Which of the following points falls outside of the region defined by

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Thu Jun 11, 2020 8:42 am

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Which of the following points falls outside of the region defined by 2y≤6x−12?

A. (5, 1)
B. (3, -8)
C. (2, 0)
D. (1, -2)
E. (0, -14)

Answer: D
Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Thu Jun 11, 2020 8:42 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: Which of the following points falls outside of the region defined by

by Brent@GMATPrepNow » Thu Jun 11, 2020 10:18 am

BTGModeratorVI wrote: ↑
Thu Jun 11, 2020 8:42 am
Which of the following points falls outside of the region defined by 2y≤6x−12?

A. (5, 1)
B. (3, -8)
C. (2, 0)
D. (1, -2)
E. (0, -14)

Answer: D
Source: Veritas Prep

One option is to sketch the region and check each point, but TESTING THE ANSWER CHOICES might be faster.

NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.

E. (0, -14)
Plug in x and y values to get: 2(-14) ≤ 6(0) − 12
Simplify: -28 ≤ -12
This satisfies the inequality, which means the point lies INSIDE the region.
ELIMINATE E

D. (1, -2)
Plug in x and y values to get: 2(1) ≤ 6(-2) − 12
Simplify: 2 ≤ -24
This DOES NOT satisfy the inequality, which means the point lies OUTSIDE the region.

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Which of the following points falls outside of the region defined by

by Scott@TargetTestPrep » Wed Jun 17, 2020 3:27 am

BTGModeratorVI wrote: ↑
Thu Jun 11, 2020 8:42 am
Which of the following points falls outside of the region defined by 2y≤6x−12?

A. (5, 1)
B. (3, -8)
C. (2, 0)
D. (1, -2)
E. (0, -14)

Answer: D
Source: Veritas Prep

Solution:

If a point falls outside of the region defined by 2y ≤ 6x − 12, its coordinates will NOT satisfy the inequality. So let’s check each given choice until we find the correct answer.

A. (5, 1)

2(1) ≤ 6(5) − 12 ?

2 ≤ 18 ?

Yes

B. (3, -8)

2(-8) ≤ 6(3) − 12 ?

-16 ≤ 6 ?

Yes

C. (2, 0)

2(0) ≤ 6(2) − 12 ?

0 ≤ 0 ?

Yes

D. (1, -2)

2(-2) ≤ 6(1) − 12 ?

-4 ≤ -6 ?

No

Answer: D

Scott Woodbury-Stewart
Founder and CEO
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