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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