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In the figure above, is RS || PQ?

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Intern
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In the figure above, is RS || PQ?  [#permalink]

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New post Updated on: 26 Feb 2015, 11:21
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41% (01:25) correct 59% (01:41) wrong based on 93 sessions

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Attachment:
quant_ds_00000066.jpg
quant_ds_00000066.jpg [ 6.66 KiB | Viewed 2324 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.
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Re: In the figure above, is RS || PQ?  [#permalink]

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New post 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
statement 1 diagram.JPG [ 20.75 KiB | Viewed 2303 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
statement 2 diagram.JPG [ 19.62 KiB | Viewed 2301 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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Re: In the figure above, is RS || PQ?  [#permalink]

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New post 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.
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Re: In the figure above, is RS || PQ?  [#permalink]

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New post 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.
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In the figure above, is RS || PQ?  [#permalink]

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

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

Please explain in detail your answer.

Thank you.
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Re: In the figure above, is RS || PQ?  [#permalink]

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New post 01 Aug 2016, 04:42
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Re: In the figure above, is RS || PQ?  [#permalink]

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

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

Please explain in detail your answer.

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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New post 19 Mar 2019, 14:39
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).

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