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

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Nevernevergiveup
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Which of the following points falls outside of the region defined by [#permalink] New post   09 Aug 2016, 09:21
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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)
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D
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BrentGMATPrepNow
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Re: Which of the following points falls outside of the region defined by [#permalink] New post   09 Aug 2016, 10:07
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Nevernevergiveup 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.

For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions

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:
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D


Cheers,
Brent
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KarishmaB
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Which of the following points falls outside of the region defined by [#permalink] New post   Updated on: 11 Oct 2022, 00:28
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Nevernevergiveup 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)


Simplify the inequality to get: y <= 3x - 6

Plot y = 3x - 6. The two points through which it passes are (0, -6) and (2, 0). Now put (0, 0) and you will find that the inequality is not satisfied. So the region we are considering is the one other than the one where (0, 0) lies. Now you can easily see which points do lie and which do not lie in our region.

Originally posted by KarishmaB on 10 Aug 2016, 03:43.
Last edited by KarishmaB on 11 Oct 2022, 00:28, edited 1 time in total.
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Re: Which of the following points falls outside of the region defined by [#permalink] New post   09 Aug 2016, 11:26
Nevernevergiveup 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)


Equation given is 2y<=6x-12
Simplifying this; y<=3x-6
Plug in the values provided in the options,

A. 1<=11
B. -8<=3
C. 0<=0
D. -2<=-3
E. -14<=-12

Option D is the answer.
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Re: Which of the following points falls outside of the region defined by [#permalink] New post   16 Jun 2017, 01:41
Nevernevergiveup 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)


This question is simply saying which coordinate pair does not satisfy the equation- just plug in the answer choices

Thus

"D"
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Re: Which of the following points falls outside of the region defined by [#permalink] New post   25 Jun 2017, 09:01
this question can be easily solved by simplifying the equation to 3x-y >= 6. only option D does not satisfy the equation. hence answer is D
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Re: Which of the following points falls outside of the region defined by [#permalink] New post   03 Sep 2017, 11:43
no need of plotting any graph.simple put down options in question and check if condition still holds true..

Option D.
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Which of the following points falls outside of the region defined by [#permalink] New post   11 Apr 2020, 05:25
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Nevernevergiveup 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)


If a point falls outside 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
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Re: Which of the following points falls outside of the region defined by [#permalink] New post   28 Oct 2023, 14:16
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Re: Which of the following points falls outside of the region defined by [#permalink]
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