Last Updated on May 6, 2023

GMAT OFFICIAL GUIDE DS

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.

Answer: C