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 crossmultiplying, 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.
