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Problem Solving
If w, x, y and z are positive and w/x=y/z, which of the following is NOT always TRUE?
(A) wz = xy
(B) x/w = z/y
(C) x/y = z/w
(D) (w + x) x = (y + z) z
(E) (x + w) w = (z + y) y
It is given that w/x = y/z.
By cross-multiplying, we get wz = xy.
So, (A) is always true.
By reversing the ratios in the given equation, we get x/w = z/y.
So, (B) is also always true.
Since w/x = y/z, [w/x] + 1 = [y/z] + 1. This can be simplified as (w + x)/x = (z + y)/x.
So, (D) is also always true.
Similarly, by adding 1 to each side of the equation in (B), we get (x + w)/w = (z + y)/y.
So, (E) is also always true.
It is (C) which need not be true and that is the answer.
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