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

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On the number line, if r < s, if p is halfway between rand s [#permalink] New post 19 Feb 2014, 00:25
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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 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


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Re: On the number line, if r < s, if p is halfway between rand s [#permalink] New post 19 Feb 2014, 00:25
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SOLUTION

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

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.

Answer: D.

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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: On the number line, if r < s, if p is halfway between rand s [#permalink] New post 19 Feb 2014, 01:45
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] New post 22 Feb 2014, 05:12
Expert's post
SOLUTION

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

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.

Answer: D.

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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

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Re: On the number line, if r < s, if p is halfway between rand s [#permalink] New post 24 Feb 2014, 04:02
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:
1. Please provide your solutions to the questions;
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] New post 24 Feb 2014, 05:53
I would say the difficulty is little more than 600 :P

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] New post 23 Apr 2014, 23:35
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] New post 17 Jul 2014, 00:38
Though this is a algebraic equation, plug-in would be the best to solve it :)

Refer diagram below:

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

Answer = D
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Re: On the number line, if r < s, if p is halfway between rand s   [#permalink] 17 Jul 2014, 00:38
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