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Manager  Joined: 25 Jul 2012
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Points P, R, M and S lie on the number line shown. The coor  [#permalink]

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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

From the GMAT Question pack 1
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Math Expert V
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Re: Points P, R, M and S lie on the number line shown. The coor  [#permalink]

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8 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.

Hope it's clear.
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Manager  Joined: 25 Jul 2012
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Re: Points P, R, M and S lie on the number line shown. The coor  [#permalink]

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

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

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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.

Hope it's clear.

Can you please outline step by step how to get S = -2P exactly? Thanks
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Points P, R, M and S lie on the number line shown. The coor  [#permalink]

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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.

Hope it's clear.

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

$$-P = \frac{1}{3}*(S - P)$$

$$-3P = S - P$$

$$-3P + P = S$$

$$S = -2P$$
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Points P, R, M and S lie on the number line shown. The coor  [#permalink]

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1
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
$$-2P + P = 2M$$

$$-P = 2M$$
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Re: Points P, R, M and S lie on the number line shown. The coor  [#permalink]

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Option D

Let's assume PS = X
PM = MS = X/2
PR = X/3; RM = PM - PR = X/6

I) M = 1.5 (lies on X-axis)

Hence, RM = 1.5 = X/6
X = 9.
PR = X/3 = 9/3 = 3
R coordinates : 0,0
P coordinates : -3,0
Sufficient

II) S = 6
Therefore, RS = 6 = RM + MS = X/3 + X/2 = 2X/3
X = PS = 9
S : 6,0
Hence, P: -3,0

Sufficient

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

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