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# Geometry

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Geometry [#permalink]  19 Feb 2018, 23:05
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Question Stats:

50% (00:54) correct 50% (01:27) wrong based on 8 sessions
P and Q are two different points on line l and R & S are two different points on line m. Line l is parallel to line m and the distance between P & Q is same as the distance between R & S. Point 'T' is the midpoint of line segment PQ.

 Quantity A Quantity B Distance from T to R Distance from T to S

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

Last edited by Carcass on 20 Feb 2018, 03:19, edited 2 times in total.
Edited by Carcass
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Re: Geometry [#permalink]  19 Feb 2018, 23:15
3
KUDOS
In a geometry problem with no picture, you should just draw a picture to help visualize. But beware! The reason that they didn't provide a picture is that there is an easy assumption to be made when drawing it yourself. In this problem, drawing a picture of two parallel lines with two points on each seems simple enough. But the assumption that most will make is that because lines l and m are parallel, points P and Q, and points R and S are next to each other. If they are, then T will be equidistant from R and S and the answer would be C.

But if you realize that points R and S can slide anywhere they want on line m as long as they stay the same distance apart, you'll see that the distance from T to either R or S can be basically anything. Thus the real answer is D.
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Manager
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Re: Geometry [#permalink]  20 Feb 2018, 23:43
I gave my answer C). Even if the points can be anywhere, shouldn't their distance be essentially the same? What I mean is that the distance between P and Q is the same as Q and P and the distance of R and S is the same as P and Q. So T is the midpoint and my answer followed from that.
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Re: Geometry [#permalink]  24 Feb 2018, 18:06
D

T is fixed on line L, whereas R and S can be moving points on line M (with same distance between them as PQ). This means that the perpendicular distance of T from line m is fixed, rest everything can be changed. R could be right below point T, so TR would be perpendicular distance (shortest), whereas TS will be some slanting distance OR point S could be right below T, so vice versa.
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Re: Geometry [#permalink]  19 Jan 2019, 18:02
gremather wrote:
I gave my answer C). Even if the points can be anywhere, shouldn't their distance be essentially the same? What I mean is that the distance between P and Q is the same as Q and P and the distance of R and S is the same as P and Q. So T is the midpoint and my answer followed from that.

NO, Please check it. As per question, P and Q are two different points on line l and R & S are two different points on line m. Line l is parallel to line m and the distance between P & Q is same as the distance between R & S. Point 'T' is the midpoint of line segment PQ.

_______________P_______________T_______________Q__________________ l

Yes, l and are parallel.

Is Distance from T to R equal to Distance from T to S? _______________R_______________________________S__________________ n

No, Ans D
Re: Geometry   [#permalink] 19 Jan 2019, 18:02
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