GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Sep 2019, 13:02 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern  Joined: 06 Dec 2012
Posts: 23
Concentration: Finance, International Business
GMAT 1: 510 Q46 V21 GPA: 3.5
The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =  [#permalink]

### Show Tags

6
36 00:00

Difficulty:   95% (hard)

Question Stats: 42% (02:18) correct 58% (01:57) wrong based on 502 sessions

### HideShow timer Statistics

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, 06:01.
Last edited by Bunuel on 11 Oct 2014, 11:47, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 58092
Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =  [#permalink]

### Show Tags

1
6
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

Similar questions to practice:
the-area-bounded-by-the-curves-x-y-1-and-x-y-1-is-93103.html
if-equation-x-2-y-2-5-encloses-a-certain-region-126117.html
in-the-x-y-plane-the-area-of-the-region-bounded-by-the-86549.html
if-equation-x-2-y-2-5-enclose-a-certain-region-101963.html
what-is-the-area-of-the-region-enclosed-by-lines-y-x-x-y-150487.html
new-set-of-mixed-questions-150204-100.html#p1208441

Hope this helps.
_________________
Senior Manager  Joined: 13 Jun 2013
Posts: 269
Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =  [#permalink]

### Show Tags

4
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)
Attachments final.jpg [ 19.58 KiB | Viewed 9613 times ]

##### General Discussion
Intern  B
Joined: 17 Jan 2015
Posts: 35
Location: India
GMAT 1: 620 Q42 V34 GMAT 2: 710 Q49 V38 Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =  [#permalink]

### Show Tags

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
Intern  Joined: 29 Mar 2015
Posts: 11
Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =  [#permalink]

### Show Tags

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!
Intern  B
Joined: 17 Jan 2015
Posts: 35
Location: India
GMAT 1: 620 Q42 V34 GMAT 2: 710 Q49 V38 Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =  [#permalink]

### Show Tags

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.
Manager  B
Joined: 14 Jun 2016
Posts: 71
Location: India
GMAT 1: 610 Q49 V21 WE: Engineering (Manufacturing)
Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =  [#permalink]

### Show Tags

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....
_________________
Please help me with Kudos dear friends-need few more to reach the next level. Thanks. Intern  B
Joined: 04 Jul 2018
Posts: 2
Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =  [#permalink]

### Show Tags

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
Intern  B
Joined: 06 Aug 2017
Posts: 6
Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =  [#permalink]

### Show Tags

Bunuel - We get x+y= -1 and x+y= 1. How do I plot the given equation |x + y | = 1 on the graph? Re: The area bounded by the three curves |x + y | = 1, |x| = 1, and |y| =   [#permalink] 23 Aug 2018, 08:29
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  