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Number theory Difficulty 2.0 Junior Find the answer United Kingdom

Four cousins Alan, Bob, Carl and Dan are 3, 8, 12 and 14 years old, although not necessarily in that order. Alan is younger than Carl. The sum of the ages of Alan and Dan is divisible by 5. The sum of the ages of Carl and Dan is divisible by 5. What is the sum of the ages of Alan and Bob?

(A) $26$ (B) $22$ (C) $17$ (D) $15$ (E) $11$

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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.