2020 AMC 8 Problem 19
Attempt Problem 19 of the 2020 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
A number is called flippy if its digits alternate between two distinct digits. For example, and are flippy, but and are not. How many five-digit flippy numbers are divisible by
Answer: B
Small hint:
A five-digit flippy number has form
Big hint:
Divisibility by forces
Video solution:
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Written solution:
A five-digit flippy number has the form where and Divisibility by requires the last digit to be or Since we must have
The number therefore has the form Its digit sum is so divisibility by requires to be a multiple of The possibilities are and giving numbers.
Thus, the correct answer is B.
Problem 19 in other years
- 1985 AMC 8
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