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GMAT Quantitative Practice, Data Sufficiency

Question 3

What is the average (arithmetic mean) of x and y ?

(1)  The arithmetic mean of (x + 1) and (y – 1) is equal to the arithmetic mean of x and y.

(2)  The arithmetic mean of x, y and –1 is 1.

  1. Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is NOT sufficient.
  2. Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is NOT sufficient.
  3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
  4. Each statement ALONE is sufficient to answer the question.
  5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question.

Explanatory Answer

Statement (1) is true of any two numbers x and y because (x + 1) + (y – 1) = x + y. Thus, Statement (1) alone is insufficient to answer the question.

Statement (2) alone suffices to answer the question. The statement provides the average of the three terms x, y and –1, and so you can set up an equation using the arithmetic mean formula, and then solve it for 1/2(x + y). Although you don't need to actually solve the equation, here's how to do it:

equation system

The correct response is (B). (The arithmetic mean of x and y is 2.)