CEMC Cayley, 2025

Algebra Difficulty 1.6 Junior Find the answer Canada

For each non-zero real number $a$ , we define $a^* = \dfrac{5}{a}$ .

The expression $(100^*)^*$ is equal
to

Pick one

Solution

Since $a^*=\dfrac{5}{a}$ , then
$100^*=\dfrac{5}{100}$ , and so $(100^*)^*=\left(\dfrac{5}{100}\right)^*$ .

Evaluating, $\left(\dfrac{5}{100}\right)^*=\dfrac{5}{\left(\frac{5}{100}\right)}=5\times\dfrac{100}{5}=100$ ,
and so $(100^*)^*=100$ .

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