Question 1
In the table below each of the three rows is a correct calculation (the symbol $\div$ denotes division). Also each of the three columns (read from top to bottom) is a correct calculation. However, the digits in the table have been replaced by letters. Different letters represent different digits and no digits are $0$.
$$
\begin{array}{lclcl}
\text{ABC} & - & \text{ADF} & = & \text{F} \\
+ & & - & & - \\
\text{ADD} & \div & \text{GC} & = & \text{C} \\
= & & = & & = \\
\text{CEF} & \div & \text{GD} & = & \text{D}
\end{array}
$$
Which digit does $E$ represent?
A) $1$ B) $3$ C) $5$ D) $7$ E) $9$
$$
\begin{array}{lclcl}
\text{ABC} & - & \text{ADF} & = & \text{F} \\
+ & & - & & - \\
\text{ADD} & \div & \text{GC} & = & \text{C} \\
= & & = & & = \\
\text{CEF} & \div & \text{GD} & = & \text{D}
\end{array}
$$
Which digit does $E$ represent?
A) $1$ B) $3$ C) $5$ D) $7$ E) $9$