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

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Math Expert
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On the number line, if r < s, if p is halfway between rand s [#permalink]

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19 Feb 2014, 01:25
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Difficulty:

5% (low)

Question Stats:

85% (01:11) correct 15% (01:44) wrong based on 601 sessions

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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

Problem Solving
Question: 105
Category: Algebra Factoring; Simplifying algebraic expressions
Page: 75
Difficulty: 600

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[Reveal] Spoiler: OA

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On the number line, if r < s, if p is halfway between rand s [#permalink]

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19 Feb 2014, 01:25
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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: $$\frac{m+n}{2}=k$$.
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Re: On the number line, if r < s, if p is halfway between rand s [#permalink]

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19 Feb 2014, 02:45
Option D.
We can assume any values for p,r,s,t that fit the conditions.
For eg,r=2,s=4,p=3,t=2.5
=>(s-t)/(t-r)=>1.5/0.5=3

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Re: On the number line, if r < s, if p is halfway between rand s [#permalink]

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24 Feb 2014, 05:02
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 105
Category: Algebra Factoring; Simplifying algebraic expressions
Page: 75
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

p is halfway b/w r and s hence p=(r+s)/2
Again t is halfway b/w p and r hence t=(p+r)/2=((r+s)/2+r)/2=(3*r+s)/4
take r, s as 0,4 for easy calculation
=> p=2, t=1
=>(s-t)/(t-r)=3

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Re: On the number line, if r < s, if p is halfway between rand s [#permalink]

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24 Feb 2014, 06:53
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.

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Re: On the number line, if r < s, if p is halfway between rand s [#permalink]

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24 Apr 2014, 00:35
p = (r+s)/2;

t = (p+r)/2;

we need the value of (s-t)/(t-r) .

We need to get s and t in terms of p and r ;

[(2p-r) - (p+r)/2]/ [(p+r)/2 -r]= 3(p-r)/(p-r) = 3;

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Re: On the number line, if r < s, if p is halfway between rand s [#permalink]

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17 Jul 2014, 01:38
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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 6870 times ]

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Re: On the number line, if r < s, if p is halfway between rand s [#permalink]

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26 Jan 2017, 07:59
What was the thing that made you start with 0 for r? Why not any other value like 1?

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Re: On the number line, if r < s, if p is halfway between rand s [#permalink]

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26 Jan 2017, 10:07
Ndkms wrote:
What was the thing that made you start with 0 for r? Why not any other value like 1?

Did you try any other value for r? If yes, what did you get? You should get the same answer with other values.
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Re: On the number line, if r < s, if p is halfway between rand s [#permalink]

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20 Aug 2017, 00:32
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 ?

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Math Expert
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Re: On the number line, if r < s, if p is halfway between rand s [#permalink]

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20 Aug 2017, 02:39
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.
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Re: On the number line, if r < s, if p is halfway between rand s   [#permalink] 20 Aug 2017, 02:39
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