Data Sufficiency

A certain circle in the xy-plane has its center at the origin. If P is a point on the circle,
what is the sum of the squares of the coordinates of P?

(1) The radius of the circle is 4.
(2) The sum of the coordinates of P is 0.

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.

OA: A

Explanation: When center of circle is origin (0,0) and points (x,y) on the circle...the distance from origin is SQRT(x^2+y^2).
this distance is nothing but the radius of the circle. therefore statement A is sufficient.

In B, points can lies on I, II, III, or IV quadrant. But as said, the sum of points is 0. It means the points can be (x,-y) or (x,-y). Two answer. Statement B is insufficient.

farooq wrote:A certain circle in the xy-plane has its center at the origin. If P is a point on the circle,
what is the sum of the squares of the coordinates of P?

(1) The radius of the circle is 4.
(2) The sum of the coordinates of P is 0.

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.

OA: A

Explanation: When center of circle is origin (0,0) and points (x,y) on the circle...the distance from origin is SQRT(x^2+y^2).
this distance is nothing but the radius of the circle. therefore statement A is sufficient.

In B, points can lies on I, II, III, or IV quadrant. But as said, the sum of points is 0. It means the points can be (x,-y) or (x,-y). Two answer. Statement B is insufficient.

In st (2), sum 0 means, P is either in II or in IV quadrant, with its abscissa and ordinate being additive inverse of each other. Not only 2 but there are numberless possibilities here, hence insufficient.