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Sample Question 8:
When a student multiplied the number \(66\) by the repeating decimal, \(\underline{1}.\underline{a} \ \underline{b} \ \underline{a} \ \underline{b}\ldots=\underline{1}.\overline{\underline{a} \ \underline{b}},\) where \(a\) and \(b\) are digits, he did not notice the notation and just multiplied \(66\) times \(\underline{1}.\underline{a} \ \underline{b}.\) Later he found that his answer is \(0.5\) less than the correct answer. What is the \(2\)-digit number \(\underline{a} \ \underline{b}?\)
\(\textbf{(A) }15 \qquad \textbf{(B) }30 \qquad \textbf{(C) }45 \qquad \textbf{(D) }60 \qquad \textbf{(E) }75\)