36ªOlimpíada Brasileira de Matemática -OBM

www.obm.org.br

A cada ano, mais e mais estudantes de escolas públicas e priva-das em todo o Brasil são desafiados pelos problemas originais ecriativos daOlimpíada Brasileira de Matemática -OBM.

Além receberem medalhas e prêmios, os vencedores participamdo processo de seleção para formar as equipes que representamo Brasil nas diversas competições internacionais de Matemática.

Faça a sua inscrição na OBM com o coordenador responsável nasua escola.

•Nível 1 -

•Nível 2 -

•Nível 3 -

alunos dos 6º e 7º anos do ensino fundamental.

alunos dos 8º e 9º anos do ensino fundamental.

alunos do ensino médio.

Primeira Fase- terça-feira, 3 de junho de 2014 - níveis 1, 2 e 3.

Segunda Fase

- sábado, 6 de setembro de 2014 - níveis 1, 2 e 3.

Terceira Fase- sábado, 25 de outubro de 2014 - níveis 1, 2 e 3;- domingo, 26 de outubro de 2014 - níveis 2 e 3 (segundo diade prova).

Período de inscrições para escolas24 de março a 9 de maio de 2014 (apenas no site daOBM).

Veja o regulamento completo em:

OlimpíadaBrasileira deMatemática

2014

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Realização Apoio Secretaria da Olimpíada Brasileira de MatemáticaEstrada Dona Castorina, 110

Jardim Botânico, Rio de Janeiro - RJTel: (21) 25295077

Fax: (21) 25295023e-mail: obm@impa.brsite: www.obm.org.br

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Respostas: 1) A 2) B 3) B

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2x + 2y = 83y - 2y = x

12 45 6023 14 4024 15 27

Problema:

1) A professora Marli propôs uma eleição para

representante da sala do sexto ano.

Cinco alunos se apresentaram como candidatos.

Todos os alunos votaram e quem venceu foi

Pedrinho, com 10 votos.

Os outros quatro candidatos tiveram diferentes

números de votos cada um. No mínimo, quantos

são os alunos dessa sala?

A) 16 B) 30 C) 34 D) 36 E) 40

2) Determine o maior divisor comum de todos

os números de 9 algarismos distintos formados

com os algarismos 1, 2, 3, 4, 5, 6, 7, 8, 9.

A) 3 B) 9 C) 18 D) 27 E) 123456789

3) Considere cinco pontos no plano. Qual é a

quantidade máxima de triângulos equiláteros

com vértices em três desses cinco pontos?

A) 2 B) 3 C) 4 D) 5 E) 6