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MathNet 2019-part-06 — 184 problems (EN–VI) Question 102

Math Olympiad Vault · MathNet 2019-part-06 — 184 problems (EN–VI)

Question 102

David thought of a three-digit natural number with three different digits. He replaced each digit of this number by a letter and obtained the word $E N A$, which represents his number. He noticed that his number satisfies $c \cdot E N A = 2331$, where $c$ is some natural number. What is the value of the number $c$?

(A) 3
(B) 7
(C) 9
(D) 21
(E) 37