2018 AMC 8 Problem 21
Attempt Problem 21 of the 2018 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 2018 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
How many positive three-digit integers have a remainder of when divided by a remainder of when divided by and a remainder of when divided by
Answer: E
Small hint:
Each remainder condition says the number is less than a multiple of the divisor.
Big hint:
Count three-digit numbers of the form .
Video solution:
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Written solution:
Each required remainder is less than its divisor, so must be divisible by and . Hence is a multiple of
For a three-digit , we have . The multiples of in this interval are , giving possible integers.
Thus, E is the correct answer.
Problem 21 in other years
- 1985 AMC 8
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