Quiz — 65cb529149014_Corrigé2-Série N°1-Arithmétique.pdf

Question 1 sur 10 20:00

[{"id":30620,"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 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\": \"24\"}}","_debug_options_count":4},{"id":30621,"question":"Le nombre 123456789 est-il divisible par 3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un nombre est divisible par 3 si la somme de ses chiffres est divisible par 3. 1+2+3+4+5+6+7+8+9 = 45, et 45 est divisible par 3.","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":30622,"question":"Quel est le PPCM de 12 et 15 ?","option_a":"30","option_b":"60","option_c":"90","option_d":"180","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\": \"180\"}}","_debug_options_count":4},{"id":30623,"question":"Si a ≡ 3 (mod 5) et b ≡ 2 (mod 5), alors a + b ≡ ? (mod 5)","option_a":"0","option_b":"1","option_c":"5","option_d":"10","option_e":"","option_f":"","bonne_reponse":"b","explication":"a ≡ 3 (mod 5) signifie que a = 5k + 3, et b ≡ 2 (mod 5) signifie que b = 5m + 2. Donc a + b = 5(k+m) + 5 ≡ 0 (mod 5), mais 5 ≡ 0 (mod 5), donc a + b ≡ 5 ≡ 0 (mod 5). Cependant, 5 ≡ 0 (mod 5), donc la réponse correcte est 0. Correction : l'option correcte est 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\": \"10\"}}","_debug_options_count":4},{"id":30624,"question":"Le nombre 17 est-il un nombre premier ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un nombre premier n'a que deux diviseurs : 1 et lui-même. 17 ne peut être divisé que par 1 et 17, donc c'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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30625,"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":30626,"question":"Si a et b sont deux entiers tels que a = 5 et b = 7, alors a×b + a + b = ?","option_a":"35","option_b":"47","option_c":"42","option_d":"52","option_e":"","option_f":"","bonne_reponse":"b","explication":"a×b + a + b = 5×7 + 5 + 7 = 35 + 12 = 47.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"35\", \"b\": \"47\", \"c\": \"42\", \"d\": \"52\"}}","_debug_options_count":4},{"id":30627,"question":"Le théorème de Bézout s'applique-t-il toujours à deux entiers quelconques ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème de Bézout s'applique à tous les entiers a et b : il existe toujours deux entiers u et v tels que a×u + b×v = PGCD(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":30628,"question":"Quel est le reste de la division de 1234 par 11 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Pour trouver le reste de 1234 ÷ 11, on utilise la méthode des congruences : 1234 = 11×112 + 2, donc le reste est 2.","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\": \"2\", \"d\": \"3\"}}","_debug_options_count":4},{"id":30629,"question":"Si a ≡ 4 (mod 7), alors a² ≡ ? (mod 7)","option_a":"1","option_b":"2","option_c":"4","option_d":"16","option_e":"","option_f":"","bonne_reponse":"b","explication":"Si a ≡ 4 (mod 7), alors a² ≡ 4² ≡ 16 ≡ 2 (mod 7), car 16 - 2 = 14 est divisible par 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\": \"1\", \"b\": \"2\", \"c\": \"4\", \"d\": \"16\"}}","_debug_options_count":4}]