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Repeating decimal denominator

Source: 2014-2015 SDML Middle School 1a Problem 10

August 28, 2016

Problem Statement

Suppose aa and bb are digits which are not both nine and not both zero. If the repeating decimal .AB‾.\overline{AB} is expressed as a fraction in lowest terms, how many possible denominators are there?
(A) 2(B) 3(C) 4(D) 5(E) 6\text{(A) }2\qquad\text{(B) }3\qquad\text{(C) }4\qquad\text{(D) }5\qquad\text{(E) }6
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