9000084905
Level:
B
In the following list find the number such that the prime factorization of this
number contains just two different primes or powers of two different primes.
\(100\)
\(5\)
\(25\)
\(120\)
\(121\)
B
9000083610
Level:
B
Assuming \(x\neq \pm y\)
and \(y\neq 2x\),
simplify the expression:
\[
\left ( \frac{2x}
{x + y} + \frac{y}
{x - y} - \frac{y^{2}}
{x^{2} - y^{2}}\right ) : \left ( \frac{1}
{x + y} + \frac{x}
{x^{2} - y^{2}}\right )
\]
\(x\)
\(2x - y\)
\(\frac{x}
{2x-y}\)
\(1\)
9000084910
Level:
B
In the following list find the number such that the prime factorization of this
number contains only one prime.
\(125\)
\(15\)
\(100\)
\(250\)
\(768\)
9000080907
Level:
B
Find \(B'_{A}\) (the
complement to \(B\)
in \(A\))
for \(A =\mathbb{Z}\)
and \(B = \{x\in \mathbb{Z},\left |x\right | > 3\}\).
\(\{ - 3,-2,-1,0,1,2,3\}\)
\(\{ - 2,-1,0,1,2\}\)
\(\{0,1,2,3\}\)
\(\{1,2,3\}\)
9000085302
Level:
B
There are \(32\) students
in the class (\(20\)
boys and \(12\)
girls). One quarter of the boys and one quarter of the girls are excellent students.
Suppose that one boy and one girl, both excellent students, move to another school.
Find the difference in the ratio of excellent students in the class before and after the
change in the class.
\(5\, \%\)
\(6.25\, \%\)
\(7.5\, \%\)
\(8.25\, \%\)
9000080908
Level:
B
Find the set difference \(A\setminus B\)
for \(A = \{ - 2,-1,0,1,2\}\)
and \(B = \{x\in \mathbb{Z},x < 2\}\).
\(\{2\}\)
\(\{ - 2,-1,0,1,2\}\)
\(\{0,1\}\)
\(\emptyset \)
9000085303
Level:
B
The shop received \(30\)
pieces of TV from the manufacturer NoName. Five TVs in this delivery
were defect. The shop also received TVs from the manufacturer
GoodName. All these TVs were perfect. The final inspection revealed that
\(10\, \%\) of
TVs were defect in total. Use these information to find out how many TVs have been
supplied from the producer GoodName.
\(20\)
\(25\)
\(18\)
\(16\)
9000080909
Level:
B
Find the set difference \(B\setminus A\)
for \(A = \{x\in \mathbb{Z},x < 2\}\)
and \(B = \{x\in \mathbb{Z},x < 5\}\).
\(\{2,3,4\}\)
\(\{x\in \mathbb{Z},x < 2\}\)
\(\{3,4\}\)
\(\emptyset \)
9000085304
Level:
B
The final score of the hockey match between teams
\(A\) and
\(B\) was
\(2 : 2\). The goaltender
of \(A\) had
success rate \(90\, \%\)
(he stopped \(90\, \%\)
of all shots on goal) and the goaltender of the team
\(B\) had fail
rate \(20\, \%\)
(\(20\, \%\) of all
shots on goal went into his net). How many shots on goal has been in the match in
total?
\(30\)
\(25\)
\(35\)
\(40\)
9000080910
Level:
B
Find the set difference \(A\setminus B\)
for \(A = \{x\in \mathbb{Z},\left |x\right | < 3\}\)
and \(B = \{x\in \mathbb{N},x < 5\}\).
\(\{ - 2,-1,0\}\)
\(\emptyset \)
\(\{- 2,-1\}\)
\(\{3,4\}\)