BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Co-ordinate system question

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members

Co-ordinate system question

by gmattesttaker2 » Sun Dec 22, 2013 6:15 pm
Hello,

Can you please assist with this:

In a coordinate system, how many points (x,y) simultaneously satisfy the conditions
|x| + |y| ≤ 1 and x^2 + y^2 = 1?

(A) exactly one
(B) exactly two
(C) exactly three
(D) exactly four
(E) infinite points

OA: D

Thanks,
Sri
Top
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 283
Joined: Sun Jun 23, 2013 11:56 pm
Location: Bangalore, India
Thanked: 97 times
Followed by:26 members
GMAT Score:750

by ganeshrkamath » Sun Dec 22, 2013 8:27 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this:

In a coordinate system, how many points (x,y) simultaneously satisfy the conditions
|x| + |y| ≤ 1 and x^2 + y^2 = 1?

(A) exactly one
(B) exactly two
(C) exactly three
(D) exactly four
(E) infinite points

OA: D

Thanks,
Sri
Some points that satisfy |x| + |y| ≤ 1
(0,1), (0.25,0.75), (0.5,0.5), (0.75,0.25), (1,0), (0.5,-0.5), (0,-1), (-0.5,-0.5), (-1,0), (-0.5,0.5)

On plotting, we realize that this set of points forms a square with vertices (0,1), (1,0), (0,-1), (-1,0)

The equation x^2 + y^2 = 1 represents a circle with center at (0,0) and radius = 1.
The only points where the circle meets the above square are at the square's four vertices.

Choose D

Cheers
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Dec 22, 2013 8:39 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this:

In a coordinate system, how many points (x,y) simultaneously satisfy the conditions
|x| + |y| ≤ 1 and x^2 + y^2 = 1?

(A) exactly one
(B) exactly two
(C) exactly three
(D) exactly four
(E) infinite points

OA: D

Thanks,
Sri
x² + y² = r² is the equation of circle centered at the origin.

Thus:
x² + y² = 1 is a circle centered at the origin with a radius of 1:
Image
The 4 points shown -- (0,1), (1,0), (0,-1), and (-1,0) -- all satisfy the constraint that |x| + |y| ≤ 1.

If we choose ANY OTHER POINT on the circle, we get something like this:
Image
Since the hypotenuse of the yielded triangle has a length of 1, the sum of the two legs -- |x| + |y| -- must be GREATER than 1.

Thus, only 4 points on circle x² + y² = 1 satisfy the constraint that |x| + |y| ≤ 1:
(0,1), (1,0), (0,-1), and (-1,0).

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1