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Problem 685

AMC 10/12, early questions

Combinatorics Difficulty 3.0 Find the answer UKMT Junior Mathematical Challenge · United Kingdom · 2021

I choose four different integers. When I add all the pairs of these numbers in turn, the totals that I obtain are 23, 26, 29, 32 and 35, with one of these totals being repeated. What is the largest of the four integers?

(A) $18$ (B) $19$ (C) $20$ (D) $21$ (E) $22$

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