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CEMC Gauss (Grade 8), 1998

Algebra Difficulty 1.0 Junior Find the answer Canada

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) $4$

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