1993 AMC 8 Problem 2

Attempt Problem 2 of the 1993 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 1993 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

2.

When the fraction 4984\dfrac{49}{84} is expressed in simplest form, then the sum of the numerator and the denominator will be
1111
1717
1919
3333
133133
Answer: C
Concepts:fractiongreatest common divisor
Small hint:
Find the greatest common factor of 4949 and 8484
Big hint:
49=7249 = 7^2 and 84=7×12,84 = 7 \times 12, so divide both by 77
Solution:
Since 49=7×749 = 7 \times 7 and 84=7×12,84 = 7 \times 12, the fraction reduces to 712.\dfrac{7}{12}.
The sum of numerator and denominator is 7+12=19.7 + 12 = 19.
Thus, the correct answer is C .
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