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Manager  Joined: 25 Jul 2010
Posts: 93
In the figure above, if x and y are each less than 90 and PS  [#permalink]

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Difficulty:   5% (low)

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 PS||QR, 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 ]
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

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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.

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 ]

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Mike McGarry
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General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

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9
12 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.

Attachment: untitled.PNG [ 38.85 KiB | Viewed 38870 times ]

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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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Exactly the explanation given by Bunuel... +1 for A
Veritas Prep GMAT Instructor V
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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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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 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.

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Manager  Joined: 10 Nov 2010
Posts: 122
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

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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 V
Joined: 02 Sep 2009
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In the figure above, if x and y are each less than 90 and PS  [#permalink]

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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 ]

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Intern  Joined: 27 Dec 2014
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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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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 V
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]

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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 29775 times ]

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Intern  B
Joined: 02 Oct 2017
Posts: 20
Re: In the figure above, if x and y are each less than 90 and PS  [#permalink]

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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 V
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]

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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?
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Re: DS: Lines (GMATPrep)  [#permalink]

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