The student locker numbers at Olympic High are numbered consecutively…
2025
The student locker numbers at Olympic High are numbered consecutively beginning with locker number 1. The plastic digits used to number the lockers cost two cents apiece. Thus, it costs two cents to label locker number 9 and four centers to label locker number 10. If it costs $137.94 to label all the lockers, how many lockers are there at the school?
- A.
2003
- B.
2000
- C.
2001
- D.
2004
Attempted by 535 students.
Show answer & explanation
Correct answer: C
Each plastic digit costs $0.02. Count the digits needed by ranges of locker numbers and multiply by $0.02.
Lockers 1–9: 9 lockers × 1 digit = 9 digits → 9 × $0.02 = $0.18
Lockers 10–99: 90 lockers × 2 digits = 180 digits → 180 × $0.02 = $3.60
Lockers 100–999: 900 lockers × 3 digits = 2700 digits → 2700 × $0.02 = $54.00
Lockers 1000–1999: 1000 lockers × 4 digits = 4000 digits → 4000 × $0.02 = $80.00
Subtotal for lockers 1–1999: $0.18 + $3.60 + $54.00 + $80.00 = $137.78
Total available is $137.94, so the remaining amount is $137.94 − $137.78 = $0.16
$0.16 buys 8 digits at $0.02 each. Lockers starting at 2000 each require 4 digits, so 8 digits allow labeling two additional lockers: 2000 and 2001.
Answer: 2001