The problem should read as follows:
If 2ˣ = 4ʸ = 8ᶻ and xyz=288, what is the value of 1/(2x) + 1/(4y) + 1/(8z)?
A) 18/74
B) 18/96
C) 11/74
D) 11/96
Let 2ˣ = 4ʸ = 8ᶻ = 64.
In this case, x=6, y=3 and z=2.
Implication:
x:y:z = 6:3:2.
Test multiples of this ratio until a product of 288 is yielded:
6*3*2 = 36.
12*6*4 = 288.
The option in red works.
Since x=12, y=6, and z=4, we get:
1/(2x) + 1/(4y) + 1/(8z) = 1/24 + 1/24 + 1/32 = 4/96 + 4/96 + 3/96 = 11/96.
The correct answer is
D.
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