in the co ordinate plane

a)The are overlapping and finite

b)They are overlapping and infinite

c)They are not overlapping and finite

d)They are not overlapping and infinite

How do you fiind the point of intersection of an inequality?

Like this post

Source: Beat The GMAT — Problem Solving | Sat Jun 26, 2010 11:09 am

albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Sat Jun 26, 2010 11:22 am

Plot the lines A: 3x + 2y = 12 and B: x + y = 3 as the border lines for each of these inequality solution sets.

To plot a line on a graph, find out 2 points that satisfy each equation.

Line A: (4,0) and (0,6)
Line B: (3,0) and (0,3)

See attached picture for bad amateurish drawing of these lines

Now, you can see clearly that both regions are infinite, they extend indefinitely into the co-ordinate space.

Are they overlapping? Simple test, compare their slopes or try to find a solution for x,y to both those equations.

You'll see that you can actually find a value for x and y that satisfies both equations, or that their slopes are different. This is sufficient to realise that they are overlapping.

Thus the 2 areas are OVERLAPPING AND INFINITE.

Pick B.

Attachments

Like this post

winnerhere: Master | Next Rank: 500 Posts; Posts: 231; Joined: Thu Apr 12, 2007 2:45 amFollowed by: 1 member; Thanked: 5 times

by winnerhere » Sun Jun 27, 2010 1:21 am

thanks albatross

thats very clearly put

Like this post

sanabk: Master | Next Rank: 500 Posts; Posts: 174; Joined: Fri Apr 02, 2010 3:41 pmFollowed by: 1 member; Thanked: 6 times

by sanabk » Wed Aug 18, 2010 1:21 pm

Hi Abhay,
Could you please kindly cross check once again if the area is overlapping?

Thanks,
Sana

Like this post

albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Wed Aug 18, 2010 7:24 pm

sanabk wrote:Hi Abhay,
Could you please kindly cross check once again if the area is overlapping?

Thanks,
Sana

Sure,

The lines are 3x + 2y = 12 and x + y = 3 solving these two equations gives us x = 6 and y = -3

Thus the point of intersection of the two "border lines" of the inequality is (6,-3) which should be sufficient to see that they are in fact overlapping

Hope that helps!

~Abhay

Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 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