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Which of the following points falls outside of the region defined by 2

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Carcass
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Which of the following points falls outside of the region defined by 2 [#permalink] New post   23 Mar 2021, 06:07
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Which of the following points falls outside of the region defined by \(2y \leq 6x-12\)?

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

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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Which of the following points falls outside of the region defined by 2 [#permalink] New post   23 Mar 2021, 07:16
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Carcass wrote:
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)


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(-2) ≤ 6(1) − 12
Simplify: -4 ≤ -6
This DOES NOT satisfy the inequality, which means the point lies OUTSIDE the region.

Answer: D

Cheers,
Brent
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Re: Which of the following points falls outside of the region defined by 2 [#permalink] New post   24 Mar 2021, 00:18
Since making the boundary and then comparing points would be a hassle,
we can simplify the given inequality and check the answer choices

The given inequality can be simplified as y ≤ 3(x-2)

After simplifying, the only remaining part is to check each answer choice and verify if it satisfies the inequality.

All points except Option D satisfy the given inequality hence we can safely say that point D is outside the given region
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Re: Which of the following points falls outside of the region defined by 2 [#permalink] New post   13 Jul 2022, 03:38
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GreenlightTestPrep wrote:
Carcass wrote:
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)


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


For plugging the points (x.y) given in option D, isn't y = -2 and x= 1? Because plugged-in values seem the opposite of this.
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Re: Which of the following points falls outside of the region defined by 2 [#permalink] New post   13 Jul 2022, 06:31
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TAYYABGRE wrote:
For plugging the points (x.y) given in option D, isn't y = -2 and x= 1? Because plugged-in values seem the opposite of this.


You're absolutely right. I have edited my response accordingly.
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Re: Which of the following points falls outside of the region defined by 2 [#permalink] New post   13 Jul 2022, 06:37
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GreenlightTestPrep wrote:
TAYYABGRE wrote:
For plugging the points (x.y) given in option D, isn't y = -2 and x= 1? Because plugged-in values seem the opposite of this.


You're absolutely right. I have edited my response accordingly.
Kudos for you!!!!

Thank you sir.
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Re: Which of the following points falls outside of the region defined by 2 [#permalink] New post   09 Sep 2023, 06:03
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Re: Which of the following points falls outside of the region defined by 2 [#permalink]
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