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MathNet 2017-part-03 — 176 problems (EN–VI) Question 151

Math Olympiad Vault · MathNet 2017-part-03 — 176 problems (EN–VI)

Question 151

Let $n$ be a positive integer such that the decimal representation of $2^{n}$ begins with the digit 7 (that is, its leftmost nonzero digit is 7). With which digit does the decimal representation of $5^{n}$ begin?

(A) 1
(B) 2
(C) 5
(D) 7
(E) It depends on $n$