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GRE Quantitative Practice, Quantitative Comparison

Question 1

Distribution A: {m, 2m, 3m}
Distribution B: {m, m + 2, m + 3}

Quantity A

The arithmetic mean
(simple average)
of Distribution A

Quantity B

The arithmetic mean
(simple average)
of Distribution B

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

Explanatory Answer

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).