Quadratic equations and inequalities

1003085408

Level: 
C
A swimming pool can be filled by two pipes in \( 5 \) hours. It takes \( 24 \) hours longer to fill the pool by only the first pipe than by only the second one. In how many hours does the first pipe fill the pool, in how many hours does the second one? Find the sum of both times.
\( 36 \) hours
\( 20 \) hours
\( 18 \) hours
\( 32 \) hours

1003085405

Level: 
C
Little Red Riding Hood ran (at instantaneous speed) through the forest to see her grandmother, who lives in a cottage, which is \( 4\,\mathrm{km} \) distant. If she ran by \( 4\,\mathrm{km/h} \) faster, she would meet her grandmother \( 10 \) minutes sooner. What was Little Red Riding Hood’s speed?
\( 8\,\mathrm{km/h} \)
\( 12\,\mathrm{km/h} \)
\( 10\,\mathrm{km/h} \)
\( 6\,\mathrm{km/h} \)

1003085401

Level: 
B
On their birthday students bring candies for their classmates. The birthday person gives a candy to every other student, not to himself or herself. During a year, \( 650 \) candies have been given away. Find out how many students are there in the class. (Note: All students’ birthdays were on school days.)
\( 26 \)
\( 25 \)
\( 27 \)
\( 24 \)

1003067810

Level: 
C
Find the solution set of the following equation. \[ |x-4|\cdot(x+4)=4 \]
\( \left\{-2\sqrt3;2\sqrt3;2\sqrt5\right\} \)
\( \{ -4; 4 \} \)
\( \left\{ -2\sqrt3;2\sqrt3\right\} \)
\( \left\{ 2\sqrt3;2\sqrt5\right\} \)
\( \left\{-2\sqrt5;-2\sqrt3;2\sqrt3;2\sqrt5 \right\} \)