C

9000089006

Level: 
C
A questionnaire on popular singers has been filled by \(200\) girls from a high-school. The girls had to mark the singers from three most popular (Justin Timberlake, Justin Bieber and Axl Rose) which they like. Justin Timberlake got \(78\) votes, Justin Bieber got \(75\) votes and Axl Rose \(101\) votes. There were \(28\) girls which voted for all three singers. There were \(22\) girls which voted for two singers. One half of this amount are fans of the pair Bieber and Rose. The number of the girls which like only Justin Bieber is smaller by \(7\) comparing to the number of girls which like only Justin Timberlake. How many girls did not like any of these three singers?
\(24\)
\(32\)
\(11\)

9000089004

Level: 
C
Students in a university are allowed to buy either lunch or dinner in a student's canteen. There are \(129\) freshmen students in total. Altogether \(116\) freshmen students buy the lunch or dinner. From this amount, \(62\) students buy just one meal. The number of freshmen students which buy lunch is bigger by \(46\) than the number of freshmen students which buy dinner. How many freshmen students buy only the dinner?
\(8\)
\(54\)
\(62\)

9000089002

Level: 
C
Students from a class decided to order books for forthcoming holiday. The book-shop in the neighborhood had two bestsellers on the stock: a crime novel and a horror stories. There were \(31\) students in the class in total. From this total, \(22\) students bought horror stories. Altogether \(12\) students bought just one of the books. Two students did not buy any of these books. How many students bought the crime novel?
\(24\)
\(7\)
\(5\)

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?
\(58\)
\(39\)
\(19\)

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. \[ (-5x^{4} + 4x^{2} + 3x - 4) : (x^{3} - 4x^{2} + 3x) \]
\(- 5x - 20 + \frac{-61x^{2}+63x-4} {x^{3}-4x^{2}+3x} \)
\(- 5x - 20 + \frac{16x^{2}+23x+36} {x^{3}-4x^{2}+3x} \)
\(- 5x - 10 + \frac{-61x^{2}+63x-4} {x^{3}-4x^{2}+3x} \)
\(- 5x - 10 + \frac{-16x^{2}+23x-36} {x^{3}-4x^{2}+3x} \)