Question

Assume every $7$ -digit whole number is a possible telephone number except those that begin with $0$ or $1.$ What fraction of telephone numbers begin with $9$ and end with $0?$

$\dfrac{1}{63}$

$\dfrac{1}{80}$

$\dfrac{1}{81}$

$\dfrac{1}{90}$

$\dfrac{1}{100}$

Solution:

The first digit is one of $8$ allowed digits ( $2$ through $9$ ), so $\dfrac18$ of the numbers begin with $9.$ The last digit is any of $10$ digits, so $\dfrac{1}{10}$ end in $0.$

These conditions are independent, so the fraction is $\dfrac18 \cdot \dfrac{1}{10} = \dfrac{1}{80}.$

Thus, the correct answer is B .

1985 AMC 8 Problem 22

Solution:

Problem 22 in Other Years