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# Figure is attached. In the figure above if x and y each are

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Intern
Joined: 04 Dec 2009
Posts: 19
Figure is attached. In the figure above if x and y each are [#permalink]

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26 Jun 2010, 03:26
1
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Difficulty:

15% (low)

Question Stats:

91% (00:49) correct 9% (00:04) wrong based on 35 sessions

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Figure is attached.

In the figure above if x and y each are 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-above-if-x-and-y-are-each-less-than-90-and-ps-100461.html

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Manager
Joined: 13 Dec 2009
Posts: 235
Re: Figure is attached. In the figure above if x and y each are [#permalink]

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26 Jun 2010, 05:17
1
gautamsubrahmanyam wrote:
Figure is attached.

In the figure above if x and y each are 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

Since PS||QR the shortest distance between the lines PS and QR is the perpendicular between the lines. Whichever segment PQ or SR is closer to becoming a perpendicular is the shorter of the two segments. For this to happen the angles x or y must get maximized towards 90 degrees for their length to become minimum.

Statement 1
x > y
this implies that x is closer to 90 degrees than y. Hence PQ is closer to being perpendicular and thus we can say that PQ is shorter than SR. Sufficient.

Statement 2
x + y > 90
Does not tell us the relation between x and y. Here x could be greater than y (x = 80, y= 70) and satisfy the inequality, or x could be lesser than y (x = 70, y = 80) and still satisfy the inequality. Hence we cannot say which angle is closer to 90 degrees so we cannot determine which line is closer to becoming perpendicular and thus shorter. Not sufficient.
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My debrief: done-and-dusted-730-q49-v40

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Joined: 21 Jun 2010
Posts: 71
Location: Toronto
Re: Figure is attached. In the figure above if x and y each are [#permalink]

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29 Jun 2010, 19:16
Hi,

remember that the shortest distance between any two points is a straight line. So, the question is basically asking you whether the statements will tell you which line travels more "perpendicularly" from bottom to top (or top to bottom).
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Re: Figure is attached. In the figure above if x and y each are [#permalink]

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17 Oct 2010, 02:03
These type of DS questions are real time savers.

The minimum distance between a point and a line can be calculated by drawing a perpendicular passing through the given point to the line.

If you decrease the angle the distance increased. Since x>y => PQ< RS

Thus A. B is irrelevant.

What if it was not stated x and y both less than 90?? Then the answer would have been E.

Very nice question.
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Manager
Joined: 19 Aug 2010
Posts: 69
Re: Figure is attached. In the figure above if x and y each are [#permalink]

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17 Oct 2010, 02:11
Can somebody tell me if that is a 700-level question?
Joined: 19 Feb 2010
Posts: 365
Re: Figure is attached. In the figure above if x and y each are [#permalink]

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17 Oct 2010, 03:06
medanova wrote:
Can somebody tell me if that is a 700-level question?

I don't think so. I'd say it's a 600-700 level question.
I'm not an expert but I didn't find this question difficult, when I don't seem to solve correctly most of the 700-level questions.
Math Expert
Joined: 02 Sep 2009
Posts: 47017
Re: Figure is attached. In the figure above if x and y each are [#permalink]

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21 Aug 2017, 05:34

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-above-if-x-and-y-are-each-less-than-90-and-ps-100461.html

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: Figure is attached. In the figure above if x and y each are   [#permalink] 21 Aug 2017, 05:34
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