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MathNet 2016-part-02 — 184 problems (EN–VI) Question 93

Math Olympiad Vault · MathNet 2016-part-02 — 184 problems (EN–VI)

Question 93

An ancient text states that Methuselah lived $150\ast$ years, where the symbol $\ast$ replaces the units digit, which scholars are unable to read. Fortunately we have 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 multiple of 3 years, the third that he lived a multiple of 5 years. Knowing that exactly one of these three manuscripts contains false information, how many different digits could be hiding behind the symbol $\ast$?

(A) None
(B) One
(C) Two
(D) Three
(E) Four