What are the coordinates of point A in the rectangular coordinate system? (1) A is 2 units away from (0, 4). (2) A is 3 units away from (0, 0).
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.
(E) All the points that lie at some specific distance from a given one are situated on the circle, which center is the given point and the radius is the distance. Therefore each statement by itself defines a circle (infinitively many points). So each statement by itself is NOT sufficient. If we use the both statements together, we have two circles. Point A belongs to each one of them. Two circles can cross each other in one or two points. (Two circles can also have no common points at all, but it is NOT our case). The distance between the centers, (0, 0) and (0, 4), is √(0² + 4²) = 4. The sum of the radii is 5. If you draw a segment, which connects these two centers, it’s length will be 4. The circle, which center is (0, 0), will cross the segment 3 units away from (0, 0). The circle, which center is (0, 4), will cross the segment 2 units away from (0, 4). It’s clear, that the circles cross each other in exactly TWO different points. So statements (1) and (2) taken together are NOT sufficient to answer the question. The correct answer is E.  How can you tell from the question that you are referring to circles?
