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1987 AJHSME Problems/Problem 21

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Problem

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

i) 3^*+6^*=9^*
ii) 6^*-4^*=2^*
iii) 2^*\cdot 6^*=12^*
iv) 10^*\div 2^* =5^*

\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 4

Solution

We can just test all of these statements: \begin{align*}3^*+6^* &= \frac{1}{3}+\frac{1}{6} \\&= \frac{1}{2} \neq 9^* \\6^*-4^* &= \frac{1}{6}-\frac{1}{4} \...

The last two statements are true and the first two aren't, so \boxed{\text{C}}

See Also

1987 AJHSME (ProblemsResources)
Preceded by
Problem 20
Followed by
Problem 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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