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Difficulty:   75% (hard)

Question Stats: 56% (02:10) correct 44% (02:08) wrong based on 852 sessions

HideShow timer Statistics In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR ?

(1) The measure of angle QPR is 30°.
(2) The sum of the measures of angles PQR and PRQ is 150°.

Attachment: Angles.JPG [ 67.58 KiB | Viewed 10452 times ]

Attachment: TriangleQPS.JPG [ 2.39 KiB | Viewed 12080 times ]

Originally posted by Sylvan on 26 Sep 2010, 02:40.
Last edited by Bunuel on 27 Nov 2018, 01:55, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
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In the figure shown, the measure of angle PRS is how many degrees grea  [#permalink]

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16 In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR.

Question: $$\angle PRS - \angle PQR=?$$

(1) The measure of angle QPR is 30°.

$$\angle QPR=30°$$;
In triangle QPR three angles sum $$= 180° = \angle QPR+\angle PQR +\angle PRQ$$;
$$180°=30°+\angle PQR+(180°-\angle PRS)$$;
$$30° = \angle PRS-\angle PQR$$. SUFFICIENT.

(2) The sum of the measures of angles PQR and PRQ is 150°.

Basically the same information is given $$\angle PQR + \angle PRQ=150°$$;
$$\angle PQR + 180° - \angle PRS=150°$$;
$$30° = \angle PRS - \angle PQR$$. SUFFICIENT.

Attachment: TriangleQPS.JPG [ 2.5 KiB | Viewed 53816 times ]

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GMAT 1: 760 Q50 V44 Re: In the figure shown, the measure of angle PRS is how many degrees grea  [#permalink]

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This is a hard problem to solve without a pen and a paper. Hope Img makes it clear.
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File comment: Img should help Angles.jpg [ 77.72 KiB | Viewed 35649 times ]

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Re: In the figure shown, the measure of angle PRS is how many degrees grea  [#permalink]

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grafical solution is always easier.
Attachments grafik.JPG [ 9.73 KiB | Viewed 12615 times ]

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Re: In the figure shown, the measure of angle PRS is how many degrees grea  [#permalink]

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1) Angle PRS = QPR + PQR
PRS = 30 + PQR
PRS - PQR = 30 SUFFICIENT
2) PQR + PRQ = 150
PQR + 180-PRS = 150
PRS - PQR = 30 SUFFICIENT

ANS. D
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Re: In the figure shown, the measure of angle PRS is how many degrees grea  [#permalink]

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Hi, there! I'm happy to help with this one. What's tricky about this problem is that there are three different triangles in the diagram, and we have to apply the "180 degree Triangle Theorem" in each one.

First of all, from the diagram, we know in triangle PRS, that (angle SPR) + (angle PRS) + 90 = 180, or in other words, (angle SPR) + (angle PRS) = 90

In triangle PQS, we know that (angle SPQ) + (angle SQR) + 90 = 180, or in other words, (angle SPQ) + (angle PQR) = 90.

Set those two equal:

(angle SPR) + (angle PRS) = (angle SPQ) + (angle PQR)

(angle SPQ) - (angle SPR) = (angle PRS) - (angle PQR)

The question is asking: "the measure of angle PRS is how many degrees greater than the measure of angle PQR?" In other words, they are asking for (angle PRS) - (angle PQR), and our equation above tells us that: if we know (angle SPQ) - (angle SPR), then we know (angle PRS) - (angle PQR).

Statement #1: (angle QPR) = 30 degrees

We know that (angle SPQ) = (angle SPR) + (angle QPR) (big angle equals the sum of the two little angles the comprise it)

Therefore (angle SPQ) = (angle SPR) + 30 --> (angle SPQ) - (angle SPR) = 30 ---> (angle PRS) - (angle PQR) = 30

Statement #1 is sufficient by itself. .

Statement #2: (angle PQR) + (angle PRQ) = 150 degrees

Well, in triangle PQR, we know that: (angle PQR) + (angle PRQ) + (angle QPR) = 180 degrees

If (angle PQR) + (angle PRQ) = 150 degrees, then 150 + (angle QPR) = 180 degrees ---> (angle QPR) = 30, and we have the same information we had in statement #1, so statement #2 is also sufficient by itself.

Answer Choice D. Does that make sense?

Here's another GMAT DS question on the 180 degree Triangle Theorem, just for practice.

https://gmat.magoosh.com/questions/1009

The question at that link should be followed by a video explanation of the answer.

Please let me know if you have any more questions.

Mike Attachments triangle PQS.jpg [ 14.73 KiB | Viewed 37912 times ]

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Re: In the figure shown, the measure of angle PRS is how many degrees grea  [#permalink]

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Bunuel wrote:
In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR.

Attachment:
TriangleQPS.JPG
Q: <PRS-<PQR=?

(1) The measure of angle QPR is 30°. <QPR=30 --> in triangle QPR three angles sum=180=<QPR+<PQR+<PRQ -->180=30+<PQR+(180-<PRS) --> 30=<PRS-<PQR SUFFICIENT

(2) The sum of the measures of angles PQR and PRQ is 150°. Basically the same information is given <PQR+<PRQ=150 --> <PQR+180-<PRS=150 --> 30=<PRS-<PQR SUFFICIENT

Hi, sorry for the stupid question but it is something I can't grasp.

The text when it refers to angles PRS or PGR to which angles is it visually referring to?

I literally can't understand on the chart which are the angles the problem is asking about.

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Re: In the figure shown, the measure of angle PRS is how many degrees grea  [#permalink]

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jzpat wrote:
Bunuel wrote:
In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR.

Attachment:
The attachment TriangleQPS.JPG is no longer available
Q: <PRS-<PQR=?

(1) The measure of angle QPR is 30°. <QPR=30 --> in triangle QPR three angles sum=180=<QPR+<PQR+<PRQ -->180=30+<PQR+(180-<PRS) --> 30=<PRS-<PQR SUFFICIENT

(2) The sum of the measures of angles PQR and PRQ is 150°. Basically the same information is given <PQR+<PRQ=150 --> <PQR+180-<PRS=150 --> 30=<PRS-<PQR SUFFICIENT

Hi, sorry for the stupid question but it is something I can't grasp.

The text when it refers to angles PRS or PGR to which angles is it visually referring to?

I literally can't understand on the chart which are the angles the problem is asking about.

An angle can be identified like this: ∠PQR. The angle symbol, followed by three points that define the angle, with the middle letter being the vertex, and the other two on the legs.

Attachment: Angle.png [ 5.63 KiB | Viewed 36500 times ]
So in the figure above the red angle would be ∠PQR or ∠RQP (so long as the vertex is the middle letter, the order is not important).

Hope it's clear.
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Re: In the figure shown, the measure of angle PRS is how many degrees grea  [#permalink]

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angle PRS = QPR ( 30) + PQR is this exterior angle property?
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Re: In the figure shown, the measure of angle PRS is how many degrees grea  [#permalink]

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fozzzy wrote:
angle PRS = QPR ( 30) + PQR is this exterior angle property?

Yes it is. Angle PRS is an exterior angle of angle PRQ: <PRS = 180 - <PRQ = 180 - (180 - <QPR - <PQR) = <QPR + <PQR
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Re: In the figure shown, the measure of angle PRS is how many degrees grea  [#permalink]

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Hi I used the following method. Turned out to be the quickest for me.

Theorem: An exterior angle of a triangle is equal to the sum of the opposite interior angles.

So, as per the theorem, for Triangle PRQ we have ...
PRS = RPQ + PQR

which gives,

RPQ= PRS - PQR .

Now if we know the measure of RPQ. We are sorted. :D

1) RPQ = 30. SUFFICIENT.

2) same as 1. SUFFICIENT

So D. Director  G
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Re: In the figure shown, the measure of angle PRS is how many degrees grea  [#permalink]

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(1) angle QPR = angle SPQ - angle SPR = 30º

Now in two triangles PQS and PRS one angle is 90 implies that sum of other two angles would also be 90º.

angle SQP + angle SPQ = 90º
angle SPR + angle SRP = 90º

Increase in one of the angles would decrease the other angle by same degree. Therefore, the difference among the angles should be 30º.
So, (1) is SUFFICIENT.

(2) Same explanation as above. So, (2) is SUFFICIENT.

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_________________ Re: In the figure shown, the measure of angle PRS is how many degrees grea   [#permalink] 13 Jun 2019, 02:51
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