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Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Two of the following four facts about a positive integer $N$ are true and two are false.

$N$ is divisible by 5
$N$ is divisible by 11
$N$ is divisible by 55
$N$ is less than 10

What is the value of $N$ ?

(A) $5$ (B) $10$ (C) $11$ (D) $55$ (E) $110$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.