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

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

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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: https://gmatclub.com/forum/in-the-figur ... 00461.html
[Reveal] Spoiler: OA

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Re: Figure is attached. In the figure above if x and y each are [#permalink]

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New post 26 Jun 2010, 05:17
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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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Re: Figure is attached. In the figure above if x and y each are [#permalink]

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New post 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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New post 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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Re: Figure is attached. In the figure above if x and y each are [#permalink]

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New post 17 Oct 2010, 02:11
Can somebody tell me if that is a 700-level question?

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Re: Figure is attached. In the figure above if x and y each are [#permalink]

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New post 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.

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Re: Figure is attached. In the figure above if x and y each are [#permalink]

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New post 21 Aug 2017, 05:34
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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.

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-the-figur ... 00461.html
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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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