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# In the figure above, if x and y are each less than 90 and PS

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Manager
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In the figure above, if x and y are each less than 90 and PS  [#permalink]

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05 Sep 2010, 12:50
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In the figure above, if x and y are each less than 90 and PS||QR, is the length of segment PQ less than the length of segment SR ?

(1) x>y

(2) x+y>90
Magoosh GMAT Instructor
Joined: 28 Dec 2011
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02 Jan 2012, 16:01
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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.

Does that make sense? Let me know if you have any questions on that.

Mike
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Mike McGarry
Magoosh Test Prep

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In the figure above, if x and y are each less than 90 and PS  [#permalink]

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05 Sep 2010, 13:15
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In the figure above, if x and y are each less than 90 and PS||QR, 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 PS||QR). 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.

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Re: Length of segment PQ less than segment SR  [#permalink]

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07 Sep 2010, 10:56
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Exactly the explanation given by Bunuel... +1 for A
Veritas Prep GMAT Instructor
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Re: Need help with these 5 GMAT Prep questions...  [#permalink]

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08 Dec 2010, 18:02
14
2
MisterEko wrote:
Guys,
as my G-day 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!

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 [ 2.61 KiB | Viewed 29701 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.

_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here > GMAT self-study has never been more personalized or more fun. Try ORION Free! Manager Joined: 29 Jul 2011 Posts: 94 Location: United States Re: Geometry Problem [#permalink] ### Show Tags 07 Jan 2012, 15:57 My two cents in as well... Re-phrase: 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 = 3-4 min Intern Joined: 15 Feb 2012 Posts: 7 Location: India Concentration: General Management, Operations Schools: ISB '14 GPA: 3.09 WE: Operations (Manufacturing) Re: Geometry [#permalink] ### Show Tags 18 Mar 2012, 06:52 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, 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 (180-y). 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: 8188 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 1 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 (180-y). 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 22178 times ] _________________ Karishma Veritas Prep GMAT Instructor Save up to$1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

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

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30 Sep 2017, 06:35
VeritasPrepKarishma Bunuel

Quote:
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: 23
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

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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 G-day 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.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8188
Location: Pune, India
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

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18 Jan 2018, 08:28
1
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 G-day 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.

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/in-the-figur ... 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

Save up to \$1,000 on GMAT prep through 8/20! Learn more here >

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Intern
Joined: 02 Oct 2017
Posts: 23
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

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19 Jan 2018, 11:05
Thanks VeritasPrepKarishma ! :-)

ucb2k7

VeritasPrepKarishma wrote:
MisterEko wrote:
Guys,
as my G-day 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.

[/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]
Manager
Joined: 10 Sep 2014
Posts: 74
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

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01 Apr 2018, 20:05
Re: In the figure above, if x and y are each less than 90 and PS &nbs [#permalink] 01 Apr 2018, 20:05
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