2013-II-13

答案：C
設 $z=\dfrac{kx}{\sqrt{y}}$，其中 $k$ 為非零常數。設 $x_0$、$y_0$ 及 $z_0$ 分別為 $x$、$y$ 及 $z$ 的原值。

$\begin{array}{rcl}
z_0 & = & \dfrac{kx_0}{\sqrt{y_0}} \\
x_0 & = & \dfrac{1}{k}z_0\sqrt{y_0}
\end{array}$

設 $x_1$、$y_1$ 及 $z_1$ 分別為 $x$、$y$ 及 $z$ 的新值。

$\begin{array}{rcl}
y_1 & = & y_0\times(1-64\%) \\
& = & 0.36y_0
\end{array}$

及

$\begin{array}{rcl}
z_1 & = & z_0\times(1+25\%) \\
& = & 1.25z_0
\end{array}$

由此，可得

$\begin{array}{rcl}
z_1 & = & \dfrac{kx_1}{\sqrt{y_1}} \\
x_1 & = & \dfrac{1}{k} z_1\sqrt{y_1} \\
& = & \dfrac{1}{k} 1.25z_0 \sqrt{0.36y_0} \\
& = & 0.75\dfrac{1}{k}z_0\sqrt{y_0}
\end{array}$

所以，$x$ 的百分改變

$\begin{array}{cl}
= & \dfrac{x_1-x_0}{x_0} \times 100\% \\
= & \dfrac{0.75\frac{1}{k}z_0\sqrt{y_0} – \frac{1}{k}z_0\sqrt{y_0}}{\frac{1}{k}z_0\sqrt{y_0}} \times 100\% \\
= & (0.75-1)\times 100\% \\
= & -25\%
\end{array}$