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Points P, R, M and S lie on the number line shown. The coor [#permalink]

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26 Feb 2013, 08:31

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Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?

(1) The coordinate of M is 1.5 (2) The coordinate of S is 6

Re: Points P, R, M and S lie on the number line shown. The coor [#permalink]

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26 Feb 2013, 08:51

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Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?

The distance between P and R is 1/3 the distance between P and S --> -P=1/3*(S-P) (the distance between P and R=0 is -P and the distance between P and S is S-P) --> S=-2P. M is the midpoint of line segment PS --> M=(S+P)/2.

(1) The coordinate of M is 1.5 --> 1.5=(S+P)/2. We have 2 distinct linear equations (1.5=(S+P)/2 and S=-2P) with 2 unknowns, thus we can solve for both of them. Sufficient.

(2) The coordinate of S is 6 --> 6=-2P --> P=-3. Sufficient.

Re: Points P, R, M and S lie on the number line shown. The coor [#permalink]

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26 Feb 2013, 09:13

Bunuel wrote:

Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?

The distance between P and R is 1/3 the distance between P and S --> -P=1/3*(S-P) (the distance between P and R=0 is -P and the distance between P and S is S-P) --> S=-2P. M is the midpoint of line segment PS --> M=(S+P)/2.

Thanks!

Question tho, are you getting -P (because it's to the left of 0) by subtracting -P-R ---> -P-(0) = -P ?

Then isn't the distance between S and P ---> S-(-P) = S+P? _________________

If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^

Re: Points P, R, M and S lie on the number line shown. The coor [#permalink]

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26 Feb 2013, 10:01

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Expert's post

DelSingh wrote:

Bunuel wrote:

Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?

The distance between P and R is 1/3 the distance between P and S --> -P=1/3*(S-P) (the distance between P and R=0 is -P and the distance between P and S is S-P) --> S=-2P. M is the midpoint of line segment PS --> M=(S+P)/2.

Thanks!

Question tho, are you getting -P (because it's to the left of 0) by subtracting -P-R ---> -P-(0) = -P ?

Then isn't the distance between S and P ---> S-(-P) = S+P?

Use numbers to test.

What is the distance between -3 and 0? It's 3. What is the distance between -3 and 6? It's 6-(-3)=9. _________________

Re: Points P, R, M and S lie on the number line shown. The coor [#permalink]

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01 Jul 2014, 21:30

Hello from the GMAT Club BumpBot!

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Re: Points P, R, M and S lie on the number line shown. The coor [#permalink]

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13 Aug 2015, 14:49

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Points P, R, M and S lie on the number line shown. The coor [#permalink]

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26 Dec 2015, 17:18

Bunuel wrote:

Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?

The distance between P and R is 1/3 the distance between P and S --> -P=1/3*(S-P) (the distance between P and R=0 is -P and the distance between P and S is S-P) --> S=-2P. M is the midpoint of line segment PS --> M=(S+P)/2.

(1) The coordinate of M is 1.5 --> 1.5=(S+P)/2. We have 2 distinct linear equations (1.5=(S+P)/2 and S=-2P) with 2 unknowns, thus we can solve for both of them. Sufficient.

(2) The coordinate of S is 6 --> 6=-2P --> P=-3. Sufficient.

Answer: D.

Hope it's clear.

Can you please outline step by step how to get S = -2P exactly? Thanks

Re: Points P, R, M and S lie on the number line shown. The coor [#permalink]

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27 Dec 2015, 04:42

Expert's post

sagnik242 wrote:

Bunuel wrote:

Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?

The distance between P and R is 1/3 the distance between P and S --> -P=1/3*(S-P) (the distance between P and R=0 is -P and the distance between P and S is S-P) --> S=-2P. M is the midpoint of line segment PS --> M=(S+P)/2.

(1) The coordinate of M is 1.5 --> 1.5=(S+P)/2. We have 2 distinct linear equations (1.5=(S+P)/2 and S=-2P) with 2 unknowns, thus we can solve for both of them. Sufficient.

(2) The coordinate of S is 6 --> 6=-2P --> P=-3. Sufficient.

Answer: D.

Hope it's clear.

Can you please outline step by step how to get S = -2P exactly? Thanks

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