# 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 ofxandy.(2) The arithmetic mean of

x,yand –1 is 1.

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

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