UPSC 2016 CDS I Math Paper

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
It is given that ab leaves the remainder 1 when divided by 15.
∴(ab−1) is divisible by 15
So, the possible pairs (a, b) are (2, 8), (8, 2), (7, 13) and (13, 7).
Thus, the possible number of pairs (a, b) is 4.