2000002901
Level:
B
Determine all the natural numbers that are solutions of the inequality:
\[
-\frac{x}{7} < \frac{5}{7}
\]
\( x \in \mathbb{N} \)
\( x \in \{0;1;2;3;4\} \)
\( x \in \{1;2;3;4\} \)
\( x \in \mathbb{N} \cup \{0;-1;-2;-3;-4\} \)
Linear equations and inequalities
2000002305
Level:
A
Find a real number, so that when placed into the box, the given equation has the root \(x = 3\).
\[\frac{2}{3}x-5= \fbox{$\phantom{5}$}\cdot x-1 \]
\( -\frac{2}{3} \)
\( 6 \)
\( 2 \)
\( \frac{4}{3} \)
2000002304
Level:
A
Find a real number, so that when placed into the box, the given equation has the root \(x = 0\).
\[-3x+10= \fbox{$\phantom{5}$}\cdot x-6 \]
such a number does not exist
any real number
\( 16 \)
\( -4 \)
2000002303
Level:
A
Find a real number, so that when placed into the box, the given equation has the root \(x = 0\).
\[-3x+10= \fbox{$\phantom{5}$}+2x \]
\( 10 \)
\( 5 \)
\( -10 \)
\( 0 \)
2000002302
Level:
A
Find a real number, so that when placed into the box, the given equation has the root \(x = -2\).
\[-x+10= \fbox{$\phantom{5}$}\cdot x-6 \]
\( -9 \)
\( -8\)
\(2 \)
\( 9\)
2000002301
Level:
A
Find a real number, so that when placed into the box, the given equation has the root \(x = 2\).
\[-x+10= \fbox{$\phantom{5}$} \cdot x-6 \]
\( 7 \)
\( 8 \)
\( 2 \)
\( 6 \)
1003197408
Level:
C
The painter \( A \) takes \( 15 \) hours to paint a flat. The painter \( B \) takes \( 12 \) hours to paint the same flat and the painter \( C \) takes \( 10 \) hours to complete the same task. The painter \( A \) starts to paint alone and after \( 2 \) hours joins him the painter \( B \). After the next hour the painter \( C \) starts to paint with them too. How long will all three painters paint together before completing the work?
\( 2\,\mathrm{h}\ 52\,\mathrm{min} \)
\( 3\,\mathrm{h}\ 8\,\mathrm{min} \)
\( 3\,\mathrm{h}\ 24\,\mathrm{min} \)
\( 4\,\mathrm{h} \)
1003197407
Level:
C
A hose can fill the garden pool in \( 20 \) hours. The owners bought a pump that guarantees filling the pool in \( 8 \) hours. However, a crack appeared in the pool's shell which can drain all the water from the full pool within \( 5 \) days. How long will it take to fill the pool with the hose and the pump at the same time as the water runs off through the crack?
exactly \( 6 \) hours
approximately \( 5.7 \) hours
approximately \( 5.5 \) hours
approximately \( 6.8 \) hours
1003197406
Level:
C
Each of two companies should deliver the same amount of raw material. While inspecting it was found out that the company \( A \) delivered \( 150\,\mathrm{kg} \) and the company \( B \) delivered \( 194\,\mathrm{kg} \). At the moment of inspection, company \( A \) has to deliver yet three times more than what is left to be delivered by company \( B \). Choose the equation which does NOT correspond to the described situation.
\( 3(x-150)=x-194 \), where \( x \) represents the total planned delivery of both companies.
\( x-150=3(x-194) \), where \( x \) represents the total planned delivery of both companies.
\( 150+3x=194+x \), where \( x \) represents the amount of raw material which is left to be delivered by company \( B \).
\( 150+x=194+\frac x3 \), where \( x \) represents the amount of raw material which is left to be delivered by company \( A \).
1003197405
Level:
C
Nine people travel by bus. The same number of people gets off the bus at each of three bus stops and then so many people get in to double the number of remaining bus passengers. After the third bus stop there are \( 30 \) people in the bus. How many passengers get off at each bus stop?
\( 3 \)
\( 2 \)
\( 1 \)
\( 6 \)