Hi..
Not a 700 level Q. ~ 600
It has statement I, which does not mean anything to Q as no value of variables given and can be eliminated without any thinking..

We know the formula as axb, which is poorly written and must be meaning a*b, or a^b and we just require value of variables p and q..
Statement II gives the value as 2 and 2..
With2 as values 2*2 or 2^2 would both be 4. So here it does not matter what # means '*' or '^'
Sufficient
B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

In Statement 2, subsituting 2 for the values of P and Q both gives the value 4. ie 2^2 or 2x2 and hence we get a answer ie B