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# In figure below P and T lie on line L. How many different

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In figure below P and T lie on line L. How many different [#permalink]

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11 Nov 2009, 13:29
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Geometry Line problem.JPG [ 3.03 KiB | Viewed 4290 times ]
In figure below P and T lie on line L. How many different points on L are twice as for from point T as from point P?

(A) Infinite number
(B) 4
(C) 2
(D) 1
(E) None
[Reveal] Spoiler: OA

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Re: In figure below P and T lie on line L. How many different [#permalink]

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11 Nov 2009, 14:18
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2.
1-1/3 of PT
2-1/2 of PT at right of T.

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Re: In figure below P and T lie on line L. How many different [#permalink]

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12 Jan 2013, 23:08
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I did not understand the question. Could someone explain me in detail?
Thanks

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Math Expert
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Re: In figure below P and T lie on line L. How many different [#permalink]

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24 Oct 2013, 11:42
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Magdak wrote:
Banuel, I didn't understand the question. Could you pls. visualize the solution on the line? Thanks.

Consider two possible cases below:
Attachment:

Untitled.png [ 1.84 KiB | Viewed 2675 times ]

In both cases TX = 2*PX.

Hope it's clear.
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Re: In figure below P and T lie on line L. How many different [#permalink]

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23 Dec 2015, 19:11
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well, an easy one. the point can be to the left of point P and to the right of point P. so we must have 2 numbers.

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Re: In figure below P and T lie on line L. How many different [#permalink]

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11 Nov 2009, 14:27
2

1/3 of PT
and PT left to P
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Re: In figure below P and T lie on line L. How many different [#permalink]

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11 Nov 2009, 19:56
2 points: 1 before P such that PX=PT and the 2nd point between P&T such that PX=2XT

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Re: In figure below P and T lie on line L. How many different [#permalink]

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12 Nov 2009, 08:52
Yes, the OA is 2. Everyone solved it correctly.
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Re: In figure below P and T lie on line L. How many different [#permalink]

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03 Jan 2013, 21:40
Bunuel wrote:
In figure below P and T lie on line L. How many different points on L are twice as for from point T as from point P?

(A) Infinite number
(B) 4
(C) 2
(D) 1
(E) None

Let x = distance between P and T
Points of 2x distance from T will be T - 2x and T + 2x. Thus, 2.
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Re: In figure below P and T lie on line L. How many different [#permalink]

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13 Jan 2013, 00:26
2 Points.
First - left of T with distance equivalent to PT.
Second - between PT with distance PT/3 from P.
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Re: In figure below P and T lie on line L. How many different [#permalink]

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24 Oct 2013, 11:24
Banuel, I didn't understand the question. Could you pls. visualize the solution on the line? Thanks.

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Re: In figure below P and T lie on line L. How many different [#permalink]

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26 Jan 2015, 11:36
Thats 2.

P is the midpoint btw T and starting point of line L

so 2 (p--t) = distance between T and Starting point of L

so thus T is the midpoint of the line and have two possible points with that distance

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Re: In figure below P and T lie on line L. How many different   [#permalink] 26 Jan 2015, 11:36
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