Last visit was: 23 Apr 2026, 11:52 It is currently 23 Apr 2026, 11:52
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
DelSingh
User avatar
Joined: 25 Jul 2012
Last visit: 11 Sep 2013
Posts: 53
Own Kudos:
572
 [61]
Given Kudos: 137
Location: United States
Posts: 53
Kudos: 572
 [61]
Points P, R, M and S lie on the number line shown. The coor 26 Feb 2013, 08:31
8
Kudos
Add Kudos
53
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

66% (02:07) correct 34% (02:20) wrong based on 1199 sessions

History

Date
Time
Result
Not Attempted Yet
Attachment:
File comment: Number Line
Screen Shot 2013-02-26 at 10.19.44 AM.png
Screen Shot 2013-02-26 at 10.19.44 AM.png [ 9.39 KiB | Viewed 31170 times ]
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
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,783
Own Kudos:
810,837
 [27]
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,783
Kudos: 810,837
 [27]
Points P, R, M and S lie on the number line shown. The coor 26 Feb 2013, 08:51
9
Kudos
Add Kudos
18
Bookmarks
Bookmark this Post

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.
General Discussion
User avatar
DelSingh
User avatar
Joined: 25 Jul 2012
Last visit: 11 Sep 2013
Posts: 53
Own Kudos:
572
 [1]
Given Kudos: 137
Location: United States
Posts: 53
Kudos: 572
 [1]
Points P, R, M and S lie on the number line shown. The coor 26 Feb 2013, 09:13
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

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.
Show more


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?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,783
Own Kudos:
810,837
 [2]
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,783
Kudos: 810,837
 [2]
Points P, R, M and S lie on the number line shown. The coor 26 Feb 2013, 10:01
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
DelSingh
Bunuel

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?
Show more

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.
User avatar
sagnik242
User avatar
Joined: 28 Dec 2013
Last visit: 04 Oct 2016
Posts: 47
Own Kudos:
14
Given Kudos: 3
Posts: 47
Kudos: 14
Points P, R, M and S lie on the number line shown. The coor 26 Dec 2015, 17:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

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.
Show more

Can you please outline step by step how to get S = -2P exactly? Thanks
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,783
Own Kudos:
810,837
 [2]
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,783
Kudos: 810,837
 [2]
Points P, R, M and S lie on the number line shown. The coor 27 Dec 2015, 04:42
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
sagnik242
Bunuel

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
Show more

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

\(-3P = S - P\)

\(-3P + P = S\)

\(S = -2P\)
User avatar
Icecream87
User avatar
Joined: 23 Sep 2015
Last visit: 02 Aug 2018
Posts: 332
Own Kudos:
353
 [3]
Given Kudos: 72
Location: France
Schools: Insead Sept '17 (M$)
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE:Real Estate (Mutual Funds and Brokerage)
Products:
My Reviews
Schools: Insead Sept '17 (M$)
GMAT 2: 700 Q48 V38
Posts: 332
Kudos: 353
 [3]
Points P, R, M and S lie on the number line shown. The coor 26 Jan 2016, 08:56
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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
\(-2P + P = 2M\)

\(-P = 2M\)
avatar
RR88
avatar
Joined: 18 Oct 2016
Last visit: 16 Oct 2019
Posts: 107
Own Kudos:
150
 [3]
Given Kudos: 91
Location: India
WE:Engineering (Energy)
Posts: 107
Kudos: 150
 [3]
Points P, R, M and S lie on the number line shown. The coor 05 Mar 2017, 10:30
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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




Sent from my MotoG3-TE using GMAT Club Forum mobile app
User avatar
Basshead
User avatar
Joined: 09 Jan 2020
Last visit: 07 Feb 2024
Posts: 907
Own Kudos:
323
Given Kudos: 431
Location: United States
Posts: 907
Kudos: 323
Points P, R, M and S lie on the number line shown. The coor 24 Nov 2020, 15:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DelSingh
Attachment:
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
Show more

\(P = \frac{1}{3}(S+P)\) --------- 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.
User avatar
genericUser
User avatar
Joined: 31 Jan 2022
Last visit: 22 Dec 2023
Posts: 111
Own Kudos:
99
Given Kudos: 35
Location: Italy
Schools: SDA Bocconi "24 (M)
GMAT 1: 670 Q49 V33
GMAT 2: 690 Q47 V37
GPA: 3.9
Schools: SDA Bocconi "24 (M)
GMAT 2: 690 Q47 V37
Posts: 111
Kudos: 99
Points P, R, M and S lie on the number line shown. The coor 05 Mar 2022, 09:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,964
Own Kudos:
1,117
Posts: 38,964
Kudos: 1,117
Points P, R, M and S lie on the number line shown. The coor 02 Dec 2025, 15:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109783 posts
kingbucky
498 posts
Gmat860sanskar
212 posts