UPSC 2015 CDS I Math Paper

Sum of the digits of the number 357P25Q = 22 + P + Q
A number is divisible by 3 if the sum of the digits of the number isdivisible by 3 and a number is divisible by 5 if its unit’s digit iseither 0 or 5.
When Q = 0, then the sum of the digits is 22 + P. (22 + P) is divisible by 3 if P = 2 or P = 5 or P = 8.
When Q = 5, then the sum of the digits is 27 + P. (27 + P) is divisible
by 3 if P = 0 or P = 3 or P = 6 or P = 9.
So, the possible pairs of (P, Q) are (2, 0), (5, 0), (8, 0), (0, 5), (3, 5), (6, 5) and (9, 5).
Thus, the numbers of possible pairs of (P, Q) are 7.