2017 AMC 8 Problem 7
Attempt Problem 7 of the 2017 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 2017 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
7.
Let be a -digit positive integer, such as whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must be a factor of
Answer: A
Small hint:
Let be the three-digit block that is repeated. Express in terms of .
Big hint:
Factor .
Video solution:
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Written solution:
Let be the three-digit number formed by either repeated block. Then Therefore, must be a factor of
Thus, A is the correct answer.
Problem 7 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
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