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Difficulty: Sub 505 Level,   Algebra,                        
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Re: On the number line, if r < s, if p is halfway between r and s, and if [#permalink]
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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 r and s, and if [#permalink]
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Though this is a algebraic equation, plug-in would be the best to solve it :)

Refer diagram below:

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

Answer = D
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Re: On the number line, if r < s, if p is halfway between r and s, and if [#permalink]
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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.

Answer D
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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.

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: \(\frac{m+n}{2}=k\).



Bunuel can we also take s= 1 and r=0 i.e. the distance between the two is 1 ?
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Re: On the number line, if r < s, if p is halfway between r and s, and if [#permalink]
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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.

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: \(\frac{m+n}{2}=k\).



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 r and s, and if [#permalink]
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Expert Reply
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

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