chesstitans wrote:

On a number line, a < b < c < d. The distance from a to b is 1⁄4 of the distance from b to d. The distance from a to c is 3 times the distance from c to d. What is the value of (b - a) ⁄ (c - a)?

A. 3/ 20

B 1⁄5

C. 4⁄15 [4][/15]

D. 7⁄20

E. 3⁄5

There is a same topic that has been locked. There is also a note that requests a re-post for discussion. I still have no idea how to have the proper format for fraction.

Official explanation: Let's try to pick numbers that will be easy to work with. Let's begin by choosing a simple value for a, say a = 0. If a = 0, we'll need to pick additional values that make our calculations simple.

Refer to below image

Attachment:

number line.jpg [ 20.6 KiB | Viewed 613 times ]
Let the distance between b & d be \(4x\) so distance between a & b will be \(x\)

similarly if the distance between c & d is \(y\) then distance between c & a will be \(3y\)

We need ratio of distance between a & b and c & a i.e \(\frac{x}{3y}\)

it is evident that \(5x=4y\)

\(=>\frac{x}{y}=\frac{4}{5}\)

hence \(\frac{x}{3y}=\frac{4}{15}\)

so our ratio is \(\frac{4}{15}\)

Option C