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

Question

Screen Shot 2013-02-26 at 10.19.44 AM.png 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 Rated: Hard

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=19575 
 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.

DelSingh · Answer

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?

Bunuel · Answer

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.

sagnik242 · Answer

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

Bunuel · Answer

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

-3P = S - P

-3P + P = S

S = -2P

Icecream87 · Answer

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

RR88 · Answer

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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Basshead · Answer

P = \frac{1}{3}(S+P)  --------- P is 1/3 the distance between S and P

3P = S + P

2P = S  ---------- twice the distance of P is S

P = \frac{1}{2}S

If we can determine the value of S, we can determine the coordinate of P.

(1)  M = 1.5

M = \frac{-p + s}{2 } -------- M is the midway point between p and s. p is negative because its to the left of R, which is 0.

2M = -p + s

3 = \frac{-1}{2}s + s

3 = \frac{1}{2}s

6 = S

-3 = P ; SUFFICIENT.

(2)  S = 6

-3 = P ; SUFFICIENT.

Answer is D.

genericUser · Answer

IMO can be solved without any computation
From the quetion stem we know that all the point are "anchored" by a factor.
Fixing one point the others will follow.
Both 1) and 2) allow us to do so, so answer D

Regards

bumpbot · Answer

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

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