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In the coordinate plane, what is the area of the region encl

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by Max@Math Revolution » Mon Sep 24, 2018 4:13 am

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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 encl

by fskilnik@GMATH » Mon Sep 24, 2018 5:07 am
Max@Math Revolution 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 the focused-region is a right isosceles triangle.
\[? = {S_\Delta } = \frac{{2 \cdot 2}}{2} = 2\]

Image

The right answer is therefore [spoiler]__(B)_____[/spoiler] .


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

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Max@Math Revolution » Wed Sep 26, 2018 3:54 am
=>

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

Image

The area of the shaded triangle above is (1/2)(3-1)(4-2) = (1/2)*2*2 = 2


Therefore, B is the answer.
Answer: B
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