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Testing Values In Algebra

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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]
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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.
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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.
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