B

2000019201

Level: 
B
People in Kocourkov pay by coins named groschen. Their coins are worth \(1\), \(5\) or \(7\) groschen. Martin and Petr, who live in Kocourkov, emptied their saving boxes and started counting their saved coins. They found out that Petr had \(6\) pieces of each type of a coin more than Martin, who had \(40\) coins in total. They were surprised to find out that Martin has the same number of \(1\)-groschen and \(7\)-groschen coins in total as Petr has of \(5\)-groschen ones. Petr was proud to have \(78\) groschen more than Martin, who was only \(2\) short of having \(200\) groschen. Which of the following systems can be used to find out how many coins of each type both boys have?
\[\begin{aligned} x +5y + 7z & = 198 & & \\ x - y+z & = 6 & & \\ x +y+z & = 40 & & \end{aligned}\]
\[\begin{aligned} x +5y+7z & = 198 & & \\x - y+z & = 6 & & \\(x+6) +5(y+6)+7(z+6) & = 276 & & \end{aligned}\]
\[\begin{aligned} x +5y+7z & = 198 & & \\x + y-z & = 6 & & \\(x+6) +5(y+6)+7(z+6) & = 276 & & \end{aligned}\]
\[\begin{aligned} x +5y+7z & = 202 & & \\x - y+z & = 6 & & \\(x+6) +(y+6)+(z+6) & = 58 & & \end{aligned}\]
\[\begin{aligned} x +5y+7z & = 198 & & \\x - y+z & = 6 & & \\x +5y+7z & = 40 & & \end{aligned}\]
\[\begin{aligned} x +5y+7z & = 198 & & \\x - y+z & = 6 & & \\(x-6) +5(y-6)+7(z-6) & = 276 & & \end{aligned}\]

2000021003

Level: 
B
Consider the function \(f(x)=|x+1|-2\). Which of the statements is true?
The function \(f\) has a minimum at the point \(x=-1\).
The function \(f\) has a minimum at the point \(x=-2\).
The function \(f\) has no minimum.
The function \(f\) has a maximum at the point \(x=-1\).

2000021001

Level: 
B
In the picture, there is the graph of a function \(f\). Which of the following statements is true?
The function \(f\) is bounded.
The function \(f\) has its maximum and has no minimum.
The function \(f\) is a one-to-one function and is decreasing.
The function \(f\) is an odd function and is bounded below.