2020 AMC 12A Problem 4
Attempt Problem 4 of the 2020 AMC 12A 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 2020 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
4.
How many -digit positive integers (that is, integers between and inclusive) having only even digits are divisible by
Answer: B
Small hint:
A number divisible by ends in or but the last digit must also be even
Big hint:
Count the choices for each digit: the leading digit cannot be
Solution:
To be divisible by the last digit is or and to be even it must be So the units digit is fixed.
The leading digit is a nonzero even digit: give choices. Each of the two middle digits is any even digit giving choices each.
The total is
Thus, B is the correct answer.
Problem 4 in other years
- 1950 AMC 12
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