If w y, the average of x and y is z, and the average of z and x is

Question

If w > y, the average of x and y is z, and the average of z and x is w, what is the value of (x - w)/(w - y) ?

A. 1/4
B. 1/3
C. 1/2
D. 3
E. 4

sujoykrdatta · Accepted Answer

We can always choose some values satisfying the conditions given.

Alternative: 
z = (x + y)/2 and w = (x + z)/2

Basically, we have, on the number line: z mid-way between x and y and w mid-way between x and z
x ---- w ---- z --------- y (here y > w)
OR
y --------- z ---- w ---- x (here w > y) - satisfies the given condition
Thus, if the gap between w and z is d, the gap between w and x is also d and the gap between y and z is 2d

=> (x - w)/(w - y) = d/(d+2d) = d/3d = 1/3

Answer B

gmatophobia · Answer

We can assume the value of w, x , y and z within the given constraints and find the value of (x-w) / (w-y)

The working is attached.

Option B

stne · Answer

Hi good solution , however  w>y

Hence we should take  x=2  and  y =-2

gmatophobia · Answer

Good catch ! Yeah I interchanged the values

. Corrected the solution. Thanks !

ManifestDreamMBA · Answer

Avg is also a mid point. Think of the points on the number line.

If x = 2, y = 6, z = 4(mid point)
If x = 2 and z = 4, w = 3(mid point)

So we have,
x - w - z - y 
2-3-4-6

x-w = -1
w-y = -3

(x - w)/(w - y) = 1/3

APram · Answer

I have approached it in this way:

x+z = 2w
Also x+y =2z => z=(x+y)/2

Substituting value of z in first equation

x + (x+y)/2 = 2w
3x + y = 4w
So w-y = 3x - 3w

Hence require fraction (x-w)/(w-y) 
=(x-w)/(3x-3w) = 1/3

bumpbot · Answer

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If w > y, the average of x and y is z, and the average of z and x is

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