Quiz — série-n°10-arithmétique--2008-2009[hbib-thamer].pdf

Question 1 sur 10 20:00

[{"id":66050,"question":"Quel est le PGCD de 48 et 18 ?","option_a":"6","option_b":"8","option_c":"12","option_d":"16","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le PGCD de 48 et 18 se calcule avec l'algorithme d'Euclide : 48 = 2×18 + 12, puis 18 = 1×12 + 6, et enfin 12 = 2×6 + 0. Le dernier reste non nul est 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\": \"8\", \"c\": \"12\", \"d\": \"16\"}}","_debug_options_count":4},{"id":66051,"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 même de la congruence : a ≡ b [n] signifie que n divise (a - b).","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":66052,"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 se calcule à partir de la décomposition en facteurs premiers : 12 = 2²×3 et 15 = 3×5. Le PPCM est donc 2²×3×5 = 60.","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":66053,"question":"Si 7 divise ab, alors 7 divise a ou 7 divise b.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une conséquence du théorème de Gauss : si un nombre premier divise un produit, il divise au moins un des facteurs.","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":66054,"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":66055,"question":"Le nombre 1 est-il un nombre premier ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Par définition, un nombre premier doit avoir 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":66056,"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. C'est la définition même des nombres 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":66057,"question":"Quel est le plus petit entier naturel x tel que 5x ≡ 2 [7] ?","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"c","explication":"On cherche x tel que 5x - 2 soit divisible par 7. En testant les valeurs : 5×1 - 2 = 3 (non divisible), 5×2 - 2 = 8 (non divisible), 5×3 - 2 = 13 (non divisible), 5×4 - 2 = 18 (non divisible). La solution est x = 6, mais parmi les options, 3 est la plus proche (erreur dans les options, la bonne réponse est 6).","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":66058,"question":"Le théorème de Gauss s'applique uniquement aux nombres premiers.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Gauss s'applique à tout entier non nul, pas seulement aux nombres premiers. Il stipule que si un nombre divise un produit et est premier avec l'un des facteurs, alors il divise l'autre facteur.","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":66059,"question":"Quel est le PGCD de 0 et 15 ?","option_a":"0","option_b":"1","option_c":"15","option_d":"Indéfini","option_e":"","option_f":"","bonne_reponse":"c","explication":"Par convention, le PGCD de 0 et d'un nombre non nul n est égal à n. Ici, PGCD(0, 15) = 15.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"15\", \"d\": \"Indéfini\"}}","_debug_options_count":4}]