1985 AMC 8 Problem 1

Attempt Problem 1 of the 1985 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 1985 AMC 8 solutions, or check the answer key.

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

1.

What is the value of the following product?
3×59×11×7×9×113×5×7\dfrac{3 \times 5}{9 \times 11} \times \dfrac{7 \times 9 \times 11}{3 \times 5 \times 7}
11
00
4949
149\dfrac{1}{49}
5050
Answer: A
Concepts:fraction
Small hint:
Multiply the numerators together and the denominators together before simplifying
Big hint:
The same factors 3,3, 5,5, 7,7, 9,9, 1111 appear in both the numerator and the denominator
Solution:
Combining the two fractions, the numerator is 3⋅5⋅7⋅9⋅113 \cdot 5 \cdot 7 \cdot 9 \cdot 11 and the denominator is 9⋅11⋅3⋅5⋅7.9 \cdot 11 \cdot 3 \cdot 5 \cdot 7. These are the same product.
So the value is 1.1.
Thus, the correct answer is A .
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