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Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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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.

Re: In the xy-plane above, is angle QPR a right angle? [#permalink]

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06 Aug 2012, 08:39

1

This post received KUDOS

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
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Re: In the xy-plane above, is angle QPR a right angle? [#permalink]

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20 May 2014, 11:09

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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.

Re: In the xy-plane above, is angle QPR a right angle? [#permalink]

Show Tags

20 Jun 2015, 15:01

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.
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Re: In the xy-plane above, is angle QPR a right angle? [#permalink]

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11 Sep 2015, 00:50

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

Re: In the xy-plane above, is angle QPR a right angle? [#permalink]

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19 Sep 2015, 01:29

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.
_________________

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.
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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.]

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.
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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