2018 AMC 12B Problem 15
Attempt Problem 15 of the 2018 AMC 12B 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 2018 AMC 12B solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
15.
How many -digit positive odd multiples of do not include the digit
Answer: A
Small hint:
Choose the hundreds digit (not or ) and the units digit (odd, not ) first
Big hint:
For each such pair, the allowed tens digits split evenly into three residue classes mod
Solution:
Write the number as The hundreds digit has choices (), and the units digit has choices ().
The tens digit may be any of These split into three residue classes mod of equal size so exactly choices of make divisible by
The count is
Thus, the correct answer is A.
Problem 15 in other years
- 1950 AMC 12
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