Testing Values In Algebra

This topic has expert replies
Source: — Problem Solving |

User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Thu Jan 09, 2014 4:58 am
[email protected] wrote:Hi Experts,

Can you pls help me solve this question with test values?

Thnks
We've to look for the EXCEPTION here:

A. This is possible when x = ±10, y = 0. So, eliminate.

B. This is possible when x = 8, y = 6. So, eliminate.

C. Since the minimum absolute value of any unknown is 0, hence the absolute value of x must be more than 10, which won't make the condition above as true. Pick C and save time!

D. Who cares?

E. Who cares?

[spoiler]Answer C[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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 » Thu Jan 09, 2014 6:14 am
[email protected] wrote:Hi Experts,

Can you pls help me solve this question with test values?

Thnks
Alternate line of reasoning:

x² + y² = r² is the equation of a circle that is centered at the origin and has a radius of r.
Thus:
x² + y² = 100 is the equation of a circle that is centered at the origin and has a radius of 10.

Since every point on the circle must be 10 units from the origin, every point on the circle must have an x-coordinate no more than 10 units from the origin and a y-coordinate no more than 10 units from the origin.
In the other words:
|x| ≤ 10 and |y| ≤ 10.
Look for an answer choice that EXCEEDS this threshold.

Answer choice C:
|x| > |y| + 10.
Since the least possible value of |y| is 0, this answer choice implies that |x| > 10 -- EXCEEDING the threshold discussed above.

The correct answer is C.
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

Junior | Next Rank: 30 Posts
Posts: 17
Joined: Thu Jun 20, 2013 9:38 pm
Thanked: 3 times
Followed by:1 members

by gmaster328 » Thu Jan 09, 2014 11:02 am
Makes sense! Thanks!
GMATGuruNY wrote:
[email protected] wrote:Hi Experts,

Can you pls help me solve this question with test values?

Thnks
Alternate line of reasoning:

x² + y² = r² is the equation of a circle that is centered at the origin and has a radius of r.
Thus:
x² + y² = 100 is the equation of a circle that is centered at the origin and has a radius of 10.

Since every point on the circle must be 10 units from the origin, every point on the circle must have an x-coordinate no more than 10 units from the origin and a y-coordinate no more than 10 units from the origin.
In the other words:
|x| ≤ 10 and |y| ≤ 10.
Look for an answer choice that EXCEEDS this threshold.

Answer choice C:
|x| > |y| + 10.
Since the least possible value of |y| is 0, this answer choice implies that |x| > 10 -- EXCEEDING the threshold discussed above.

The correct answer is C.