What is the radius of the circle? a) The circumference is 20π b) The area of…

Concept: In a data-sufficiency question, a statement is sufficient on its own if it reduces the question to a single equation in the single unknown asked for. For a circle, the circumference formula C = 2πr and the area formula A = πr² each involve only the radius r — so if either statement gives one such equation, that statement alone fixes r uniquely, independent of the other statement.

Application:

1. Statement A gives the circumference as 20π. Using C = 2πr: 2πr = 20π, so r = 10. This is one equation in the one unknown r, so statement A alone determines r.

2. Statement B gives the area as 100π. Using A = πr2: πr2 = 100π, so r2 = 100, giving r = 10 (taking the positive root, since a radius cannot be negative). This is also one equation in the one unknown r, so statement B alone determines r.

Cross-check: Both routes independently arrive at the same value of r, which confirms the two statements are consistent with each other. But for a data-sufficiency verdict, what matters is only that EACH statement, taken alone, is one equation in one unknown — neither statement needs to borrow information from the other.

Result: Since statement A alone is sufficient and statement B alone is sufficient, the correct classification is that either statement, by itself, is sufficient to answer the question — option "Either of statement A or B is sufficient" is correct.