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
OA is E
please explain this question
This topic has expert replies
- ganeshrkamath
- Master | Next Rank: 500 Posts
- Posts: 283
- Joined: Sun Jun 23, 2013 11:56 pm
- Location: Bangalore, India
- Thanked: 97 times
- Followed by:26 members
- GMAT Score:750
The region extends to the line 2x + 3y = 6sana.noor wrote: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
OA is E
3y = -2x + 6
y = (-2/3)x + 2
Statement 1: From the figure it is clear that not all the points on this line fall under the shaded region.
Statement 2: Again from figure we see that this statement alone is insufficient.
Combination: Again insufficient.
Choose E
Every job is a self-portrait of the person who did it. Autograph your work with excellence.
Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
I see that ganeshrkamath already posted a graphical solution. Since I finally just finished my solution, I'll post it as well, since it describes a few steps in between.sana.noor wrote: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
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.
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.
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.
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.
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
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi sana.noor,
Here's a video explanation that I think you'll find helpful:
Watch Rich CRUSH this DS question...
GMAT assassins aren't born, they're made,.
Rich
Here's a video explanation that I think you'll find helpful:
Watch Rich CRUSH this DS question...
GMAT assassins aren't born, they're made,.
Rich