A wooden rod is cut into two pieces. What is the length of the longer piece?
(1) One of the pieces is 20 inches longer than the other piece.
(2) The length of the shorter piece is ~$\frac{1}{3}$~ the length of the longer piece.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.