Question

The student lockers at Olympic High are numbered consecutively beginning with locker number $1.$ The plastic digits used to number the lockers cost $2$ cents apiece. Thus, it costs $2$ cents to label locker number $9$ and $4$ cents to label locker number $10.$ If it costs $\$137.94$ to label all the lockers, how many lockers are there at the school?

$2001$

$2010$

$2100$

$2726$

$6897$

Answer: A

Concepts:digits counting integers in a range

Difficulty rating: 1450

Solution:

Labeling costs $\$137.94 / \$0.02 = 6897$ digits. Lockers $1$ - $9$ use $9$ digits, lockers $10$ - $99$ use $2 \cdot 90 = 180$ digits, and lockers $100$ - $999$ use $3 \cdot 900 = 2700$ digits.

The remaining digits number $6897 - 2700 - 180 - 9 = 4008,$ which label $4008 / 4 = 1002$ four-digit lockers. In all there are $999 + 1002 = 2001$ lockers.

Thus, the correct answer is A.

1999 AMC 12 Problem 11

Answer: A

Difficulty rating: 1450

Solution:

Problem 11 in Other Years