GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Sep 2018, 16:50

### 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

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

Author Message
Senior Manager
Joined: 27 Aug 2005
Posts: 329
In the figure shown, the measure of angle PRS is how many  [#permalink]

### Show Tags

22 Sep 2005, 20:05
1
4
00:00

Difficulty:

75% (hard)

Question Stats:

62% (01:14) correct 38% (01:39) wrong based on 203 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: in-the-figure-attached-measure-of-angle-prs-is-how-many-102829.html
Senior Manager
Joined: 03 Nov 2004
Posts: 470

### Show Tags

22 Sep 2005, 20:35
answer E. both statements say the same thing , so its either D or E. given the info in either of the statemenst we cannot test the relationship between angles PRS and PQR. therefore answer E.
SVP
Joined: 05 Apr 2005
Posts: 1649
Re: DS: Angles in triangles  [#permalink]

### Show Tags

22 Sep 2005, 21:30
D. 30 deg.

from i, Lprs=Lpqr+Lqpr.
so Lprs-Lpqr=Lqor = 30

from ii, if Lpqr+Lprq =150,
Lqpr = 30, because Lprq+Lpqr+Lqpr =180 and 150+Lqpr =180. so again Lqpr =180-150= 30. therefore the angle prs is 30 degree greater than the angle pqr.
Manager
Joined: 15 Jul 2005
Posts: 105

### Show Tags

23 Sep 2005, 00:22
3
I too get (D)

note: we dont need to find individual angle values, just the difference between angles PRS and PQR (lets call them x,y respectively), so we need to find x-y

let angle PRQ=z

statement I: angle QPR=30, so y+z=150, also z+x=180, therefore z=150-y, and 150-y+x=180 OR x-y=30. Sufficient.

Statement II: angles y+z=150, and we also know that z+x=180, so x-y=30, Sufficient.
Senior Manager
Joined: 13 May 2013
Posts: 430
Re: In the figure shown, the measure of angle PRS is how many  [#permalink]

### Show Tags

09 Dec 2013, 15:04
I've just had a bit of a revelation in solving this problem.

Looking at triangle PRS we have the 90 degree angle at S and the two other angles adding up to 90. Now looking at the 30 degree angle of triangle PRQ. We know that PRS = 180 - PRQ but for the life of me I couldn't figure out why we knew the exact angle difference. Then it dawned on me, PRQ obviously has to add up to 180. Assuming angle PRQ remains constant, for every degree change in in QPR, there has to be an equal and opposite change in PQR. In other words, if QPR got 10 degrees larger, PQR would have to shrink by 10 degrees. If the line PQ were to be flat then obviously the "angle" measurement would be the same but it's 30 degrees "higher" meaning it's degree measure is 30 degrees less. If QPR changes, PQR must change by the same, but opposite amount.

It may not be anything special to the math geniuses here but it is to be :D
Math Expert
Joined: 02 Sep 2009
Posts: 49206
Re: In the figure shown, the measure of angle PRS is how many  [#permalink]

### Show Tags

10 Dec 2013, 03:59
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
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 8063
Re: In the figure shown, the measure of angle PRS is how many  [#permalink]

### Show Tags

04 Sep 2018, 07:27
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In the figure shown, the measure of angle PRS is how many &nbs [#permalink] 04 Sep 2018, 07:27
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.