1960 AMC 12 Problem 8

Attempt Problem 8 of the 1960 AMC 12 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 1960 AMC 12 solutions, or check the answer key.

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

8.

The number 2.5252525…2.5252525\ldots can be written as a fraction. When reduced to lowest terms the sum of the numerator and denominator of this fraction is:
77
2929
141141
349349
none of these
Answer: D
Concepts:repeating decimalfractiongreatest common divisor
Small hint:
Write the repeating part 0.525252…0.525252\ldots using a denominator of 9999
Big hint:
Add the integer part and then reduce the fraction
Solution:
We have 2.525252…=2+5299=25099. 2.525252\ldots=2+\frac{52}{99}=\frac{250}{99}. This fraction is already in lowest terms, and 250+99=349.250+99=349.
Therefore, the correct answer is D.
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