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) $12^{*} \div 3^{*}=4^{*}$
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
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) $12 * \div 3^{*}=4^{*}$
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Solution
(i) $\frac{1}{2}+\frac{1}{4}=\frac{3}{4} \neq \frac{1}{6}$,
(i) is not true
(ii) $\frac{1}{3} \times \frac{1}{5}=\frac{1}{15}$,
(ii) is true
(iii) $\frac{1}{7}-\frac{1}{3}=\frac{3}{21}-\frac{7}{21}=\frac{4}{21} \neq \frac{1}{4}$,
(iii) is not true
(iv) $\frac{\frac{1}{12}}{\frac{1}{3}}=\frac{1}{12} \times \frac{3}{1}=\frac{1}{4}$,
(iv) is true

Only two of these statements is correct.

ANSWER: (C)