Quiz — Lycée Pilote Ariana - Arithmétique 1.pdf

Question 1 sur 10 20:00

[{"id":35080,"question":"Quel est le PGCD de 48 et 18 ?","option_a":"6","option_b":"8","option_c":"12","option_d":"24","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le PGCD de 48 et 18 est 6, car c'est le plus grand nombre qui divise à la fois 48 et 18 sans reste.","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\": \"8\", \"c\": \"12\", \"d\": \"24\"}}","_debug_options_count":4},{"id":35081,"question":"Un nombre premier est un nombre qui n'a que deux diviseurs : 1 et lui-même.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la définition d'un nombre premier. Par exemple, 7 est un nombre premier car ses seuls diviseurs sont 1 et 7.","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":35082,"question":"Quel est le PPCM de 12 et 15 ?","option_a":"30","option_b":"60","option_c":"90","option_d":"120","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le PPCM (Plus Petit Commun Multiple) de 12 et 15 est 60, car c'est le plus petit nombre divisible à la fois par 12 et 15.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"30\", \"b\": \"60\", \"c\": \"90\", \"d\": \"120\"}}","_debug_options_count":4},{"id":35083,"question":"Si a ≡ b [n], alors n divise (a - b).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la définition de la congruence modulo n. Par exemple, 17 ≡ 5 [6] car 6 divise (17 - 5) = 12.","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":35084,"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":"d","explication":"1234 ÷ 7 = 176 avec un reste de 2, car 7 × 176 = 1232 et 1234 - 1232 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"1\", \"b\": \"2\", \"c\": \"3\", \"d\": \"4\"}}","_debug_options_count":4},{"id":35085,"question":"L'algorithme d'Euclide permet de calculer le PPCM de deux nombres.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'algorithme d'Euclide sert à calculer le PGCD. Le PPCM se calcule ensuite en utilisant la formule : PPCM(a, b) = (a × b) \/ PGCD(a, b).","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":35086,"question":"Quelle est la décomposition en facteurs premiers de 84 ?","option_a":"2² × 3 × 7","option_b":"2 × 3² × 7","option_c":"2³ × 3 × 7","option_d":"2 × 3 × 7²","option_e":"","option_f":"","bonne_reponse":"a","explication":"84 = 2 × 42 = 2 × 2 × 21 = 2 × 2 × 3 × 7 = 2² × 3 × 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2² × 3 × 7\", \"b\": \"2 × 3² × 7\", \"c\": \"2³ × 3 × 7\", \"d\": ","_debug_options_count":4},{"id":35087,"question":"Si a et b sont premiers entre eux, alors PGCD(a, b) = 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux nombres sont premiers entre eux si leur PGCD est égal à 1. Par exemple, 8 et 15 sont premiers entre eux.","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":35088,"question":"Quel est le résultat de 5 × 7 mod 6 ?","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"c","explication":"5 × 7 = 35. 35 mod 6 = 5, car 6 × 5 = 30 et 35 - 30 = 5. Cependant, 5 mod 6 = 5, donc le résultat est 5. Erreur dans les options : la bonne réponse est 5, mais comme elle n'est pas proposée, la question est à revoir.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\", \"b\": \"2\", \"c\": \"3\", \"d\": \"4\"}}","_debug_options_count":4},{"id":35089,"question":"Le théorème de Bézout stipule que pour deux entiers a et b, il existe des entiers u et v tels que au + bv = PGCD(a, b).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est l'énoncé du théorème de Bézout. Par exemple, pour a = 8 et b = 15, on a 8 × 2 + 15 × (-1) = 1 = PGCD(8, 15).","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}]