# GMAT Quantitative Practice, Data Sufficiency

*Question 2*

In the above figure, does *x* equal *z* ?

(1)

w+y= 180(2) l

_{1}∥ l_{2}

- 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

First consider statement (1) alone. Angles *w* and *z* are supplementary (they form a straight line), and so the sum of their degree measures is 180. Consider this fact along with statement (1):

By simple substitution,w+z= 180

w+y= 180 (statement 1)

*y*=

*z*. Now, vertical angles

*x*and

*y*are by definition congruent (equal in size). Accordingly,

*x*=

*y*. Given that

*y*=

*z*, by substitution

*x*=

*z*. Statement (1) alone suffices to answer the question.

Next, consider statement (2) alone. Given that l_{1} and l_{2} are parallel, corresponding angles formed by the transversal are congruent (equal in size). Accordingly, *y* = *z*. Since *y* = *x* (they are vertical angles), by substitution *x* = *z*. Statement (2) alone suffices to answer the question. The correct response is (D).