Experts,
I'm taking my GMAT in about 2 weeks and have been spending time on my weaker areas. This graphing question seems different from a lot of the other graphing questions I've done. What's the best way to deal with it?
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
OG13 Data Sufficiency Question 129
This topic has expert replies
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
Target question: Is the point (r, s) in region R?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
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
- GMATinsight
- Legendary Member
- Posts: 1100
- Joined: Sat May 10, 2014 11:34 pm
- Location: New Delhi, India
- Thanked: 205 times
- Followed by:24 members
If (r,s) lie in region R, 2x + 3y <6 then the points (r,s) must satisfy the given equationIn 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
Question Rephrased : IS 2r + 3s <6?
Statement 1) 3r + 2s = 6
Case 1: r=1, s=1.5 But 2r + 3s = 6.5>6 NO
Case 2: r=2, s=0 But 2r + 3s = 4<6 YES
INSUFFICIENT
Statement 2) r < 3 and s < 2
i.e. 2r < 6 and 3s < 6
i.e. 2r + 3s <6+6
i.e. 2r + 3s <12
i.e.2r + 3s May or May NOT be less than 6
INSUFFICIENT
Combining the two statements
3r + 2s = 6 and r < 3 and s < 2
Case 1: r=3, s=2 But 2r + 3s = 6.5>6 NO
Case 2: r=2, s=0 But 2r + 3s = 4<6 YES
INSUFFICIENT
Answer: Option E
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
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 MBAGRL,
You can see my approach to this question here, including how TESTing VALUES can help you to do the work:
https://www.youtube.com/watch?v=WkaW7HnaM24
GMAT assassins aren't born, they're made,
Rich
You can see my approach to this question here, including how TESTing VALUES can help you to do the work:
https://www.youtube.com/watch?v=WkaW7HnaM24
GMAT assassins aren't born, they're made,
Rich