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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.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

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.

WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)

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

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06 Aug 2012, 07:39

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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Regards SD ----------------------------- Press Kudos if you like my post. Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

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

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10 Sep 2015, 23:50

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, 00:29

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.
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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. (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

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

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05 Jul 2017, 11:19

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.
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Kudosity killed the cat but your kudos can save it.

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.
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