GRE Quantitative Practice, Quantitative Comparison
You don't need to calculate any averages to make the comparison. Instead, think about what occurs as the value of m increases from zero (0): the sum (and hence the average) of the terms in Distribution A increases more than the sum (and average) of the terms in Distribution B. If m = 0, Quantity A = 0 while Quantity B is clearly greater than 0. But increase the value of m to just 2, and the inequality reverses. Since the relationship between the two quantities varies with m, the correct answer must be (D).