Quiz — 65cb8934f0b75_énoncé_Série n° 30-Arithmétique.pdf

Question 1 sur 10 20:00

[{"id":28990,"question":"Quel est le PGCD de 56 et 98 ?","option_a":"12","option_b":"14","option_c":"16","option_d":"18","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le PGCD de 56 et 98 est 14, car 14 est le plus grand nombre qui divise à la fois 56 (56 = 14 × 4) et 98 (98 = 14 × 7).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"12\", \"b\": \"14\", \"c\": \"16\", \"d\": \"18\"}}","_debug_options_count":4},{"id":28991,"question":"Si a ≡ 3 [5] et b ≡ 2 [5], alors a + b ≡ ? [5]","option_a":"0","option_b":"1","option_c":"5","option_d":"7","option_e":"","option_f":"","bonne_reponse":"b","explication":"En ajoutant les congruences, on obtient a + b ≡ 3 + 2 ≡ 5 ≡ 0 [5]. La bonne réponse est donc 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"5\", \"d\": \"7\"}}","_debug_options_count":4},{"id":28992,"question":"Vrai ou Faux ? Tout nombre premier est impair.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux : 2 est un nombre premier et il est pair. C'est le seul nombre premier pair.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":28993,"question":"Quel est le PPCM de 12 et 18 ?","option_a":"24","option_b":"36","option_c":"48","option_d":"72","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le PPCM de 12 et 18 est 36, car 36 est le plus petit multiple commun à 12 (12 × 3) et 18 (18 × 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"24\", \"b\": \"36\", \"c\": \"48\", \"d\": \"72\"}}","_debug_options_count":4},{"id":28994,"question":"Si n est un entier tel que n ≡ 1 [3], alors n² ≡ ? [3]","option_a":"0","option_b":"1","option_c":"2","option_d":"3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Si n ≡ 1 [3], alors n² ≡ 1² ≡ 1 [3]. La bonne réponse est donc 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"3\"}}","_debug_options_count":4},{"id":28995,"question":"Vrai ou Faux ? Le nombre 1 est un nombre premier.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux : Par définition, un nombre premier a exactement deux diviseurs distincts : 1 et lui-même. Le nombre 1 n'a qu'un seul diviseur, donc il n'est pas premier.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":28996,"question":"Quel est le reste de la division de 1234 par 7 ?","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"a","explication":"1234 ÷ 7 = 176 avec un reste de 2, car 7 × 176 = 1232 et 1234 - 1232 = 2. Le reste est donc 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\", \"b\": \"2\", \"c\": \"3\", \"d\": \"4\"}}","_debug_options_count":4},{"id":28997,"question":"Vrai ou Faux ? Si a ≡ b [n], alors a² ≡ b² [n].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai : Si a ≡ b [n], alors a = b + kn pour un certain entier k. En élevant au carré, on obtient a² = b² + 2bkn + k²n², donc a² ≡ b² [n].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":28998,"question":"Quel est le plus petit nombre premier supérieur à 50 ?","option_a":"51","option_b":"53","option_c":"57","option_d":"59","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le plus petit nombre premier supérieur à 50 est 53, car 51 = 3 × 17 (non premier) et 53 est un nombre premier.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"51\", \"b\": \"53\", \"c\": \"57\", \"d\": \"59\"}}","_debug_options_count":4},{"id":28999,"question":"Si a ≡ 4 [7] et b ≡ 5 [7], alors a × b ≡ ? [7]","option_a":"6","option_b":"20","option_c":"28","option_d":"35","option_e":"","option_f":"","bonne_reponse":"a","explication":"En multipliant les congruences, on obtient a × b ≡ 4 × 5 ≡ 20 ≡ 6 [7] (car 20 - 2 × 7 = 6). La bonne réponse est donc 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6\", \"b\": \"20\", \"c\": \"28\", \"d\": \"35\"}}","_debug_options_count":4}]