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 theĀ 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).
If you believe you have found an error in this question or explanation, please contact us and include the question title or URL in your message.