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

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.

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

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

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.

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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