Bunuel wrote:

What are the coordinates of the point A?

(1) A is 2 units away from (3, 4).

(2) A is 3 units away from (0, 0).

Kudos for a correct solution.

A=(x,y) = ?

Per statement 1, coordinates at a distance of 2 units from (3,4) lie on the circumference of a circle with center (3,4) and radius 2 units. Thus all the points on the circumference of this circle can be A's coordinates. Thus this statement is not sufficient.

Per statement 2, coordinates at a distance of 3 units from (0,0) lie on the circumference of a circle with center (0,0) and radius 3 units. Thus all the points on the circumference of this circle can be A's coordinates. Thus this statement is not sufficient.

Combining, we see that the radii of the circles = 2+3 = 5 = distance between the centers of the 2 circles (= ((3-0)^2+)4-0)^2)^0.5) ----> The circles intersect each other at only 1 point. Thus we get a unique coordinate value for A---> C is the correct answer.