P = { 3, 6, 9, 12..........3n}
Q = { 5, 10, 15, 20......5m}
Sum of a series of elements in P = R=n/2 [a + l ] where a = first term and l = last term
Sum of series of elements in Q = S=m/2 [ a + l ]
R = n/2[ 3 + 3n ]; R is dependent on the value of n
Q = m/2[ 5 + 5m ]; S is dependent on the value of m
Question => is R - S = odd number?
Statement 1 => m is odd and n is even
If m = 3, then s = 3/2 [5+(5*3)] = 30 = even
But if m = 1 then s = 1/2[5 + 5] = 5 = odd
If n = 4 then R = 4/2 [3 +(3*4)] = 30 = even
If n = 2 then R = 2/2 [3 +(3*2)] = 9 = odd
Therefore, R - S results can either even or odd, statement 1 is NOT SUFFICIENT

Statement 2 => m = 4x + 3 and n = 2x this means m = (multiple of 4) + (odd number)
m = even + odd = odd number
n = multiple of 2 which will always be even
Therefore, m = odd and n = even; this is the same thing as information in statement 1. Hence statement 2 is NOT SUFFICIENT
Combining both statements together =>
Both statements contain the same information, m = odd and n = even, and from the test data in statement 1, it cannot be determined if R - S is even or odd. Hence, both statement together are NOT SUFFICIENT
Answer = C