C

9000089005

Level: 
C
There are two types of cheese in a shop. Altogether \(153\) customer were in the shop during a day. From this total, \(65\) customers bought the first cheese. From the same total, \(49\) customers bought the second cheese. \(20\%\) of customers which bought at least one of the types of cheese bought actually both types. How many customers did not buy any of these two cheeses?
\(58\)
\(39\)
\(19\)

9000089007

Level: 
C
A class in the school has \(35\) students. On the last holiday the students visited Slovakia, Croatia and Bulgaria. From the total amount of \(35\), \(7\) students have been in Slovakia, \(7\) students have been in Croatia, \(5\) students have been in Bulgaria, \(21\) students have not been abroad, one student was in every of these countries, two students have been in both Bulgaria and Croatia but not in Slovakia, one student has been in both Bulgaria and Slovakia but not in Croatia. How many students visited either Slovakia or Croatia?
\(11\)
\(7\)
\(3\)

9000089003

Level: 
C
Students from a class bought a snack in the school lunch-room. There were \(31\) students in the class in total. Altogether \(8\) students had snack from their home and they did not buy anything. Altogether \(12\) students bought hamburger and \(15\) students bought hot-dog. How many students bought both hamburger and hot-dog?
\(4\)
\(19\)
\(8\)

9000087504

Level: 
C
Assuming \(x\in \mathbb{R}\setminus \left \{-\frac{3} {5}\right \}\), find the quotient of the polynomials. \[ (5x^{3} - 2x^{2} + x + 1) : (5x + 3) \]
\(x^{2} - x + \frac{4} {5} - \frac{\frac{7} {5} } {5x+3}\)
\(x^{2} - x + \frac{4} {5} + \frac{\frac{7} {5} } {5x+3}\)
\(x^{2} - x + \frac{4} {5} - \frac{\frac{9} {5} } {5x+3}\)
\(x^{2} - x + \frac{4} {5} + \frac{\frac{9} {5} } {5x+3}\)

9000087505

Level: 
C
Assuming \(x\in \mathbb{R}\setminus \left \{-\frac{1} {2}\right \}\), find the quotient of the polynomials. \[ (4x^{3} - 1) : (2x + 1) \]
\(2x^{2} - x + \frac{1} {2} - \frac{\frac{3} {2} } {2x+1}\)
\(2x^{2} + x + \frac{1} {2} - \frac{\frac{3} {2} } {2x+1}\)
\(2x^{2} - x + \frac{1} {4} - \frac{\frac{3} {2} } {2x+1}\)
\(2x^{2} + x + \frac{1} {4} - \frac{\frac{3} {2} } {2x+1}\)

9000087508

Level: 
C
Assuming \(x\in \mathbb{R}\setminus \left \{0, 1, 3\right \}\), find the quotient of the polynomials. \[ (-5x^{4} + 4x^{2} + 3x - 4) : (x^{3} - 4x^{2} + 3x) \]
\(- 5x - 20 + \frac{-61x^{2}+63x-4} {x^{3}-4x^{2}+3x} \)
\(- 5x - 20 + \frac{16x^{2}+23x+36} {x^{3}-4x^{2}+3x} \)
\(- 5x - 10 + \frac{-61x^{2}+63x-4} {x^{3}-4x^{2}+3x} \)
\(- 5x - 10 + \frac{-16x^{2}+23x-36} {x^{3}-4x^{2}+3x} \)