DS Line

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DS Line

by dunnec3 » Sat Mar 26, 2016 10:54 am
Can someone please provide a good explanation to this? I cant get my head around the OG explanation.

In the XY plane, region R consists of all 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

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by Brent@GMATPrepNow » Sat Mar 26, 2016 11:18 am
In the xy-plane region R consists of all the points (x,y) such that 2x + 3y <6. Is the point (r, s) in region R?

1) 3r + 2s = 6
2) r < 3 and s < 2
Target question: Is the point (r, s) in region R?

Given: Region R consists of all the points (x,y) such that 2x + 3y <6
So, what does Region R look like?
To find out, let's first graph the EQUATION, 2x + 3y = 6
Image

Since Region R is described as an INEQUALITY, we can choose any point on the coordinate plane to test whether or not it is in Region R. An easy point to test is (0,0).
So, does x=0 and y=0 satisfy the inequality 2x + 3y <6? YES
2(0) + (3)(0) is less than or equal to 6.
So, the point (0,0) is in Region R. More importantly, EVERY POINT on the same side of the line will also be in Region R.
Image

Statement 1: 3r + 2s = 6
The target question refers to the point (r, s)
In other words, the x-coordinate is r and the y-coordinate is s.
So, all of the points (r, s) that satisfy the above equation can be found on the line 3x + 2y = 6
In other words, statement 1 tells us that the point (r,s) lies somewhere on the red line below.
Image
As you can see, some points are in Region R, and some points are not in Region R
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: r < 3 and s < 2
There are many points that satisfy this condition.
In fact, the point (r,s) can be ANYWHERE inside the red box shown below.
Image
As you can see, some points are in Region R, and some points are not in Region R
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the statements, we are saying that the point (r,s) is on the red line (2x + 3y = 6) AND inside the red box.
Image

As you can see by the two blue points below, it's possible to have a point in Region R, and it's possible to have a point not in Region R
Image

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

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Brent
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by [email protected] » Sat Mar 26, 2016 4:52 pm
Hi dunnec3,

Here's a discussion of this question, including a video explanation of how to solve it by TESTing VALUES:

https://www.beatthegmat.com/please-expla ... tml#689366

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Rich
Contact Rich at [email protected]
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