Maths Olympiad Prep

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, 2015

Number theory Difficulty 5.0 AIME, harder Find the answer United Kingdom

Five positive integers (not necessarily all different) are written on five cards. Boris calculates the sum of the numbers on every pair of cards. He obtains only three different totals: 5757, 7070 and 8383. What is the largest integer on any card?

(A) 3535 (B) 4242 (C) 4848 (D) 5353 (E) 8282

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