10) Knowing that $\frac{1}{a}=a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{d}=2$ what is the value of the product $a b c d$?
(A) $\frac{5}{16}$
(B) $\frac{1}{5}$
(C) $\frac{3}{7}$
(D) $\frac{9}{16}$
(E) $\frac{5}{4}$.
10) The answer is (B)

The values of $a, b, c, d$ can be derived successively. From $\frac{1}{a}=2$ we get $a=\frac{1}{2}$; from $a+\frac{1}{b}=2$ we get $b=\frac{2}{3}$; from $b+\frac{1}{c}=2$ we get $c=\frac{3}{4}$; from $c+\frac{1}{d}=2$ we get $d=\frac{4}{5}$. It follows that $a b c d=\frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdot \frac{4}{5}=\frac{1}{5}$.