1997 AJHSME Problems/Problem 11

Problem

Let $\boxed{N}$ mean the number of whole number divisors of $N$ . For example, $\boxed{3}=2$ because 3 has two divisors, 1 and 3. Find the value of

$\boxed{\boxed{11}\times\boxed{20}}.$

$\text{(A)}\ 6 \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 12 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 24$

$\boxed{\boxed{11}\times\boxed{20}}$

$11$ has $2$ factors, and $20$ has $\{1, 2, 4, 5, 10, 20\}$ as factors, for a total of $6$ factors. Plugging $\boxed{11} = 2$ and $\boxed {20}= 6$ :

$\boxed{2 \times 6}$

$\boxed{12}$

$12$ has factors of $\{1, 2, 3, 4, 6, 12\}$ , so $\boxed{12} = 6$ , and the answer is $\boxed{A}$

1997 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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