Question

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

$6$

$8$

$12$

$16$

$24$

Answer: A

Concepts:factor counting prime factorization

Difficulty rating: 1140

Solution:

We know that $11$ is prime, which means that it only has $2$ divisors.

The prime factorization of $20$ is $2^2 \cdot 5.$ Recall that the number of divisors a number has is the product of all the exponents plus one in the prime factorization.

Here, that product would be $(2 + 1) (1 + 1) = 3 \cdot 2 = 6.$

Then $2 \cdot 6 = 12.$ We have the prime factorization of $12$ is $2^2 \cdot 3.$ This also has $(2 + 1) (1 + 1) = 3 \cdot 2 = 6$ divisors.

Thus, A is the correct answer.

1997 AMC 8 Problem 11

Answer: A

Difficulty rating: 1140

Solution:

Problem 11 in Other Years