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# Which of the following is the area of the region that

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Intern
Joined: 10 Apr 2018
Posts: 4
Which of the following is the area of the region that  [#permalink]

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13 Aug 2019, 03:02
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Difficulty:

45% (medium)

Question Stats:

58% (01:40) correct 42% (02:02) wrong based on 48 sessions

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Which of the following is the area of the region that includes all the points that satisfy the inequalities : X+Y-3<=0, X>=0, Y>=0?

1) 1.5
2) 2.5
3) 3
4) 4.5
5) 5

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Intern
Joined: 23 Jun 2018
Posts: 5
Re: Which of the following is the area of the region that  [#permalink]

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13 Aug 2019, 03:35
1
X+Y-3>=0 can be written as X+Y>= 3,

To find the area we can take 2 points that lie on line X+Y>=3
(0,3) and (3,0)
as we already know x>=0 and y>=0.

The line X+Y>=3 forms a triangle with x and y axis
area of triangle = $$\frac{1}{2}$$*b*h
Here B = 3 taking distance from (0,0) to (3,0)
H = 3, taking distance from (0,0) to (0,3)
=$$\frac{1}{2}$$*3*3 = 4.5

So, option D.
Senior Manager
Joined: 09 Jan 2017
Posts: 314
Location: India
Re: Which of the following is the area of the region that  [#permalink]

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14 Aug 2019, 07:46
1
Basically it is asking to find the area of the triangle enclosed between the two axis & the st line - Y=-X+3

Point of intersection with X axis of this line is (3,0) & with Y axis (0,3)

So the Right triangle having base is 3 units & Height is 3 Units.

So area (1/2 * Base * Height) = 4.5

D is correct answer
CEO
Joined: 03 Jun 2019
Posts: 2887
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: Which of the following is the area of the region that  [#permalink]

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14 Aug 2019, 08:54
1
arunabh12345 wrote:
Which of the following is the area of the region that includes all the points that satisfy the inequalities : X+Y-3<=0, X>=0, Y>=0?

1) 1.5
2) 2.5
3) 3
4) 4.5
5) 5

Posted from my mobile device

These equations form a triangle with base 3 and height 3.
Area = 3*3/2 = 4.5

IMO D
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Re: Which of the following is the area of the region that   [#permalink] 14 Aug 2019, 08:54

# Which of the following is the area of the region that

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