Answer: B. B is correct, and the point of the question is to notice what the data does NOT fix. Rearranging log S = log C + Z log A gives Z = (log S − log C)/log A. With log 500 = 2.699 over log 10000 = 4, Z_X = (2.699 − log C)/4. With log 200 = 2.301 over log 1000 = 3, Z_Y = (2.301 − log C)/3. Subtracting: Z_Y − Z_X = [4(2.301 − log C) − 3(2.699 − log C)]/12 = (1.107 − log C)/12. So the sign of the difference depends entirely on log C. If log C < 1.107, meaning C < 12.8, then Z_Y is larger; if C > 12.8, Z_X is larger; and at C = 12.8 exactly they are equal. Knowing only that the two regions SHARE a value of C does not tell you what that value is, so no comparison can be made. Being told two quantities are equal is not the same as being told what they equal.
Why A is wrong: A is wrong not because Region X definitely has the smaller Z, but because it cannot be established either way. Region X does have the higher Z whenever C > 12.8, which the data neither rules in nor out.
Why C is wrong: C is wrong because the two regions have equal Z only in the single special case C = 12.8. For every other value of C the two Z values differ, so equality is not the general answer.
Why D is wrong: D is wrong for the same reason as A: Region Y has the higher Z only when C < 12.8. That happens to cover the small values of C typical of real species-area data, but the question supplies no value of C, so it remains an assumption rather than a result.