AMC 10A 2021 Spring Problem 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}.\bar{\underline{a} \ \underline{b}},

where a and b are digits, he did not notice the notation and just multiplied 66 times 1 . a b. Later he found that his answer is 0.5 less than the correct answer. What is the 2-digit integer \underline{a} \ \underline{b}?

Answer Choices
A. 15
B. 30
C. 45
D. 60
E. 75