In the xy-plane above, is angle QPR a right angle? : GMAT Data Sufficiency (DS)
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# In the xy-plane above, is angle QPR a right angle?

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

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06 Aug 2012, 02:05
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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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PQR.png [ 6.44 KiB | Viewed 13434 times ]
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.

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

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06 Aug 2012, 02:06
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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.

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

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20 May 2014, 10:09
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Re: In the xy-plane above, is angle QPR a right angle? [#permalink]

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06 Aug 2012, 06:53
Choice C. Given same axis i could visualize it as a right angled one.
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Re: In the xy-plane above, is angle QPR a right angle? [#permalink]

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06 Aug 2012, 07:39
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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10 Aug 2012, 03:24
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.

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

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20 Jun 2015, 14:01
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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

1+2 gives the ans
hence C
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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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Re: In the xy-plane above, is angle QPR a right angle? [#permalink]

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08 May 2016, 06:01
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
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Re: In the xy-plane above, is angle QPR a right angle? [#permalink]

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14 May 2016, 05:51
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Attachment:
PQR.png
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.

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

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22 Jul 2016, 11:22
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Attachment:
PQR.png
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.

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Re: In the xy-plane above, is angle QPR a right angle?   [#permalink] 22 Jul 2016, 11:22
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