Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. What is the length of the original sheet of paper?

Correct Answer: (D) 30 units

The single-digit odd prime numbers are 3, 5, and 7, so the first piece length is $L_1 =$$\frac{3+5+7}{3}$ = 5. The other pieces satisfy $L_2 = 5 +$$\frac{L_3}{3}$ and $L_3 = L_1 + L_2 = 5 + L_2$. Substituting gives $L_3 = 10 +$$\frac{L_3}{3}$ $\implies$ $\frac{2}{3}$L_3 = 10 $\implies$ L_3 = 15. Then $L_2 = 10$, and the original sheet length was $L_1 + L_2 + L_3 = 5 + 10 + 15 = 30$$\text{ units}$.