CONCURS #005
12-08-2022 17:10:34Problema 1 [350 puncte]
$Stiind\ ca\ 5\cdot x=6\cdot y\ si\ x=y+4,\ aflati\ x+y.$
Problema 2 [530 puncte]
$ Care\ este\ cel\ mai\ mare\ numar\ natural\ n\ pentru\ care\ 3^{n}\ divide\ pe\ 1\cdot\ 2\cdot\ 3\cdot\ ...\cdot\ 31?$
Problema 3 [710 puncte]
$Aflati\ suma\ numerelor\ naturale\ de\ trei\ cifre,\ care\ impartite\ la\ 50\ dau\ restul\ 13.$
Problema 4 [890 puncte]
$Aflati\ numarul\ \overline{abcd}\ stiind\ ca\ \overline{d6b9}+\overline{5c2a}=9014.$
Problema 5 [1070 puncte]
$Numerele\ divizibile\ cu\ 3\ se\ impart\ in\ grupe\ astfel:$
$\{0\},\{3,6\},\{9,12,15\},.... Care\ este\ primul\ numar\ din\ cea\ de-a\ 100-a\ grupa? $