CONCURS #022
15.03.2022, ora 20:00Problema 1 [295 puncte]
$Daca\ 5\ caiete\ costa\ 45\ lei,\ aflati\ cat\ costa\ 13\ caiete.$
Problema 2 [390 puncte]
$Numerele\ a\ si\ b\ sunt\ direct\ proportionale\ cu\ 3\ si\ 7,\ iar\ suma\ lor\ este\ 240.\ Calculati\ a\cdot b.$
Problema 3 [485 puncte]
$Aflati\ x\ din\ proportia\ \frac{2\cdot x+1}{24}=\frac{49}{56}.$
Problema 4 [580 puncte]
$Triunghiul\ ABC\ este\ isoscel\ cu\ AB=12,\ AC=25.\ Calculati\ perimetrul\ triunghiului\ ABC.$
Problema 5 [675 puncte]
$Aflati\ numarul\ divizorilor\ numarului\ A=6^{31}.$
Problema 6 [770 puncte]
$Fie\ A,\ B,\ C\ cele\ mai\ mici\ numare\ naturale\ cu\ 3,\ 5,\ respectiv\ 6\ divizori.$ $Aflati\ numarul\ divizorilor\ numarului\ A\cdot\ B\cdot C.$
Problema 7 [865 puncte]
$Aflati\ cardinalul\ multimii\ A=\{ a\in \mathbb{N}\ |\ (a+2)/(a^{2}+5a+78) \}.$
Problema 8 [960 puncte]
$Pentru\ cate\ valori\ ale\ lui\ n,\ numerele\ n+5\ si\ n+149\ sunt\ simultan\ patrate\ perfecte?$