Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Jul 2010
Posts: 140

In the figure above, if x and y are each less than 90 and PS [#permalink]
Show Tags
05 Sep 2010, 11:50
3
This post received KUDOS
16
This post was BOOKMARKED
Question Stats:
80% (00:43) correct 20% (00:52) wrong based on 586 sessions
HideShow timer Statistics
Attachment:
Figure.PNG [ 5.28 KiB  Viewed 25270 times ]
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
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 43361

In the figure above, if x and y are each less than 90 and PS [#permalink]
Show Tags
05 Sep 2010, 12:15
6
This post received KUDOS
Expert's post
13
This post was BOOKMARKED
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 26708 times ]
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 15 Apr 2010
Posts: 159

Re: Length of segment PQ less than segment SR [#permalink]
Show Tags
07 Sep 2010, 09:56
1
This post received KUDOS
Exactly the explanation given by Bunuel... +1 for A



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7875
Location: Pune, India

Re: Need help with these 5 GMAT Prep questions... [#permalink]
Show Tags
08 Dec 2010, 17:02
13
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
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 25907 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 My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4650

Re: Geometry Problem [#permalink]
Show Tags
02 Jan 2012, 15:01
19
This post received KUDOS
Expert's post
5
This post was BOOKMARKED
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 25467 times ]
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Manager
Joined: 29 Jul 2011
Posts: 103
Location: United States

Re: Geometry Problem [#permalink]
Show Tags
07 Jan 2012, 14:57
My two cents in as well... Rephrase: Since PS  QR, PQ inversely proportional to angle x, and SR is inversely proportional to angle y. That is we need relationship between Q and R to determine relationship between PQ and SR. 1. x>y > PQ < SR. Suff 2. x+y=90. x>y or x<y. Insuff. A
_________________
I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!
DS  If negative answer only, still sufficient. No need to find exact solution. PS  Always look at the answers first CR  Read the question stem first, hunt for conclusion SC  Meaning first, Grammar second RC  Mentally connect paragraphs as you proceed. Short = 2min, Long = 34 min



Intern
Joined: 15 Feb 2012
Posts: 8
Location: India
Concentration: General Management, Operations
GPA: 3.09
WE: Operations (Manufacturing)

Re: Geometry [#permalink]
Show Tags
18 Mar 2012, 05:52
subhajeet wrote: Can someone help me on this question. Statement 1 let the distance between the parallel lines be h then sinx=h/PQ & siny=h/RS, we see that PQ*sinx=constant (x in deg) as sinx increases in the domain [0,90] i.e sin60>sin30 we can say that inorder to keep the product constant, if sinx increases then PQ decreases.. for ex if x=30 and y=60 as sin30(=0.5)<sin60(=0.866) so PQ>RS Thus statement 1 alone is sufficient Statement 2 If x+y>90 case 1:if both x and y are equal then PQ=RS case 2: if x>y then PQ<RS case 3: if x<y then PQ>RS So insufficient. Thus the ans is A Alternatively, if We have two towers of the same height, the farther we are from the tower the lesser we need to raise our head to see the top of the tower. That is ,more is the distance between the top of the tower and our eye lesser is the head raised. I hope it makes sense.



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, 01:58
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: 7875
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, 03:38
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 18393 times ]
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 586
Location: India
WE: Engineering (Other)

Re: In the figure above, if x and y are each less than 90 and PS [#permalink]
Show Tags
30 Sep 2017, 05:35
VeritasPrepKarishma BunuelQuote: 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. Above statement I understood Quote: So if we know that x>y, then PQ < SR. Stmnt 1 Sufficient. Above statement i am not able to visualize correctly to identify opposite sides to angles x and y.



Intern
Joined: 02 Oct 2017
Posts: 5

Re: In the figure above, if x and y are each less than 90 and PS [#permalink]
Show Tags
16 Jan 2018, 21:41
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: 7875
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, 07:28
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
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 My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 02 Oct 2017
Posts: 5

Re: In the figure above, if x and y are each less than 90 and PS [#permalink]
Show Tags
19 Jan 2018, 10:05
Thanks VeritasPrepKarishma ! :) 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). [/quote] 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 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?[/quote]




Re: In the figure above, if x and y are each less than 90 and PS
[#permalink]
19 Jan 2018, 10:05






