In the xy-plane above, is angle QPR a right angle?

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.
_________________

SOLUTION



In the xy-plane above, is angle QPR a right angle?

(1) Points P and Q have the same x-coordinate. Since P and Q have the same x-coordinate, then line segment PQ is vertical. Not sufficient. (Line segment PR can be at any angle to line segment PQ).

(2) Points P and R have the same y-coordinate. Since P and R have the same y-coordinate, then line segment PR is horizontal. Not sufficient.

(1)+(2) PQ is vertical and PR is horizontal. Therefore angle QPR must be a right angle. Sufficient.

Answer: C.
_________________

St 1: insufficient: PQ is parallel to Y axis
St 2: insufficient: PR is parallel to X axis

1 + 2 : Sufficient PQ perpendicular to PR
IMO C

Statement 1 tells us that PQ is vertical line ll to Y axix
Statement 2 tells us that PR is horizontal line ll to X axis
X axis is perpendicular to Y axis

1+2 gives the ans
hence C

A. Insufficient. Since, we do not know whether the line is parallel to x axis
B. Insufficient. Since, we do not know whether the line is parallel to y axis.

Together the two statements give the answer. C.
_________________

Why C?
I understand PQ = horizontal same x coordinate
but PR can be 2,3 & 3,3 no & PQ can still be Q = 8,3 & P = 2,3

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.
_________________

This is one of the several examples where the figure is drawn to scale but we cannot make any assumptions about the angles.
Statement 1) Gives no information about R...........Insufficient
Statement 2) Gives no information about Q...........Insufficient

Together we know that PQR is a right angled triangle.

Are we supposed to assume that the points Q, P, and R are distinct?
If no, then QPR can be a zero-degree angle

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.
_________________

A.Insufficient. Since, we do not know the y axis point they can form any angle
B. Insufficient. Since, we do not know the x axis point they can form any angle
a+b is Sufficient

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________