2016 AMC 8 Problem 5
Attempt Problem 5 of the 2016 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 2016 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
5.
The number is a two-digit number with the following properties:
- When is divided by the remainder is
- When is divided by the remainder is
What is the remainder when is divided by
Answer: E
Small hint:
The remainder when divided by tells you the units digit of .
Big hint:
List the two-digit numbers ending in and test the condition modulo .
Video solution:
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Written solution:
The second condition says that ends in , so the possibilities are Of these, only leaves remainder when divided by , because its digit sum is . Finally, , so the requested remainder is .
Thus, E is the correct answer.
Problem 5 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
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
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- 1998 AMC 8
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