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# In the figure shown, the measure of angle PRS is how many degrees grea

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Manager
Joined: 17 Jan 2006
Posts: 92
In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

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30 May 2006, 17:22
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55% (hard)

Question Stats:

65% (01:56) correct 35% (01:48) wrong based on 110 sessions

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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°.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-attached-measure-of-angle-prs-is-how-many-102829.html
[Reveal] Spoiler: OA

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VP
Joined: 21 Sep 2003
Posts: 1057
Location: USA
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

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30 May 2006, 17:40
D?

Let x = angle PRS, y = angle PQS.

1. Angle QPR = 30
Angle QPR = Angle QPS - Angle RPS
Angle RPS = 90-x
Angle QPS = 90-y

30 = QPR = (90-y) - (90-x) = x-y SUFF.

2. Angle PRQ + Angle PRQ = 150
Which is same as saying angle QPR = 30. (same as condition #1). SUFF too!
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Joined: 29 Dec 2005
Posts: 1341
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

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30 May 2006, 19:15
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dinesh8 wrote:
see attchment

should be D.
from i, prs = pqr+qpr
prs = pqr+ 30
prs - pqr = 30. so suff...

from ii, pqr+prq = 150, then qpr = 30. also suff..
Manager
Joined: 10 May 2006
Posts: 186
Location: USA
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

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31 May 2006, 09:33
Agree with D

PRS = x, PQS = y. What is x-y?

1) QPR = 30

Then looking at the larger triangle PQS, add up all the angles.
180 = 90+ PQS + QPS
90 = y + 30 + RPS
60-y = RPS

Then look at the small triangle PRS
180 = 90+x+60-y
30 = x-y Sufficient

2) PRQ + PQR = 150

Y + PRQ = 150 so PRQ = 150-y.
We know that PRQ + x = 180. Substitute in PRQ

150 -y +x = 180 Therefore x-y = 30. Sufficient
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Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

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31 May 2006, 10:19
Must be D.

Let PQR = y
PRS = x
PRQ = a

We have x +a = 180......(Eq 1)

St1 : QPR = 30 that means y+a+30 =180..... (Eq 2)
Solving eq 1 and eq 2 we get x-y = 30 SUFF

St2: y+a = 150.. This statement is same as statement 1, equation 2. So this is also SUFF
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Manager
Joined: 11 Oct 2005
Posts: 94
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

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07 Jun 2006, 08:41
I agree with the explanations!!! You guys rock!
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15939
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

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04 Jun 2015, 00:24
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).

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Posts: 39626
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

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04 Jun 2015, 03:06
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In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR.

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-attached-measure-of-angle-prs-is-how-many-102829.html
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Re: In the figure shown, the measure of angle PRS is how many degrees grea   [#permalink] 04 Jun 2015, 03:06
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