withme wrote:

Is a-3b an even number?

1). b=3a+3

2). b-a is an odd number

(1) a-3b=a-3(3a+3)= -8a-9 which may be even, odd, integer, non-integer, rational, irrational... NOTE THAT WE ARE NOT TOLD ABOUT THE PROPERTIES OF a. NOT SUFF

(2) b=(2k+1)+a where k is an integer

a-3b= a-3((2k+1)+a)= -2a -6k-3 NOT SUFF for the same reason

Together we see that -8a-9=-2a-6k-3 for some integer k

-6a=-6k+6=-6(k+1) => a=k+1

Thus a is an integer, either odd or even

(2) tells us that b is also an integer and that exactly one of {a,b} is even

If a is even and b is odd, a-3b is odd

If b is even and a is odd a-3b is odd

(1) and (2) combined tell us that a-3b is an odd number, not an even one

SUFF

Answer: C