Competition problem — Number theory

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Number theory Difficulty 5.2 AIME, harder Find the answer

4. Which of the following integers are divisible by 11
a) 10763732
c) 674310976375
b) 1086320015
d) $8924310064537 ?$

This was a multiple-choice question, but the options didn't survive into the source we have. The answer given is b, and the solution below works it through.

Solution

4. a) no
b) yes
c) no
d) no

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.