1996 AMC 8 Problem 9

Attempt Problem 9 of the 1996 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 1996 AMC 8 solutions, or check the answer key.

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

9.

If 55 times a number is 2,2, then 100100 times the reciprocal of the number is
2.52.5
4040
5050
250250
500500
Answer: D
Concepts:linear equationfraction
Small hint:
The number satisfies 5n=2,5n = 2, so n=25n = \dfrac{2}{5}
Big hint:
The reciprocal of 25\dfrac{2}{5} is 52;\dfrac{5}{2}; multiply it by 100100
Solution:
The number is 25,\dfrac{2}{5}, whose reciprocal is 52.\dfrac{5}{2}.
Then 100⋅52=250.100 \cdot \dfrac{5}{2} = 250.
Thus, the correct answer is D .
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