Gmat prep data sufficiency question
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 1/3 the length of the longer piece
I thought both statements were not sufficient but the answer is both statements together are sufficient, but neither statement alone is sufficient. How?
The best way to solve such questions is to put everything into equations. The question stem does not give us anything, but let us assume that
s - length of the shorter piece.
l - length of the longer piece.
Statement 1: l = s + 20
1 equation. 2 unknowns. Therefore statement 1 is insufficient by itself.
Statement 2: s = l/3. 3s = l.
1 equation. 2 unknowns. Therefore statement 2 is insufficient by itself.
Together: We can substitute the value of l from statement 2 into statement 1.
3s = s + 20
2s = 20
s = 10
Therefore, l = 30. And hence the answer is C - Both statements together are sufficient.