2005 AMC 8 Problem 18
Attempt Problem 18 of the 2005 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
How many three-digit numbers are divisible by
Answer: C
Small hint:
A three-digit multiple of has form .
Big hint:
Find the smallest and largest possible values of .
Solution:
We want to find how many exist such that is a three-digit number.
The smallest possible such that is
The largest possible such that is
This tells us that can range from to which gives us values for
Thus, C is the correct answer.
Problem 18 in other years
- 1985 AMC 8
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