AMC 12A 2021 Spring Problem 5

When a student multiplied the number 66 by the repeating decimal,

\text { 1. } \underline{a b a b}=1 . \overline{A B}

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

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