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# In the figure above, is RS || PQ?

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Intern
Joined: 08 Jan 2015
Posts: 25
In the figure above, is RS || PQ?  [#permalink]

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Updated on: 26 Feb 2015, 11:21
2
4
00:00

Difficulty:

85% (hard)

Question Stats:

41% (01:23) correct 59% (01:39) wrong based on 99 sessions

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quant_ds_00000066.jpg [ 6.66 KiB | Viewed 2756 times ]
In the figure above, is RS || PQ?

(1) x=y ; r=s
(2) x=r ; y=s

Originally posted by Awli on 26 Feb 2015, 11:18.
Last edited by Bunuel on 26 Feb 2015, 11:21, edited 1 time in total.
Renamed the topic and edited the question.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4471
Re: In the figure above, is RS || PQ?  [#permalink]

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26 Feb 2015, 12:26
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Awli wrote:
Attachment:
The attachment quant_ds_00000066.jpg is no longer available
In the figure above, is RS || PQ?

(1) x=y ; r=s
(2) x=r ; y=s

Dear Awli
I'm happy to respond.

This is a great problem for visualization. For the relevant geometry, see:
http://magoosh.com/gmat/2013/angles-and ... -the-gmat/

In a way, everything depends on that middle line, which I will call AB.

Statement #1:
This statement has a kind of symmetry to it, and seems as if it would guarantee something, but look at a real case.
Attachment:

statement 1 diagram.JPG [ 20.75 KiB | Viewed 2734 times ]

RS isn't even pretending to be parallel to PQ. This arrangement of angles doesn't necessarily guarantee anything. This statement, alone and by itself, is not sufficient.

Statement #2:
By contrast, this is classic statement of geometry. Technically, the angles set equal here are known as "alternate interior angles," and when these are equal, the lines absolutely have to be parallel. Here's a diagram.
Attachment:

statement 2 diagram.JPG [ 19.62 KiB | Viewed 2732 times ]

Because x = r = 40, it guarantees that AB is parallel to PQ. Because s= y = 60, it guarantees that AB is parallel to RS. Well, two things parallel to the same thing must be parallel to each other, so RS is parallel to PQ. This statement, by itself, provides sufficient information.

First is not sufficient, second is sufficient. OA = (B)

Part of what is confusing about statement #2 is that it does not guarantee that the oblique lines, AD and RB, are also parallel. You see, the diagram at the top suggests two sets of parallel lines, and we would need to know that all four angles are equal in order for both pairs of lines to be parallel. That would require the combined statements, but that is above and beyond what the question is asking.

Does all this make sense?
Mike
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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
##### General Discussion
Intern
Joined: 08 Jan 2015
Posts: 25
Re: In the figure above, is RS || PQ?  [#permalink]

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28 Mar 2015, 12:20
For sure it makes sense. Thank you very much for your explanation. I've found it very useful and very clear.
Senior Manager
Joined: 07 Aug 2011
Posts: 499
GMAT 1: 630 Q49 V27
Re: In the figure above, is RS || PQ?  [#permalink]

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30 Mar 2015, 12:00
Awli wrote:
Attachment:
The attachment quant_ds_00000066.jpg is no longer available
In the figure above, is RS || PQ?

(1) x=y ; r=s
(2) x=r ; y=s

Option B is sufficient .
x=r middle line is parellel to bottom most line PQ.
y=s middle line is parallel to top one RS.

option A is in sufficient. as shown in picture.
Attachments

gmatclub.jpg [ 50.24 KiB | Viewed 2530 times ]

Manager
Joined: 24 May 2016
Posts: 134
In the figure above, is RS || PQ?  [#permalink]

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01 Aug 2016, 04:20
In the figure above, is RS || PQ?

1) x = y ; r = s
2) x = r ; y = s

Thank you.
Attachments

Captura.PNG [ 20.23 KiB | Viewed 2006 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 59588
Re: In the figure above, is RS || PQ?  [#permalink]

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01 Aug 2016, 04:42
EBITDA wrote:
In the figure above, is RS || PQ?

1) x = y ; r = s
2) x = r ; y = s

Thank you.

Merging topics. Please refer to the discussion above.
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Director
Joined: 05 Mar 2015
Posts: 980
Re: In the figure above, is RS || PQ?  [#permalink]

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11 Sep 2016, 00:43
EBITDA wrote:
In the figure above, is RS || PQ?

1) x = y ; r = s
2) x = r ; y = s

Thank you.

(b) x=r means the line having angle r and y is parallel to line RS thus if angle y=s then RS || PQ...suff...

Ans B
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Re: In the figure above, is RS || PQ?  [#permalink]

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19 Mar 2019, 14:39
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Re: In the figure above, is RS || PQ?   [#permalink] 19 Mar 2019, 14:39
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