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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectAttachment:
PQR.png
In the xy-plane above, is angle QPR a right angle?
(1) Points P and Q have the same x-coordinate.
(2) Points P and R have the same y-coordinate.
Solution:
We are given a triangle in the coordinate plane, and we must determine whether angle QPR is a right angle. Remember that a right angle measures 90 degrees.
Statement One Alone:Points P and Q have the same x-coordinate.
Statement one alone is not enough to determine whether angle QPR is a right angle. We can draw some diagrams to illustrate:
We see in the diagram above that points P and Q have the same x-coordinate; however, angle QPR
is not a right angle.
We see in the diagram above that points P and Q have the same x-coordinate, and angle QPR
is a right angle.
Statement one is insufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:Points P and R have the same y-coordinate.
Again, let's draw some diagrams to illustrate:
We see in the diagram above that points P and R have the same y-coordinate; however, angle QPR
is not a right angle.
We see in the diagram above that points P and R have the same y-coordinate, and angle QPR
is a right angle.
Statement two is insufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:From statements one and two together we know that points P and R have the same y-coordinate and points P and Q have the same x-coordinate. Thus, PR must be parallel to the x axis and QP must be parallel to the y axis and angle QPR
must be a right angle.
The answer is C.