Grace is offered two successive discounts on a movie ticket:
1. First discount:\( 20\%\) off the original sales price.
2. Second discount: $\(x \%\)$ off the reduced price after the first discount.

The total equivalent discount is $\(\mathbf{4 0 \%}\)$ off the original sales price. We need to compare:
- Quantity A: $x$
- Quantity B: 20

Step 1: Define the Original Price
Let the original sales price of the movie ticket be $\mathbf{\$ 1 0 0}$ (for simplicity).
Step 2: Apply the First Discount (20\%)
First discount $\(=20 \%\)$ of $100=20$
Price after first discount $=100-20=80$
Step 3: Apply the Second Discount ( $x \%$ )
Second discount $=x \%$ of $\(80=0.01 x \times 80=0.8 x\)$
Final price $=80-0.8 x$
Step 4: Express the Total Equivalent Discount (40\%)
A $\(\mathbf{4 0 \%}\)$ discount on the original price means the final price is:

$$
\(100-40=60\)
$$

Step 5: Set Up the Equation
Since the final price after both discounts is \$60:

$$
\(\begin{gathered}
80-0.8 x=60 \\
-0.8 x=60-80 \\
-0.8 x=-20 \\
x=\frac{-20}{-0.8}=25
\end{gathered}\)
$$


Step 6: Compare $x$ with 20
- Quantity A: $\(x=25\)$
- Quantity B: 20

Conclusion
Quantity A > Quantity B
Final Answer
\(\boxed\{A\}\)