Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Aug 2014, 18:25

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the figure above, QRS is a straight line and QR = PR. Is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 06 Sep 2012
Posts: 42
Concentration: Social Entrepreneurship
Followers: 0

Kudos [?]: 11 [0], given: 42

In the figure above, QRS is a straight line and QR = PR. Is [#permalink] New post 09 Dec 2012, 10:43
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

36% (02:28) correct 64% (01:06) wrong based on 66 sessions
Attachment:
Screen shot 2012-12-09 at 1.40.06 PM.png
Screen shot 2012-12-09 at 1.40.06 PM.png [ 19.42 KiB | Viewed 1242 times ]
In the figure above, QRS is a straight line and QR = PR. Is it true that lines TR and PQ parallel?

(1) Length PQ = Length PR
(2) Line TR bisects angle PRS
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Dec 2012, 01:19, edited 1 time in total.
Renamed the topic and edited the question.
Expert Post
4 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2030
Followers: 486

Kudos [?]: 1988 [4] , given: 30

Re: Geometry [#permalink] New post 09 Dec 2012, 14:58
4
This post received
KUDOS
Expert's post
In the figure, QRS is a straight line. QR=PR. Are TR and PQ parallel?
1) Length PQ = Length PR
2) Line TR bisects angle PRS


From the prompt, we know that triangle QPR is isosceles, with QR = PR. By the Isosceles Triangle theorem, we know that angle Q = angle P.

Statement #1 PQ = PR.
This is enough to guarantee that triangle QPR is equilateral, but we don't know anything about ray RT, so we have no idea whether that is parallel to anything else.
This statement, alone and by itself, is not sufficient.

Statement #2 Line TR bisects angle PRS
A fascinating statement. Let's think about this. We already know angle Q = angle P. Call the measure of that angle M. Look angle QRP --- call the measure of that angle K. Clearly, within triangle QPR, M + M + K = 180, but Euclid's famous theorem.
Now, look at angle PRS. This is what is known as the "exterior angle" of a triangle, and there's a special theorem about this.
The Remote Interior Angle Theorem:
If the exterior angle of a triangle is adjacent to the angle of the triangle, then the measure of the exterior angle is equal to the sum of the two "remote" interior angles of the triangle --- that is, the two angles of the triangle which the exterior angle is not touching.

If you think about this, it has to be true, because
(angle Q) + (angle P) + (angle PRQ) = 180, because they're the three angles in a triangle
(angle PRQ) + (exterior angle PRS) = 180, because they make a straight line
Subtract (angle PRQ) from both sides of both equations:
(angle Q) + (angle P) = 180 - (angle PRQ)
(exterior angle PRS) = 180 - (angle PRQ)
Since the two things on the left are equal to the same thing, they are equal to each other.
(angle Q) + (angle P) = (exterior angle PRS)
Now, going back to the letters we were using ---- if (angle Q) = (angle P) = M, this means (exterior angle PRS) = 2M. If we bisect exterior angle PRS, each piece will have a measure of M. Thus, (angle PRT) = (angle TRS) = M
Well, now we know that (angle Q) = (angle TRS) = M. If corresponding angles are congruent, then the lines must be parallel. PQ must be parallel to TR.
This statement, alone and by itself, is sufficient to answer the prompt question.

Answer = B

Does all this make sense?

Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Manager
Manager
User avatar
Joined: 04 Oct 2011
Posts: 225
Location: India
Concentration: Entrepreneurship, International Business
GMAT 1: 440 Q33 V13
GMAT 2: 0 Q0 V0
GPA: 3
Followers: 0

Kudos [?]: 26 [0], given: 44

Re: Geometry [#permalink] New post 10 Dec 2012, 16:53
Hi Mike well explained,

I do have a doubt !

now we know that (angle Q) = (angle TRS) = M. If corresponding angles are congruent, then the lines must be parallel. PQ must be parallel to TR.
This statement, alone and by itself, is sufficient to answer the prompt question.


Correspoding angle means the angle made on its side?
angle Q ==> side PQ
angle TRS ==> side TR

very basic question :oops: but i understood complex things
_________________

GMAT - Practice, Patience, Persistence
Kudos if u like :)

Expert Post
1 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2030
Followers: 486

Kudos [?]: 1988 [1] , given: 30

Re: Geometry [#permalink] New post 10 Dec 2012, 17:09
1
This post received
KUDOS
Expert's post
shanmugamgsn wrote:
I do have a doubt !
Corresponding angle means the angle made on its side?


No. "Corresponding angles" is a technical term from Euclidean Geometry. It's the name of a particular pair of angles formed when a transversal crosses a pair of parallel lines.
Attachment:
parallel line diagram.JPG
parallel line diagram.JPG [ 22.96 KiB | Viewed 1141 times ]

The following pairs are corresponding angles
1 & 5
2 & 6
3 & 7
4 & 8
Corresponding angles are congruent if and only if the lines are parallel.

The following pairs are alternate interior angles
3 & 6
4 & 5
Alternate interior angles are congruent if and only if the lines are parallel

The following pairs are alternate exterior angles
1 & 8
2 & 7
Alternate exterior angles are congruent if and only if the lines are parallel

The following pairs are same side interior angles
3 & 5
4 & 6
Same side interior angles are supplementary if and only if the lines are parallel

The following pairs are same side exterior angles
1 & 7
2 & 8
Same side exterior angles are supplementary if and only if the lines are parallel

Those are all the names relating pairing an angle at one vertex with an angle at the other vertex, when a transversal intersects a pair of parallel lines.

Does all this make sense?

Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Intern
Intern
User avatar
Joined: 24 Apr 2012
Posts: 48
Followers: 0

Kudos [?]: 13 [0], given: 1

Re: In the figure above, QRS is a straight line and QR = PR. Is [#permalink] New post 11 Dec 2012, 03:40
JJ2014 wrote:
Attachment:
Screen shot 2012-12-09 at 1.40.06 PM.png
In the figure above, QRS is a straight line and QR = PR. Is it true that lines TR and PQ parallel?

(1) Length PQ = Length PR
(2) Line TR bisects angle PRS


Ans: For lines TR and PQ to be parallel angle PQR= angle TRS. From statement 1 we get angle PQR=x=60 but nothing about angle TRS.
From statement 2 we get PRQ=180-2X , therefore PRS=180-(180-2x)=2x and TR bisects it so angle TRS=x which is equal to PQR. Therefore the answer is (B).
_________________

www.mnemoniceducation.com

TURN ON YOUR MINDS!!!

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1627
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 11

Kudos [?]: 152 [0], given: 254

GMAT ToolKit User
Re: In the figure above, QRS is a straight line and QR = PR. Is [#permalink] New post 22 Apr 2014, 07:36
Let's solve. So we need to know if TR is parallel to PQ.

Now then, let's hit the first statement. We are told that PQ=QR. Now we know that PQR is an equilateral triangle but still no info on TR. Therefore, insufficient.

Statement 2, we have that TR bisects PRS. Now let's see. So we know that QR=PR from the question stem. Hence angle QRP is 180-2x, 'x' being the angles P and Q respecively. Therefore angle PRS will be 2x since QRS is a straight line with total measure of 180 degrees. Now if TRS bisects then angle TRS is x only. Which means that the angles Q and R are equal and thus PQ // TR.

B stands

Cheers!
J :)
Re: In the figure above, QRS is a straight line and QR = PR. Is   [#permalink] 22 Apr 2014, 07:36
    Similar topics Author Replies Last post
Similar
Topics:
11 Experts publish their posts in the topic In the figure shown above, line segment QR has length 12, an Bunuel 11 06 Mar 2014, 02:07
7 Experts publish their posts in the topic In the figure shown above, line segment QR has length 12. oss198 11 05 Jan 2014, 15:49
In the figure above, QRS is a straight line and line TR Jasontuyj2012 1 06 Aug 2011, 03:46
2 Experts publish their posts in the topic In PQR, if PQ = x, QR = x + 2, and PR = y, which of the Lolaergasheva 7 05 Mar 2011, 04:56
In the figure above, QRS is a straight and line TR bisects bigtreezl 3 06 Oct 2008, 23:47
Display posts from previous: Sort by

In the figure above, QRS is a straight line and QR = PR. Is

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.