OG 144 2016

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Mon Oct 05, 2015 10:32 am

OG 144 2016

by sushantsahaji » Thu May 05, 2016 11:38 pm
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.

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu May 05, 2016 11:42 pm
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 & s≤2
2x+3y ≤ 6
y ≤ (-2/3)x + 2.
Region R consists of all the points on or below the line y=(-2/3)x + 2.

Approach 1: DRAW

Statement 1: s = (-3/2)r + 3.
Image
The figure above shows that some points on s=(-3/2)r + 3 lie BELOW y=(-2/3)x + 2, while others lie ABOVE y=(-2/3)x + 2.
INSUFFICIENT.

Statement 2: r≤3 and s≤2.
Image
Inside the green box are points such that r≤3 and s≤2.
Some of the points inside the green box lie BELOW y=(-2/3)x + 2, while others lie ABOVE y=(-2/3)x + 2.
INSUFFICIENT.

Statements 1 and 2 combined:
Image
Inside the green box are points on s=(-3/2)r + 3 such that r≤3 and s≤2.
Some of these points lie BELOW y=(-2/3)x + 2, while others lie ABOVE y=(-2/3)x + 2.
INSUFFICIENT.

The correct answer is E.

Approach 2: TEST VALUES

An alternate way to combine the two statements is to treat this as MAX/MIN problem.
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 & s≤2
R MAXIMIZED:
In statement 2, the maximum possible value of r is 3.
If r=3 and s=0, both statements 1 and 2 are satisfied.
Check whether (3,0) is within the region defined by y ≤ (-2/3)x + 2:
0 = (-2/3)(3) + 2
0 ≤ 0.
YES.

S MAXIMIZED:
In statement 2, the maximum possible value of s is 2.
If s=2 and r=(2/3), both statements 1 and 2 are satisfied.
Check whether (2/3, 2) is within the region defined by y ≤ (-2/3)x + 2:
2 ≤ (-2/3)(2/3) + 2
2 ≤ 2/3
NO.

Since in the first case (r,s) is within the required region, but in the second case (r,s) is not within the required region, the two statements combined are INSUFFICIENT.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
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

by [email protected] » Fri May 06, 2016 10:05 am
Hi sushantsahaji,

This question was discussed in detail here:

https://www.beatthegmat.com/og13-data-su ... 77916.html

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image