2. An ancient text states that Methuselah lived 150 years, where the symbol replaces the unit digit, which scholars cannot read. Fortunately, we possess three other manuscripts about the life of Methuselah; the first claims that he lived an even number of years, the second that he lived a number of years that is a multiple of 3, the third that he lived a number of years that is a multiple of 5. Knowing that exactly one of these three manuscripts contains false information, how many different digits could be behind the symbol?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
2. The answer is (B). There are three possible cases to analyze:

(a) 150 is a multiple of 2 and 3, but not of 5;

(b) 150 is a multiple of 2 and 5, but not of 3;

(c) 150 is a multiple of 3 and 5, but not of 2.

First, we notice that 1500 is a multiple of $2 \cdot 3 \cdot 5=30$, and there are no other multiples of 10 or 15 between 1500 and 1509. The last two cases are therefore excluded. The only multiple of 6 that is not also a multiple of 5 among the 10 possible values is 1506, so only the first of the three cases can be correct, and there is only one possible choice for the missing digit.