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Algebra Difficulty 2.0 Junior Find the answer United Kingdom

The sum of the squares of three consecutive positive integers is 770. What is the largest of these integers?

(A) $15$ (B) $16$ (C) $17$ (D) $18$ (E) $19$

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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.