if a and b are positive integers , what is the value of a+b ?

a) a/b = 5/8

b) the greatest common divisor of a and b is 1.

From a) we know the ratio of a:b is 5:8 but we don't know if it is 5+8=13 or possibly 20+36=56

From b we find that a and b share no prime factors but don't know anything about the two numbers.

Combining the two statements we know the ratio and that they share no prime factors, therefore a must equal 5 and b must equal 8 because multiplying the ratio by any number would provide a common divisor greater than 1.