Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Oct 27 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. One hour of live, online instruction
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Jul 2010
Posts: 93

In the figure above, if x and y are each less than 90 and PS
[#permalink]
Show Tags
05 Sep 2010, 12:50
Question Stats:
82% (01:18) correct 18% (01:38) wrong based on 466 sessions
HideShow timer Statistics
In the figure above, if x and y are each less than 90 and PSQR, is the length of segment PQ less than the length of segment SR ? (1) x > y (2) x + y > 90 Attachment:
Figure.PNG [ 5.28 KiB  Viewed 36831 times ]
Official Answer and Stats are available only to registered users. Register/ Login.




Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4472

Re: In the figure above, if x and y are each less than 90 and PS
[#permalink]
Show Tags
02 Jan 2012, 16:01
Hi there. I'm happy to help with this. So, the lines PS & RQ are parallel, angles X & Y are each less than 90 degrees. Statement #1 tells us angle X is greater than angle Y. In the diagram, I showed an exaggerated example of this  if Y is a much smaller angle, it follows a less steep diagonal, which travels a longer distance between the two lines, as shown in the diagram. Therefore, if (angle X) > (angle Y), then segment RS is longer than segment PQ. Statement #1 is sufficient. (Notice that this logic depends on both angles staying less than 90 degrees. If X had a value greater than 90 degrees, it would start making a longer, less steep, line segment on the left side.) Statement #2 says only that the sum (x + y) is greater than 90. The trouble with that is: it doesn't give us any way to distinguish x vs. y  either one could be much bigger than the other, or they both could be equal. No way to distinguish x vs. y ==> no way to distinguish RS vs. PQ. Insufficient. Correct answer = A Does that make sense? Let me know if you have any questions on that. Mike
Attachments
parallel lines, unequal angles.PNG [ 7.81 KiB  Viewed 36823 times ]
_________________
Mike McGarry Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)




Math Expert
Joined: 02 Sep 2009
Posts: 58434

Re: In the figure above, if x and y are each less than 90 and PS
[#permalink]
Show Tags
05 Sep 2010, 13:15
In the figure above, if x and y are each less than 90 and PSQR, is the length of segment PQ less than the length of segment SR ?(1) x>y > if the angles x and y were equal then the length of segment PQ would be equal to the length of segment SR (as PSQR). Now, as x>y it means that point R is to the left of the position it would be if x and y were equal (previous case), or in other words, we should drag point R to the left to the position of R2 to make angle y less than x, thus making the length of segment SR bigger than the length of segment PQ. So as x>y than SR>PQ. Sufficient. (2) x+y>90 > clearly insufficient: if \(x=y=60\) then the length of segment PQ would be equal to the length of segment SR but if \(x=60\) and \(y=45\) then the length of segment PQ would be less than the length of segment SR. Not sufficient. Answer: A. Attachment:
untitled.PNG [ 38.85 KiB  Viewed 38870 times ]
_________________



Manager
Joined: 15 Apr 2010
Posts: 105

Re: In the figure above, if x and y are each less than 90 and PS
[#permalink]
Show Tags
07 Sep 2010, 10:56
Exactly the explanation given by Bunuel... +1 for A



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: In the figure above, if x and y are each less than 90 and PS
[#permalink]
Show Tags
08 Dec 2010, 18:02
MisterEko wrote: Guys, as my Gday is approaching, I am putting more and more effort in improving my Quant. However, I seem to have troubles with some basic concepts. Below are the 5 questions which I know have simple explanations but are for some reason difficult for me to understand. If you can explain the solutions for any of them, I would greatly appreciate it! Cheers! Uploaded with ImageShack.usNote that the shortest distance between two parallel lines is the perpendicular distance. As the angle keeps decreasing, the length of the line keeps increasing. So if we know that x>y, then PQ < SR. Stmnt 1 Sufficient. Attachment:
Ques1.jpg [ 2.61 KiB  Viewed 37296 times ]
Since statement 2 doesn't give any information about relative size of x and y, nothing can be said about PQ and SR. Not sufficient. Answer (A).
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 10 Nov 2010
Posts: 122

Re: In the figure above, if x and y are each less than 90 and PS
[#permalink]
Show Tags
14 Mar 2011, 23:25
If the statement didn't contain the restriction about x and y(both are less than 90),then answer would have been "E". Am I correct in this assessment?



Math Expert
Joined: 02 Sep 2009
Posts: 58434

In the figure above, if x and y are each less than 90 and PS
[#permalink]
Show Tags
15 Mar 2011, 04:07
vjsharma25 wrote: If the statement didn't contain the restriction about x and y(both are less than 90),then answer would have been "E". Am I correct in this assessment? Yes, if we were not given that x and y are each less than 90 then PQ and SR could be mirror images of each other and thus have equal length.
Attachments
untitled.PNG [ 38.85 KiB  Viewed 5989 times ]
_________________



Intern
Joined: 27 Dec 2014
Posts: 4

Re: In the figure above, if x and y are each less than 90 and PS
[#permalink]
Show Tags
06 Feb 2015, 02:58
Hi guys,
I went through the task and argued similar we would have argued in a triangle. The side which is opposite the smaller angle is also the smaller side. (in a triangle) But here in a polygon this argumentation doesnt hold.
Because I thought SR is smaller than PQ because angle x is smaller than (180y).
After reading your explanations I totally get your point, but I dont understand why we can't argue the same way we do with triangles.
Thanks !



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: In the figure above, if x and y are each less than 90 and PS
[#permalink]
Show Tags
06 Feb 2015, 04:38
gmatstrong wrote: Hi guys,
I went through the task and argued similar we would have argued in a triangle. The side which is opposite the smaller angle is also the smaller side. (in a triangle) But here in a polygon this argumentation doesnt hold.
Because I thought SR is smaller than PQ because angle x is smaller than (180y).
After reading your explanations I totally get your point, but I dont understand why we can't argue the same way we do with triangles.
Thanks ! First of all, think, which side of the quadrilateral is the opposite side to any given angle. Look at the diagram, the angle has 2 sides opposite to it (which don't form the angle). You can make one of the opposite sides smaller and the other greater at whim. So there is no defined relation between the angle and the opposite sides. Attachment:
Ques3.jpg [ 4.6 KiB  Viewed 29775 times ]
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 02 Oct 2017
Posts: 20

Re: In the figure above, if x and y are each less than 90 and PS
[#permalink]
Show Tags
16 Jan 2018, 22:41
VeritasPrepKarishma Can you elaborate this explanation from scratch. Not able to understand what all rules it is using concerning the parallel lines given. Cannot understand Bunuel's post. Thanks! ucb2k7 VeritasPrepKarishma wrote: MisterEko wrote: Guys, as my Gday is approaching, I am putting more and more effort in improving my Quant. However, I seem to have troubles with some basic concepts. Below are the 5 questions which I know have simple explanations but are for some reason difficult for me to understand. If you can explain the solutions for any of them, I would greatly appreciate it! Cheers! :war Note that the shortest distance between two parallel lines is the perpendicular distance. As the angle keeps decreasing, the length of the line keeps increasing. So if we know that x>y, then PQ < SR. Stmnt 1 Sufficient. Attachment: Ques1.jpg Since statement 2 doesn't give any information about relative size of x and y, nothing can be said about PQ and SR. Not sufficient. Answer (A).



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: In the figure above, if x and y are each less than 90 and PS
[#permalink]
Show Tags
18 Jan 2018, 08:28
ucb2k7 wrote: VeritasPrepKarishma Can you elaborate this explanation from scratch. Not able to understand what all rules it is using concerning the parallel lines given. Cannot understand Bunuel's post. Thanks! ucb2k7 VeritasPrepKarishma wrote: MisterEko wrote: Guys, as my Gday is approaching, I am putting more and more effort in improving my Quant. However, I seem to have troubles with some basic concepts. Below are the 5 questions which I know have simple explanations but are for some reason difficult for me to understand. If you can explain the solutions for any of them, I would greatly appreciate it! Cheers! :war Note that the shortest distance between two parallel lines is the perpendicular distance. As the angle keeps decreasing, the length of the line keeps increasing. So if we know that x>y, then PQ < SR. Stmnt 1 Sufficient. Attachment: Ques1.jpg Since statement 2 doesn't give any information about relative size of x and y, nothing can be said about PQ and SR. Not sufficient. Answer (A). You are given that PS is parallel to QR. The shortest distance between these two lines will be the perpendicular distance as shown by the solid line between them in the diagram above ( https://gmatclub.com/forum/inthefigur ... ml#p829762) Now as you turn the line towards the right (as shown by dotted lines above) the angle at the base keeps reducing. Consider two such lines PQ and SR. If the angle x is greater than angle y, it means PQ is less tilted than SR. So PQ is closer to the perpendicular line than is SR. So PQ is shorter than SR. Does this help?
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



NonHuman User
Joined: 09 Sep 2013
Posts: 13316

Re: DS: Lines (GMATPrep)
[#permalink]
Show Tags
04 Oct 2019, 23:48
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: DS: Lines (GMATPrep)
[#permalink]
04 Oct 2019, 23:48






