Question

4 distinct integers p, q, r and s are chosen from the set {1,2,3,…,16,17}. The minimum possible value of p/q+r/s can be written as a/b, where a and b are positive, coprime integers. What is the value of a+b?

Answer 1

we want two fractions with the smallest possible numerators and the largest possible denominators

let's try
1/17 + 2/16 = 25/36 = appr.1838..
or
1/16 + 2/17 = 49/272 = appr .18014 which is smaller than above

so a/b = 49/272 and the value of
a+b = 321