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
_________________
Visit
SC Butler, here! Get
two SC questions to practice, whose links you can find by date.
Our lives begin to end the day we become silent about things that matter. -- Dr. Martin Luther King, Jr.BLACK LIVES MATTER.