It is currently 17 Mar 2018, 19:23

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
Intern
Joined: 06 Oct 2009
Posts: 6
In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

06 Oct 2009, 12:15
1
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

18% (01:11) correct 82% (02:04) wrong based on 19 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°.

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/in-the-figure ... 02829.html
[Reveal] Spoiler: OA

Attachments

TriangleQPS.JPG [ 2.5 KiB | Viewed 2864 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 44290
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

06 Oct 2009, 12:51
1
KUDOS
Expert's post
flehnen wrote:
Hello, I am trying to understand the answer on this question. Any help would be great!!
Added a file with the question and drawing.
Attachment:
triangle.pdf

Hope you can see it. It is apparently there.
thanks,

Q: <PRS-<PQR=?

(1) <QPR=30 --> in triangle QPR three angles sum=180=<QPR+<PQR+<PRQ -->180=30+<PQR+(180-<PRS) --> 30=<PRS-<PQR SUFFICIENT

(2) Basically the same information is given <PQR+<PRQ=150 --> <PQR+180-<PRS=150 --> 30=<PRS-<PQR SUFFICIENT

D.

OR:

(1) <QPR=30 --> an exterior angle of a triangle is equal to the sum of the opposite interior angles --> <PRS =<QPR + <PQR --> <PRS - <PQR = <QPR = 30. Sufficient.

Hope it helps.
_________________
Intern
Joined: 06 Oct 2009
Posts: 6
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

06 Oct 2009, 13:14
Got you! makes it obvious now.
thanks,
Senior Manager
Joined: 30 Nov 2008
Posts: 482
Schools: Fuqua
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

07 Oct 2009, 13:40
1
KUDOS
Another solution -

Let LPRS = x and LPQR = y. Question is asking to find what is the difference between LPRS and LPQR.

IN triable PQR, LQPR and LPQR are the interior angles, LPRS is the exterior angle opposite to LQPR and LPQR. There is a rule that Exterior angle of a triangle = sum of the opposite interiod angles.

==> LPRS = LPQR + LQPR. ==> x = y + LQPR ==> x - y = LQPR. So if we know the angle of LQPR, we can solve the question.

Clue 1 = Given LQPR = 30. This is eactly what we need to solve the question. So sufficient.

Clue 2 = LPQR + LPRQ = 150 ==> From this we can deduce that LQPR= 30(since sum of all the interior angles is 180. Again we know LQPR and hence is sufficient to solve the question.

So Ans D.
VP
Joined: 05 Mar 2008
Posts: 1439
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

14 May 2010, 10:58
vannbj wrote:
I see how you can use both to get the answer but I don't get how you can use either one. Can someone help me out?

I dislike using the three letters to represent an angle. I prefer single variables.
Facts:
PRS = x
PQR = y
PRQ = z

z + x = 180
x + y + z = 180

We want to know the value of x-y

1. QPR = 30 degrees
If QPR = 30 then y + z = 150 (180-30)

y + z = 150
z + x = 180

z = 150 -y
substitute
150-y+x = 180
-y + x = 30
x - y = 30 so sufficient

2. statement two is saying y + z = 150 and that's the same equation we calculated on step 2 so sufficient
Manager
Joined: 16 Feb 2010
Posts: 167
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

15 May 2010, 09:21
great explanation Bunuel ....... Kudos
Manager
Joined: 23 Sep 2009
Posts: 144
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

18 Sep 2010, 13:38
Cn some one explain how the answer is D?
Attachment:

Angles.JPG [ 73.42 KiB | Viewed 2369 times ]

_________________

Thanks,
VP

Retired Moderator
Joined: 02 Sep 2010
Posts: 779
Location: London
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

18 Sep 2010, 16:05
vigneshpandi wrote:
Cn some one explain how the answer is D?
Attachment:
Angles.JPG

Note that PRS+SPR=PQS+SPQ
So PRS-PQS=SPQ-SPR=QPR

1) Clearly sufficient, since it tells us what QPR is

2) QPR = 180 - (PQR + PRQ), so again we know QPR. Sufficient to find out out PRS-PQS

Hence answer is (d), either statement alone is sufficient
_________________
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 400
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

18 Sep 2010, 16:11
1
KUDOS
Known angle QSP = 90 degree. We need to find difference between angle PQR and PRS. Let PQR be x degree and PRS be y degree. We need the value of (y-x) degree.

Statement A: angle QPR is 30 degree.

Using the exterior angle concept, we know that angle QPR + angle PQR = angle PRS.

=> 30 + angle PQR = angle PRS => 30 + x = y => y-x = 30 degree. Hence we have got the required angle. Sufficient.

Statement B: angle PQR and PRQ = 150 degree.

In the triangle QPR, sum of the interior angles is 180 degree. That is angle QPR + angle PQR + angle PRQ = 180 degree.

Hence angle QPR = 180 - 150 = 30 degree. Here we have got the same angle as the one mentioned in statement A. Also we have proved that Statement A is sufficient. Hence Statement B is also sufficient.

_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Manager
Joined: 23 Sep 2009
Posts: 144
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

18 Sep 2010, 16:18
Thanks for the explanation...I am feeling very bad when I am unable to recollect the basic principles:(
+1
_________________

Thanks,
VP

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 400
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

18 Sep 2010, 16:24
vigneshpandi wrote:
Thanks for the explanation...I am feeling very bad when I am unable to recollect the basic principles:(
+1

Nothing to worry. With practice you should be able to recollect it comfortably. The trick is to not to look for the answer quickly but to keep prodding with the information presented in the question.
_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Manager
Joined: 19 Aug 2010
Posts: 70
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

16 Oct 2010, 10:36
grafical solution is always easier.
Attachments

grafik.JPG [ 9.73 KiB | Viewed 2092 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 44290
Re: In the figure shown, the measure of angle PRS is how many degrees grea [#permalink]

### Show Tags

21 Aug 2017, 05:24
flehnen wrote:

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: http://gmatclub.com/forum/in-the-figure ... 02829.html

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: http://gmatclub.com/forum/in-the-figure ... 02829.html
_________________
Re: In the figure shown, the measure of angle PRS is how many degrees grea   [#permalink] 21 Aug 2017, 05:24
Display posts from previous: Sort by