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GMAT Quantitative Practice, Data Sufficiency

Question 2

transversal

In the above figure, does x equal z ?

(1)  w + y = 180

(2)  l1 l2

  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

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):

w + z = 180
w + y = 180 (statement 1)
By simple substitution, 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 l1 and l2 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).