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The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =

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The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| = [#permalink]

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The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| = 1, is equal to

A. 1
B. 2
C. 3
D. 4
E. 8


I have tried to plot graph of lines and I got area from |x|=1 and |y|=1. but what about line |x+y|=1???
Confused and need to clarify the concepts?

Source: GMAT Tutor Question bank
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Oct 2014, 11:47, edited 1 time in total.
Renamed the topic and edited the question.

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Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| = [#permalink]

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New post 11 Oct 2014, 10:55
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sunny3011 wrote:
The area bounded by the three curves |x + y | = 1, | x | = 1, and | y | = 1, is equal to
a. 1
b. 2
c. 3
d. 4
e. 8


I have tried to plot graph of lines and I got area from |x|=1 and |y|=1. but what about line |x+y|=1???
Confused and need to clarify the concepts?

Source: GMAT Tutor Question bank



|x+y|=1 can be written as x+y=1 or x+y=-1. These are two straight lines, which are mirror image of each as shown in the following graph.

|x|=1 and |y|=1 are also drawn on the graph with red and blue lines respectively. The required area is shown in the grey blocks. which is equal to 3(2+1/2+1/2). (2 block of area 1 and two triangles of area =1/2)
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Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| = [#permalink]

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New post 11 Oct 2014, 13:11
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sunny3011 wrote:
The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| = 1, is equal to

A. 1
B. 2
C. 3
D. 4
E. 8


I have tried to plot graph of lines and I got area from |x|=1 and |y|=1. but what about line |x+y|=1???
Confused and need to clarify the concepts?

Source: GMAT Tutor Question bank


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Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| = [#permalink]

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Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| = [#permalink]

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New post 14 Jul 2016, 05:27
I am sorry but I don't understand how do we arrive at the shaded region whose area is required. So, can anyone out there help me out? Thanks.

Regards,
Pallavi

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Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| = [#permalink]

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pallaviisinha wrote:
I am sorry but I don't understand how do we arrive at the shaded region whose area is required. So, can anyone out there help me out? Thanks.

Regards,
Pallavi


We have to make a graph with 6 equations:
x=1
x=-1
y=1
y=-1
x+y=1
x+y=-1

The shaded region is one with the overlap..two squares of side 1 & two right triangles with area 1/2 each..which gives the answer as 3.

Unfortunately in the photo accompanying the explanation, in place of the line x=-1, the line x=-2 is drawn. Perhaps that caused the confusion.

Hope it helped!

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Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| = [#permalink]

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New post 24 Aug 2016, 07:45
ytsejam wrote:
pallaviisinha wrote:
I am sorry but I don't understand how do we arrive at the shaded region whose area is required. So, can anyone out there help me out? Thanks.

Regards,
Pallavi


We have to make a graph with 6 equations:
x=1
x=-1
y=1
y=-1
x+y=1
x+y=-1

The shaded region is one with the overlap..two squares of side 1 & two right triangles with area 1/2 each..which gives the answer as 3.

Unfortunately in the photo accompanying the explanation, in place of the line x=-1, the line x=-2 is drawn. Perhaps that caused the confusion.

Hope it helped![/quoteTh

Indeed, thanks.

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Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| = [#permalink]

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New post 06 Aug 2017, 09:13
manpreetsingh86 wrote:
sunny3011 wrote:
The area bounded by the three curves |x + y | = 1, | x | = 1, and | y | = 1, is equal to
a. 1
b. 2
c. 3
d. 4
e. 8


I have tried to plot graph of lines and I got area from |x|=1 and |y|=1. but what about line |x+y|=1???
Confused and need to clarify the concepts?

Source: GMAT Tutor Question bank



|x+y|=1 can be written as x+y=1 or x+y=-1. These are two straight lines, which are mirror image of each as shown in the following graph.

|x|=1 and |y|=1 are also drawn on the graph with red and blue lines respectively. The required area is shown in the grey blocks. which is equal to 3(2+1/2+1/2). (2 block of area 1 and two triangles of area =1/2)


The solution is correct.
However,I think the line x=-1 is not represented properly here...
It should just be shifted to right side so that the area is covered by all the lines...
2 square boxes and two triangles must be covered by all the lines....
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Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =   [#permalink] 06 Aug 2017, 09:13
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