Read the results of a survey conducted in Pec pod Snezkou, where 1240 people were approached:

"46% of the respondents believe in the existence of Krkonose (rounded to the nearest whole number), 31% do not believe in its existence (rounded to the nearest whole number). The rest of the respondents refused to respond to this question."

a) What is the minimum number of people who could have responded in the survey that they believe in the existence of Krkonose?

b) What is the maximum number of people who could have refused to answer the survey? Provide specific numbers, not percentages.
The number of people who responded positively will be denoted by $x$. The number of people who responded negatively will be denoted by $y$. For these numbers, the following applies:

$$
\begin{aligned}
0.455 \cdot 1240 & \leqq x < 0.465 \cdot 1240, \\
564.2 & \leqq x < 576.6, \\
0.305 \cdot 1240 & \leqq y < 0.315 \cdot 1240, \\
378.2 & \leqq y < 390.6 .
\end{aligned}
$$

At least 565 people responded positively (question a). At least 379 people responded negatively. Therefore, the maximum number of people who refused to respond is $1240 - 565 - 379 = 296$ (question b).

[Question a) is worth 2 points; question b) is worth 4 points. For the incorrect reasoning that the maximum number of people who refused to respond is $100 - 45.5 - 30.5 = 24\%$, i.e., 297 people, because $0.24 \cdot 1240 = 297.6$, 1 point can be awarded.]