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

Attachment:

TriangleQPS.JPG [ 2.5 KiB | Viewed 31308 times ]

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

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.

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)

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.

To determine the difference between PQR and PRS, we need some sort of equation between them.

1. QPR=30, which means 180-(PQR+PRQ)=30, which give PQR+PRQ=150. Now PQR+(180-PRQ)=150. This gives us the difference. Suff 2. PQR + PRQ = 150. Same solution as above. Suff.

D
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DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

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

Answer: D.

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.

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

Answer: D.

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.

Thanks for your help.

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 18953 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).

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

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06 May 2014, 11:34

Will also work just fine if we say that RPS is X and QPR is y. We then are asked to find PRS - PQR. PRS is 90-x while pqr is 90 - (x+y). Therefore, translating algebraically, we will need the value of 'y' to solve.

Statement 1, we are directly given the value of y=30. Statement 2, 180 - (PQR+PRQ=150)=30=y.

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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