2018 AMC 8 Problem 7
Attempt Problem 7 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).
7.
The -digit number is divisible by What is the remainder when this number is divided by
Answer: B
Small hint:
Use the divisibility-by- rule to determine .
Big hint:
Once is known, only the last three digits matter for the remainder modulo .
Video solution:
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Written solution:
Notice that a number is divisible by if and only if the sum of its digits is also divisible by
The sum of the digits of the -digit number in the problem is: As is divisible by must also be divisible by Also, as is a digit, we know that This means that can only be
Now we know that the -digit number in question is and we want to find the remainder when we divide by To solve this, simply use long division to see that Therefore, the remainder is
Thus, the correct answer is B.
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
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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