1998 AMC 8 Problem 22
Attempt Problem 22 of the 1998 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 1998 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
Terri produces a sequence of positive integers by following three rules. She starts with a positive integer, then applies the appropriate rule to the result, and continues in this fashion.
Rule If the integer is less than multiply it by
Rule If the integer is even and greater than divide it by
Rule If the integer is odd and greater than subtract from it.
For example, consider the sample sequence
Find the th term of the sequence that begins
Answer: D
Small hint:
Generate terms until a value repeats.
Big hint:
After the repeat begins, reduce the index modulo the cycle length.
Solution:
The sequence begins
After the first three terms, the cycle repeats. Since is a multiple of the th term is the fifth term of the cycle,
Thus, the correct answer is D .
Problem 22 in other years
- 1985 AMC 8
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