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In the coordinate plane, what is the area of the region enclosed by x≥

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Math Revolution GMAT Instructor
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In the coordinate plane, what is the area of the region enclosed by x≥  [#permalink]

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New post 24 Sep 2018, 05:20
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

52% (01:39) correct 48% (01:23) wrong based on 25 sessions

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[Math Revolution GMAT math practice question]

In the coordinate plane, what is the area of the region enclosed by x ≥ 1, y ≥ 2 and x + y ≤ 5?

A. 1
B. 2
C. 3
D. 4
E. 5

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In the coordinate plane, what is the area of the region enclosed by x≥  [#permalink]

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New post 24 Sep 2018, 07:55
MathRevolution wrote:
[Math Revolution GMAT math practice question]

In the coordinate plane, what is the area of the region enclosed by x ≥ 1, y ≥ 2 and x + y ≤ 5?

A. 1
B. 2
C. 3
D. 4
E. 5

Please follow the image below, in which we show that the focused-region is a right isosceles triangle.

Image

\(? = {S_\Delta } = \frac{{2 \cdot 2}}{2} = 2\)

The right answer is therefore (B).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: In the coordinate plane, what is the area of the region enclosed by x≥  [#permalink]

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New post 26 Sep 2018, 04:04
=>

The region can be sketched in the xy-plane as shown below.

Attachment:
a.png
a.png [ 9.94 KiB | Viewed 142 times ]


The area of the shaded triangle above is \((\frac{1}{2})(3-1)(4-2) = (\frac{1}{2})*2*2 = 2\)


Therefore, B is the answer.

Answer: B
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Re: In the coordinate plane, what is the area of the region enclosed by x≥ &nbs [#permalink] 26 Sep 2018, 04:04
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