B

1003082201

Level: 
B
The price of the commodity did not change if
it was lowered by \( 20\% \), and the new price was increased by \( 25\% \).
it was lowered by \( 10\% \), and the new price was increased by \( 10\% \).
it was increased by \( 30\% \), and the new price was lowered by \( 30\% \).
it was increased by \( 20\% \), and the new price was lowered by \( 25\% \).

1003060504

Level: 
B
Four systems of equations are given. How many of the given systems have infinitely many solutions? \[ \begin{array}{c|c} \text{\( \begin{aligned} 4x-6y+10z&=8 \\ -2x+3y-5z&=4 \\ x+y+z&=1 \end{aligned}\)}& \text{\( \begin{aligned} 4x-6y+10z&=8\\ 6x-9y+15z&=12\\ x+y+z&=1\\ \end{aligned}\)} \\\hline \text{\(\begin{aligned} 4x-6y+10z&=8\\ -2x+3y+5z&=4\\ x+y+z&=1\\ \end{aligned}\)}& \text{\( \begin{aligned} x+y+z&=1 \\ 2x+2y+2z&=2 \\ -\frac x2-\frac y2-\frac z2&=-\frac12 \end{aligned}\)} \end{array} \]
\( 2 \)
\( 1 \)
\( 3 \)
\( 4 \)

1003060503

Level: 
B
The system of equations is given by: \[ \begin{aligned} x-y-z&=0, \\ 2x-y+3z&=1, \\ -3x+2y+z&=2. \end{aligned} \] To which of the following systems is it equivalent? (Note: An algorithm for solving a system of linear equations by transformation the system into this form (row echelon form) is known as Gaussian elimination or as row reduction.)
\( \begin{aligned} x-y-z&=0 \\ y+5z&=1 \\ 3z&=3 \end{aligned} \)
\( \begin{aligned} x-y-z&=0 \\ y+5z&=-1 \\ 3z&=-1 \end{aligned} \)
\( \begin{aligned} x-y-z&=0 \\ -3y-z&=-1 \\ 5z&=5 \end{aligned} \)
\( \begin{aligned} x-y-z&=0 \\ -3y-z&=-1 \\ 5z&=-7 \end{aligned} \)

1003060502

Level: 
B
The system of equations is given by: \[ \begin{aligned} x+y-2z&=0, \\ x+2y+3z&=0, \\ -2x+y+z&=2. \end{aligned} \] To which of the following systems is it equivalent? (Note: An algorithm for solving a system of linear equations by transformation the system into this form (row echelon form) is known as Gaussian elimination or as row reduction.)
\( \begin{aligned} x+y-2z&=0 \\ y+5z&=0 \\ 18z&=-2 \end{aligned} \)
\( \begin{aligned} x+y-2z&=0 \\ y-5z&=0 \\ 12z&=2 \end{aligned} \)
\( \begin{aligned} x+y-2z&=0 \\ y+5z&=0 \\ 18z&=2 \end{aligned} \)
\( \begin{aligned} x+y-2z&=0 \\ y+z&=0 \\ 6z&=2 \end{aligned} \)

1003060501

Level: 
B
Which of the following systems of equations has no solution?
\(\begin{aligned} 2x-y+3z&=2 \\ 6x-3y+9z&=4 \\ x+y+z&=1 \end{aligned} \)
\(\begin{aligned} 2x-y+3z&=2 \\ 6x-3y+9z&=6 \\ x+y+z&=1 \\ \end{aligned} \)
\(\begin{aligned} 2x-y+3z&=2 \\ 6x-2y+z&=4 \\ x+y+z&=1 \end{aligned} \)
\(\begin{aligned} 2x-y+3z&=2 \\ 6x-3y+9z&=6 \\ 4x-4y+6z&=4 \end{aligned} \)

1003066907

Level: 
B
The results of a survey considering the support for political parties \( Y \) and \( Z \) are presented in the table below. a) How many percentage points have the support for party \( Z \) decreased? b) How much has the percentage of people supporting party \( Y \) increased? \[\begin{array}{|c|c|c|} \hline & \text{February} & \text{March} \\\hline Y & 16\% & 20\% \\\hline Z & 10\% & 8\% \\\hline \end{array}\]
a) by \( 2 \) percentage points, b) by \( 25\% \)
a) by \( 20 \) percentage points, b) by \( 4\% \)
a) by \( 20 \) percentage points, b) by \( 25\% \)
a) by \( 2 \) percentage points, b) by \( 4\% \)

1003066906

Level: 
B
The results of a survey considering the support for political parties \( Y \) and \( Z \) are presented in the table below. a) How many percentage points have the support for party \( Y \) increased? b) How much has the percentage of people supporting party \( Z \) decreased? \[\begin{array}{|c|c|c|} \hline & \text{February} & \text{March} \\\hline Y & 16\% & 20\% \\\hline Z & 10\% & 8\% \\\hline \end{array}\]
a) by \( 4 \) percentage points, b) by \( 20\% \)
a) by \( 25 \) percentage points, b) by \( 2\% \)
a) by \( 25 \) percentage points, b) by \( 20\% \)
a) by \( 4 \) percentage points, b) by \( 2\% \)