Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 04 May 2015, 13:40

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If equation |x/2|+|y/2| = 5 encloses a certain region

Author Message
TAGS:
Manager
Joined: 03 Oct 2009
Posts: 64
Followers: 0

Kudos [?]: 49 [2] , given: 8

If equation |x/2|+|y/2| = 5 encloses a certain region [#permalink]  15 Jan 2012, 08:42
2
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

49% (01:59) correct 51% (01:16) wrong based on 444 sessions
If equation |x/2|+|y/2| = 5 encloses a certain region on the coordinate plane, what is the area of this region?

A. 20
B. 50
C. 100
D. 200
E. 400
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4228

Kudos [?]: 41006 [2] , given: 5654

Re: Area of region [#permalink]  15 Jan 2012, 10:07
2
KUDOS
Expert's post
Apex231 wrote:
I had solved till this point - So we have 4 points: (10, 0), (-10, 0), (0, 10) and (-10, 0).

But instead of joining these points i did this - 4 * (10 * 10) = 400 , which is wrong of course.

So when we join these points, how |x|+|y| = 10 stays satisfied , what's the maths behind it?

Given: $$|x|+|y|=20$$

You will have 4 case:

$$x<0$$ and $$y<0$$ --> $$-x-y=10$$ --> $$y=-10-x$$;

$$x<0$$ and $$y\geq{0}$$ --> $$-x+y=10$$ --> $$y=10+x$$;

$$x\geq{0}$$ and $$y<0$$ --> $$x-y=10$$ --> $$y=x-10$$;

$$x\geq{0}$$ and $$y\geq{0}$$ --> $$x+y=10$$ --> $$y=10-x$$;

So we have equations of 4 lines. If you draw these four lines you'll get the figure shown in my previous post.

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4228

Kudos [?]: 41006 [1] , given: 5654

Re: Area of region [#permalink]  15 Jan 2012, 09:26
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
Apex231 wrote:

If equation |x/2|+|y/2| = 5 encloses a certain region on the coordinate plane, what is the area of this region?

A 20
B 50
C 100
D 200
E 400

First of all to simplify the given expression a little bit let's multiply it be 2: $$|\frac{x}{2}|+|\frac{y}{2}|=5$$ --> $$|x|+|y|=10$$.

Now, find x and y intercepts of the region (x-intercept is a value(s) of x for y=0 and similarly y-intercept is a value(s) of y for x=0):
$$y=0$$ --> $$|x|=10$$ --> $$x=10$$ and $$x=-10$$;
$$x=0$$ --> $$|y|=10$$ --> $$y=10$$ and $$y=-10$$.

So we have 4 points: (10, 0), (-10, 0), (0, 10) and (-10, 0).

When you join them you'll get the region enclosed by $$|x|+|y|=10$$:
Attachment:

Enclosed region.gif [ 2.04 KiB | Viewed 7121 times ]
You can see that it's a square. Why a square? Because diagonals of the rectangle are equal (20 and 20), and also are perpendicular bisectors of each other (as they are on X and Y axis), so it must be a square. As this square has a diagonal equal to 20, so the $$Area_{square}=\frac{d^2}{2}=\frac{20*20}{2}=200$$.

Or the $$Side= \sqrt{200}$$ --> $$area=side^2=200$$.

Similar questions:
m06-5-absolute-value-108191.html
graphs-modulus-help-86549.html

Hope it's clear.
_________________
Manager
Joined: 03 Oct 2009
Posts: 64
Followers: 0

Kudos [?]: 49 [0], given: 8

Re: Area of region [#permalink]  15 Jan 2012, 09:58
I had solved till this point - So we have 4 points: (10, 0), (-10, 0), (0, 10) and (-10, 0).

But instead of joining these points i did this - 4 * (10 * 10) = 400 , which is wrong of course.

So when we join these points, how |x|+|y| = 10 stays satisfied , what's the maths behind it?
Manager
Joined: 03 Oct 2009
Posts: 64
Followers: 0

Kudos [?]: 49 [0], given: 8

Re: Area of region [#permalink]  15 Jan 2012, 11:10
Thanks so much Bunuel...
Director
Joined: 24 Aug 2009
Posts: 507
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 10

Kudos [?]: 445 [0], given: 241

If equation |x/2|+|y/2| = 5 encloses a certain region [#permalink]  10 Sep 2012, 11:25
CMcAboy wrote:
Can someone help me with this question:

If equation |x/2| + |y/2| = 5 encloses a certain region on the coordinate plane, what is the area of this region?

A) 20
B) 50
C) 100
D) 200
E) 400

I believe this is the simplest & the quickest solution
|x/2| + |y/2| = 5
Put x = 0 in the above equation we get |y/2| = 5, which means y= 10, - 10
Put y = 0 in the above equation we get |y/2| = 5, which means x= 10, - 10

If you see plot these four points you get a square with two equal diagonals of length 20 units
Thus area = 1/2 * (Diagonal)^2 -----> 1/2 * 400 = 200

I hope this will help many.
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 17

Kudos [?]: 257 [0], given: 11

Re: If equation |x/2|+|y/2| = 5 encloses a certain region [#permalink]  05 Dec 2012, 22:30
(1) derive all equations
x+y = 10
x-y = 10
x+y=-10
-x+y=10

(2) Get your x and y intercepts

(0,10), (10,0)
(0,-10),(10,0)
(0,-10),(-10,0)
(0,10),(-10,0)

(3) You will have a square with a diagonal of 20
(4) Calculate area = $$(10 * \sqrt{2})\sqrt{^2}$$ = 200

_________________

Impossible is nothing to God.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4767
Followers: 296

Kudos [?]: 52 [0], given: 0

Re: If equation |x/2|+|y/2| = 5 encloses a certain region [#permalink]  12 Oct 2014, 02:26
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 12 Jul 2014
Posts: 10
Location: India
Concentration: Operations, Technology
GMAT Date: 11-06-2014
GRE 1: 303 Q159 V144
Followers: 0

Kudos [?]: 7 [0], given: 40

If equation |x/2|+|y/2| = 5 encloses a certain region [#permalink]  15 Oct 2014, 18:17
Apex231 wrote:
If equation |x/2|+|y/2| = 5 encloses a certain region on the coordinate plane, what is the area of this region?

A. 20
B. 50
C. 100
D. 200
E. 400

Hello There,
Equation of a straight line whose x and y intercepts are a and b resp. is (x/a) + (y/b) = 1 i.e., coordinates of two ends of the line are (a,0) and (0,b).
Now, from the given question,
|x/2|+|y/2| = 5, reducing this to intercept form we get,
|x/10|+|y/10| = 1
Considering the equation without modulus, coordinates are (10,0) and (0,10). Since there is modulus, other two coordinates are (-10,0) and (0,-10).
Now coordinates (10,0), (0,10), (-10,0) and (0,-10) form a square with diagonal length = 20.
Here diagonal length can be obtained by calculating the distance between (10,0) and (-10,0) or (0,10) and (0,-10).
In a square,
Diagonal = Side * sqrt(2)
Side = 10 * sqrt(2)
Area = Side * Side = 200.

Ans : D

Hope this helps!
Thanks!
_________________

Regards,
Bharat Bhushan Sunkara.

"You need to sacrifice what you are TODAY, for what you want to be TOMORROW!!"

Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4228

Kudos [?]: 41006 [0], given: 5654

Re: If equation |x/2|+|y/2| = 5 encloses a certain region [#permalink]  15 Oct 2014, 23:48
Expert's post
Re: If equation |x/2|+|y/2| = 5 encloses a certain region   [#permalink] 15 Oct 2014, 23:48
Similar topics Replies Last post
Similar
Topics:
If equation |x/2| + |y/2| + 5 encloses a certain region on the coordi 1 03 Sep 2010, 13:45
Equation |x/2| +|y/2|=5 encloses a certain region on the 13 09 Sep 2007, 14:26
Equation |x/2| + |y/2| = 5 encloses a certain region on the 3 23 May 2007, 22:10
Equation |x/2|+|y/2|=5 encloses a certain region on the 5 03 Apr 2007, 14:06
Equation |x/2| + |y/2| = 5 encloses a certain region on the 6 20 Dec 2005, 04:16
Display posts from previous: Sort by