It is currently Wed Dec 19, 2018 6:36 am

 All times are UTC - 5 hours [ DST ]

 Page 1 of 1 [ 2 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: GMAT Coordinate Geometry (Data Sufficiency)Posted: Fri Jul 16, 2010 9:03 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
A circle is drawn on the coordinate plane, with the center of the circle at the origin. If point A is located on the perimeter of the circle, what is the sum of the squares of its x and y coordinates?

(1) The radius of the circle is 2.
(2) One of the points on the perimeter of the circle is (–2, –2).

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(D) Statement (1) is sufficient by itself. For a circle with its center at the origin of the coordinate plane, the value of the sum of the squares of the coordinates of the points on the perimeter can be determined. This value is simply the square of the radius of the circle (2² = 4).
For example, one (x, y) coordinate that is on the perimeter of the circle is (2, 0). The sum of the squares of x and y would equal 4. Likewise, using the Pythagorean Theorem, for all points (x, y) on the circle, x² + y² = 4.

Statement (2) is also sufficient. The sum of the squares of the x and y coordinates given in Statement (2) is: (-2)² + (-2)² = 4.

Since both statements are sufficient individually, the correct answer is choice (D).
-------------

"Likewise, using the Pythagorean Theorem, for all points (x, y) on the circle, x² + y² = 4."

Top

 Post subject: Re: GMAT Coordinate Geometry (Data Sufficiency)Posted: Fri Jul 16, 2010 9:18 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498

For any point C (x, y) which lies on the circle but not on the axis, we can build a triangle ABC (see graphics).

When we apply Pythagorean Theorem to this triangle we will get:
AC² = AB² + BC²
2² = |x|² + |y
4 = x² + y²

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 2 posts ]

 All times are UTC - 5 hours [ DST ]

#### Who is online

Users browsing this forum: No registered users and 3 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ GMAT    GMAT: Quantitative Section (Math)    GMAT: Verbal Section    GMAT: Integrated Reasoning    GMAT: General Questions GRE    GRE: Quantitative Reasoning (Math)    GRE: Verbal Reasoning    GRE: General Questions General questions    Other questions