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Sample Question 24:

Let $f$ be a function with the following properties:

(i) $f(1) = 1$ , and

(ii) $f(2n) = n \cdot f(n)$ for any positive integer $n$ .

What is the value of $f(2^{100})$ ?

$\mathrm{(A) \ } 1 \qquad \mathrm{(B) \ } 2^{99} \qquad \mathrm{(C) \ } 2^{100} \qquad \mathrm{(D) \ } 2^{4950} \qquad \mathrm{(E) \ } 2^{9999}$

Answer Keys

Question 24: D