In the xy-plane above, is angle QPR a right angle? (1) Line segment P

Official Explanation

We're asked whether angle QPR is a right angle, a 90-degree angle. It looks like one, but that doesn't matter. If there is not a little box symbol in the corner of the angle QPR, then it's a right angle only if we can infer as much from other information. Note, however, that we are told that the angle exists in an "xy plane." We can conclude from that statement that the x-axis and the­ y-axis are perpendicular--that the angle between them is a right angle. We immediately recall having ever seen a question in which the coordinate plane was not regular in that way; a question could present you with that, but it would be very careful to let you know that the coordinate plane was irregular. These conventions can seem a bit arbitrary, but there aren't too many of them, so with a little practice, you won't risk misunderstanding the testmaker's language.

On to the statements, which, you guessed it, we will evaluate separately first. Statement (1) gives a good piece of information--it's saying that the vertical line of the triangle is parallel to the y-axis, as it appears to be. But we still don't know whether the angle QPR is a right angle, because, for all we know, the horizontal line might be a degree or two tilted away from flat. So the first statement is insufficient. The second statement is insufficient by the same logic. If we combine the statements, we know that the two sides of the triangle are parallel to the coordinate axes, so they are perpendicular to each other, so they form a right angle.

The correct answer is (C).