Data Sufficiency

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.

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]

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]

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?

Good point...Here I am assuming the point is lies on the circle and not inside the circle....If its inside the circle then its E....

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]

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]

Hi can you explain how you know s=2?

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

To make the solution easier to follow, let's replace (r, s) with (a, b):

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.

The equation for a circle centered at the origin is x² + y² = r², where r is the radius.
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.