1998 Gauss 8 Problem 16

Suppose that x* means \frac{1}{x}, the reciprocal of x. For example, 5* = \frac{1}{5}. How many of the following statements are true?

(i) 2* + 4* = 6* (ii) 3* \times 5* = 15* (iii) 7* - 3* = 4* (iv) 12* \div 3* = 4*

\textbf{(A)}\ 0\quad \textbf{(B)}\ 1\quad \textbf{(C)}\ 2\quad \textbf{(D)}\ 3\quad \textbf{(E)}\ 4

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.