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# In an ordinary number line, Points P and T lie in line l.

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Eternal Intern
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In an ordinary number line, Points P and T lie in line l. [#permalink]  29 Jul 2003, 17:11
In an ordinary number line, Points P and T lie in line l. How many different points on l are twice as far from Point T as from point P?

Hint:Don't guess the obvious:ETS knows your tendencies.
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Ride em cowboy

GMAT Instructor
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Re: Number Line Classic: Craziet Number Line one I've seen [#permalink]  29 Jul 2003, 19:13
Curly05 wrote:
In an ordinary number line, Points P and T lie in line l. How many different points on l are twice as far from Point T as from point P?

Hint:Don't guess the obvious:ETS knows your tendencies.

Hint: this is like a stolyar problem:

how many solutions for X such that: |X - P| * 2 = |X - T|?
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Eternal Intern
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Kudos [?]: 44 [0], given: 0

Please provide more hints than that.
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Ride em cowboy

Manager
Joined: 10 Jun 2003
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My answer is 2. I drew a picture, making P=1 and T=2 on a number line. The two points I see that satisfy this are 1.33333 and 0.

In any case, one of the points will be 1/3 of the distance between P and T (closer to P) and 100% of the distance between them, on the other side of P. I think this was a bad explanation

Any other takers?
Eternal Intern
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PS: Looks to be an incomplete solution [#permalink]  30 Jul 2003, 08:47
Two is right, Mciatto, but I really think you can't rely on simple solutions for test day.

The key is there is a disguised algebraic formula in the stem .
How many different points on l are twice as far from Point T as from point P?
"When you see from" this implies subtract.
So the distance from T - [b]X - Unknown point on number line=
2( P - Y[/b[b])

But, the problem with this solution is not every point fits the solution and we will have to keep searching.

Some of us will be lucky to come up with A(0), P(15), B( 20), and C( 30) for a combo that works out!

Need Akami Brah or Stolyar
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Ride em cowboy

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I see geometry in this problem. I am assuming the P and T are 2 different points on line l. See the attached diagram.

Now the point for which the condition is satisfied (twice the distance from T = distance from P) can lie
1) on the left of P (say Q)
2) on the right of T (say R)
3) between P & T (say S)

Case1
-----
Applying the condition from question, 2 * QT = PQ
which is impossible. So Q is not a valid point

Case2
-----
2 * RT = PR
Highly possible. Implies T is the midpoint of PR.
So, R is a valid point

Case 3
------
2 * ST = PS
Possible again. Implies ST is at 1/3 of PR.
So, S is a valid point

So, 2 such points are possible
Eternal Intern
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This isn't really valid for some selection of number values. Please refine!
VT
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