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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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New post Updated on: 11 Oct 2014, 10:47
6
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A
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  95% (hard)

Question Stats:

43% (02:18) correct 57% (01:59) wrong based on 485 sessions

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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

Originally posted by sunny3011 on 11 Oct 2014, 05:01.
Last edited by Bunuel on 11 Oct 2014, 10:47, 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, 12:11
1
5
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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what-is-the-area-of-the-region-enclosed-by-lines-y-x-x-y-150487.html
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Hope this helps.
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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, 09:55
3
1
5
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 14 Jul 2016, 04:27
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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New post 23 Aug 2016, 07:48
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, 06:45
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, 08:13
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]

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New post 16 Aug 2018, 13:56
1
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 red line should be 1 square to the right? looks like it represents x=-2 instead of x=-1
Please correct me if Im wrong
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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 23 Aug 2018, 07:29
Bunuel - We get x+y= -1 and x+y= 1. How do I plot the given equation |x + y | = 1 on the graph?
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Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| = &nbs [#permalink] 23 Aug 2018, 07:29
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