On the number line, if r

Question

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

Bunuel · Accepted Answer

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 .

AKG1593 · Answer

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

b2bt · Answer

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.

PareshGmat · Answer

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

generis · Answer

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

Shiv2016 · Answer

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

Bunuel · Answer

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.

ScottTargetTestPrep · Answer

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

Tarunw111 · Answer

Draw a number line.
You will get to know that (s-t)=3k/4 and (t-r)=1k/4 (using distance between two points formula), where k is some constant.
Dividing both gives 3.

Tarunw111 · Answer

Yes, but that is your assumed value.
Solving this further, distance between s and t will be 3/4 and the distance between t and r will be 1/4.
Dividing both gives 3.

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

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