2004 AMC 8 Problem 19
Attempt Problem 19 of the 2004 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 2004 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
A whole number larger than leaves a remainder of when divided by each of the numbers and The smallest such number lies between which two numbers?
and
and
and
and
and
Answer: B
Small hint:
If the number leaves remainder subtract
Big hint:
The result must be divisible by and
Solution:
Let be the number. Then is divisible by and
The least common multiple of these numbers is which makes
Thus, B is the correct answer.
Problem 19 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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- 1991 AMC 8
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