Which of the following is the correct answer?
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In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of r2 + s2?
(1) The circle has radius 2.
(2) The point (√2, -√2) lies on the circle.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
HELP please..
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Thank you Yalanand. I think I was confused by the question..does this mean R & S are the radii, since it says point (r, s) lies on a circle with center at the origin?yalanand wrote:
Answer is D
1) We know radius of circle Hence r^2+s^2=2^2 = 4
2) Distance between two points is Sqrt of ((√2-0)^2+(-√2-0)^2)) = 4[/img]
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Hi can you explain how you know s=2?yalanand wrote:
Answer is D
1) We know radius of circle Hence r^2+s^2=2^2 = 4
2) Distance between two points is Sqrt of ((√2-0)^2+(-√2-0)^2)) = 4[/img]
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- Senior | Next Rank: 100 Posts
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Hi can you explain how you know s=2?yalanand wrote:
Answer is D
1) We know radius of circle Hence r^2+s^2=2^2 = 4
2) Distance between two points is Sqrt of ((√2-0)^2+(-√2-0)^2)) = 4[/img]
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Here is the best answer. Refer to the post of Bunuel with the diagram in it. https://gmatclub.com/forum/in-the-xy-pla ... 15566.html
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To make the solution easier to follow, let's replace (r, s) with (a, b):
Since (a, b) lies on the circle, we get:
a² + b² = r².
Thus, to determine the value of a² + b², we need to know the value of r.
Question rephrased:
What is the value of r?
Statement 1: The circle has radius 2.
SUFFICIENT.
Statement 2: The point (√2, -√2) lies on the circle.
Since the radius is equal to the distance between the origin and any point on the circle -- including (√2, -√2) -- the value of r can be determined.
SUFFICIENT.
The correct answer is D.
The equation for a circle centered at the origin is x² + y² = r², where r is the radius.jkwan wrote:In the xy-plane, point (a, b) lies on a circle with center at the origin. What is the value of a² + b²?
(1) The circle has radius 2.
(2) The point (√2, -√2) lies on the circle.
Since (a, b) lies on the circle, we get:
a² + b² = r².
Thus, to determine the value of a² + b², we need to know the value of r.
Question rephrased:
What is the value of r?
Statement 1: The circle has radius 2.
SUFFICIENT.
Statement 2: The point (√2, -√2) lies on the circle.
Since the radius is equal to the distance between the origin and any point on the circle -- including (√2, -√2) -- the value of r can be determined.
SUFFICIENT.
The correct answer is D.
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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].
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