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

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Points P, R, M and S lie on the number line shown. The coor [#permalink] New post 26 Feb 2013, 07:31
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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

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Re: Points P, R, M and S lie on the number line shown. [#permalink] New post 26 Feb 2013, 07:32
If someone has links to similar problems, please post!
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Re: Points P, R, M and S lie on the number line shown. The coor [#permalink] New post 26 Feb 2013, 07:51
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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.

Answer: D.

Hope it's clear.
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Re: Points P, R, M and S lie on the number line shown. The coor [#permalink] New post 26 Feb 2013, 08:13
Bunuel wrote:
Image
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?
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Re: Points P, R, M and S lie on the number line shown. The coor [#permalink] New post 26 Feb 2013, 09:01
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DelSingh wrote:
Bunuel wrote:
Image
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.
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Re: Points P, R, M and S lie on the number line shown. The coor [#permalink] New post 01 Jul 2014, 20:30
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Re: Points P, R, M and S lie on the number line shown. The coor [#permalink] New post 13 Aug 2015, 13:49
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Re: Points P, R, M and S lie on the number line shown. The coor [#permalink] New post 26 Dec 2015, 16:18
Bunuel wrote:
Image
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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Re: Points P, R, M and S lie on the number line shown. The coor [#permalink] New post 27 Dec 2015, 03:42
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sagnik242 wrote:
Bunuel wrote:
Image
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


This should be easy:

-P = 1/3*(S - P)

-3P = S - P

-3P + P = S

S = -2P
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Points P, R, M and S lie on the number line shown. The coor [#permalink] New post 26 Jan 2016, 07:56
I do it this way:
First equation:
\(R - P = \frac{1}{3} (S - P)\)

\(3R = S + 2P\)

since R is zero
\(S = -2p\)

Second equation:
\(\frac{S + P}{2} = M\)

\(S + P = 2M\) replace P or S in the equation

replacing P
\(S-\frac{S}{2} = 2M\)

\(S= 4M\)

or replacing S
\(-2P + P = 2M\)

\(-P = 2M\)
Points P, R, M and S lie on the number line shown. The coor   [#permalink] 26 Jan 2016, 07:56
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