Last visit was: 25 Jul 2024, 03:09 It is currently 25 Jul 2024, 03:09
Toolkit
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

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.

# On the number line, if r < s, if p is halfway between r and s, and if

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94614
Own Kudos [?]: 643729 [37]
Given Kudos: 86749
Math Expert
Joined: 02 Sep 2009
Posts: 94614
Own Kudos [?]: 643729 [18]
Given Kudos: 86749
General Discussion
Manager
Joined: 20 Dec 2013
Posts: 183
Own Kudos [?]: 292 [1]
Given Kudos: 35
Location: India
Manager
Joined: 25 Sep 2012
Posts: 203
Own Kudos [?]: 567 [1]
Given Kudos: 242
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: On the number line, if r < s, if p is halfway between r and s, and if [#permalink]
1
Kudos
I would say the difficulty is little more than 600

its easy once you understand that you have to assume the value, but many folks fail to do so. Those may get into cumbersome algebra and get things difficult.
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1558
Own Kudos [?]: 7304 [3]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Re: On the number line, if r < s, if p is halfway between r and s, and if [#permalink]
3
Kudos
Though this is a algebraic equation, plug-in would be the best to solve it

Refer diagram below:

$$\frac{4-1}{1-0} = 3$$

Attachments

va.png [ 2.65 KiB | Viewed 27909 times ]

Senior SC Moderator
Joined: 22 May 2016
Posts: 5325
Own Kudos [?]: 35783 [0]
Given Kudos: 9464
Re: On the number line, if r < s, if p is halfway between r and s, and if [#permalink]
Bunuel wrote:
On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s – t)/(t – r) =

(A) 1/4
(B) 1/3
(C) 4/3
(D) 3
(E) 4

Find endpoints.

Sketch r < s. From info and logic, neither p nor t can be an endpoint; both are midpoints.

r < s, p is halfway between:

R_____________P_____________S
|------------------|------------------|

t is halfway between p and r:

R______T______P____________S
|----x---|----x---|------2x------|

Track on distance as above. Then use smallest length to define. Let RT = x. Then TP = x, and PS = 2x.

Assign integer value to x; 1 is easy. Assign cardinal values in keeping with the ratios.

Let r = 1. Then t = 2, p = 3, and s, which is 2x = (2)(1) away from p, = 5.

A. (s - t) => (5 - 2) = 3
B. (t - r) => (2 - 1) = 1

$$\frac{A}{B}$$ = $$\frac{3}{1}$$ = 3

I tested it with x=2 as well, and started with r = 3. The ratio holds.

Director
Joined: 02 Sep 2016
Posts: 525
Own Kudos [?]: 195 [0]
Given Kudos: 277
Re: On the number line, if r < s, if p is halfway between r and s, and if [#permalink]
Bunuel wrote:
SOLUTION

On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s - t)/(t - r) =

(A) 1/4
(B) 1/3
(C) 4/3
(D) 3
(E) 4

Let r=0 and s=4 --> p is halfway between r and s: p=2;
t is halfway between p=2 and r=0: t=1;

(s-t)/(t-r)=(4-1)/(1-0)=3.

P.S. On the GMAT we can often see such statement: $$k$$ is halfway between $$m$$ and $$n$$ on the number line. Remember this statement can ALWAYS be expressed algebraically as: $$\frac{m+n}{2}=k$$.

Bunuel can we also take s= 1 and r=0 i.e. the distance between the two is 1 ?
Math Expert
Joined: 02 Sep 2009
Posts: 94614
Own Kudos [?]: 643729 [0]
Given Kudos: 86749
Re: On the number line, if r < s, if p is halfway between r and s, and if [#permalink]
Shiv2016 wrote:
Bunuel wrote:
SOLUTION

On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s - t)/(t - r) =

(A) 1/4
(B) 1/3
(C) 4/3
(D) 3
(E) 4

Let r=0 and s=4 --> p is halfway between r and s: p=2;
t is halfway between p=2 and r=0: t=1;

(s-t)/(t-r)=(4-1)/(1-0)=3.

P.S. On the GMAT we can often see such statement: $$k$$ is halfway between $$m$$ and $$n$$ on the number line. Remember this statement can ALWAYS be expressed algebraically as: $$\frac{m+n}{2}=k$$.

Bunuel can we also take s= 1 and r=0 i.e. the distance between the two is 1 ?

Yes. In this case p would be 1/2 and t would be 1/4, which will make calculations a bit harder compared to the case above where all variables are integers.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19199
Own Kudos [?]: 22718 [1]
Given Kudos: 286
Location: United States (CA)
Re: On the number line, if r < s, if p is halfway between r and s, and if [#permalink]
1
Kudos
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s - t)/(t - r) =

(A) 1/4
(B) 1/3
(C) 4/3
(D) 3
(E) 4

Solution:

We can let r = 0 and s = 4. So p = 2 and t = 1. Therefore,

(s - t) / (t - r) = (4 - 1) / (1 - 0) = 3

Non-Human User
Joined: 09 Sep 2013
Posts: 34085
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: On the number line, if r < s, if p is halfway between r and s, and if [#permalink]
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: On the number line, if r < s, if p is halfway between r and s, and if [#permalink]
Moderator:
Math Expert
94614 posts