Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2601:30 AM EDT
-02:30 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
Apr 2912:30 AM EDT
-01:30 AM EDT
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
May 0306:30 AM PDT
-08:30 AM PDT
Verbal trouble on GMAT? Fix it NOW! Join Sunita Singhvi for a focused webinar on actionable strategies to boost your Verbal score and take your performance to the next level.
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
52% (02:05) correct
48%
(01:56)
wrong
based on 464
sessions
History
Date
Time
Result
Not Attempted Yet
Attachment:
Screen shot 2012-12-09 at 1.40.06 PM.png [ 19.42 KiB | Viewed 27378 times ]
(1) Length PQ = Length PR
(2) Line TR bisects angle PRS
09 Dec 2012, 15:58
Kudos
Bookmarks
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
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
General Discussion
10 Dec 2012, 17:53
Kudos
Bookmarks
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
but i understood complex things
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
but i understood complex things 
