If \(a\) and \(b\) are positive integers, what is the greatest common divisor of \(a\) and \(b?\)

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If \(a\) and \(b\) are positive integers, what is the greatest common divisor of \(a\) and \(b?\)

(1) \(a+3b=61\)

(2) \(5a-b=1\)

Answer: D

Source: GMAT Club Tests