1997 AMC 8 Problem 19
Attempt Problem 19 of the 1997 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 1997 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
If the product what is the sum of and
Answer: D
Small hint:
After cancellation, only the first denominator and last numerator remain
Big hint:
The product telescopes
Solution:
Note that the numerator of each fraction cancels with the denominator of the fraction to its right.
We can then cancel out all these terms to get a final equation of
The desired sum is then
Thus, D is the correct answer.
Problem 19 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
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