{"id":843763,"date":"2021-08-23T22:23:29","date_gmt":"2021-08-24T01:23:29","guid":{"rendered":"https:\/\/www.estrategiaconcursos.com.br\/blog\/?p=843763"},"modified":"2021-08-25T11:53:35","modified_gmt":"2021-08-25T14:53:35","slug":"recurso-pcdf-escrivao-matematica-e-raciocinio-logico","status":"publish","type":"post","link":"https:\/\/www.estrategiaconcursos.com.br\/blog\/recurso-pcdf-escrivao-matematica-e-raciocinio-logico\/","title":{"rendered":"RECURSO PCDF (Escriv\u00e3o): Matem\u00e1tica e Racioc\u00ednio L\u00f3gico"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Fala, pessoal!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sou o Eduardo Mocellin, professor de Matem\u00e1tica e de Racioc\u00ednio L\u00f3gico do Estrat\u00e9gia Concursos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Neste artigo, disponibilizo um embasamento para que o candidato elabore um recurso para uma quest\u00e3o da prova da PCDF de 2021 para o <strong>cargo de Escriv\u00e3o<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Antes de analisarmos a quest\u00e3o, convido voc\u00ea a me seguir no Instagram: <strong><a href=\"https:\/\/www.instagram.com\/edu.mocellin\"><strong>@edu.mocellin<\/strong><\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Vamos ao problema:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Seis pessoas devem se reunir em uma mesa redonda, mas duas delas n\u00e3o podem se sentar uma ao lado da outra. Nessa situa\u00e7\u00e3o, a quantidade de maneiras distintas de essas seis pessoas sentarem em torno dessa mesa \u00e9 superior a 400.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Gabarito do professor: ERRADO.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Gabarito preliminar da banca: CERTO.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-pale-cyan-blue-background-color has-background wp-block-paragraph\"><strong>An\u00e1lise da justificativa da banca<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Vejamos a justificativa apontada pela banca:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"872\" height=\"326\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221056\/image-691.png\" alt=\"\" class=\"wp-image-843765\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221056\/image-691.png 872w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221056\/image-691-300x112.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221056\/image-691-768x287.png 768w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221056\/image-691-610x228.png 610w\" sizes=\"auto, (max-width: 872px) 100vw, 872px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-vivid-red-color has-text-color wp-block-paragraph\">Observe que a banca se equivocou ao dizer que &#8220;<strong>uma das pessoas que tem restri\u00e7\u00e3o de posicionamento na mesa tem <\/strong><strong><u>seis possibilidades<\/u><\/strong><strong> de tomar assento nessa mesa<\/strong>&#8220;.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Isso porque, <strong><u>em uma disposi\u00e7\u00e3o circular<\/u><\/strong>, <strong><u>a primeira pessoa inserida na mesa apenas cria um referencial<\/u><\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Suponha que uma das pessoas que tem restri\u00e7\u00e3o de posicionamento \u00e9 a pessoa <strong>A<\/strong>. Vamos inseri-la na mesa:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"210\" height=\"209\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221143\/image-693.png\" alt=\"\" class=\"wp-image-843767\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221143\/image-693.png 210w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221143\/image-693-150x150.png 150w\" sizes=\"auto, (max-width: 210px) 100vw, 210px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Note que, observando essa mesa de um outro \u00e2ngulo (girando ela em 180 graus), temos a seguinte disposi\u00e7\u00e3o:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"209\" height=\"207\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221159\/image-695.png\" alt=\"\" class=\"wp-image-843769\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221159\/image-695.png 209w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221159\/image-695-150x150.png 150w\" sizes=\"auto, (max-width: 209px) 100vw, 209px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Em outras palavras, <strong><u>n\u00e3o existem seis possibilidades para se inserir a primeira pessoa<\/u><\/strong> pois, na verdade, essa pessoa criou apenas um referencial.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Considerando que <strong>h\u00e1 apenas <u>uma forma<\/u> de inserir a primeira pessoa<\/strong>, o restante do racioc\u00ednio da banca est\u00e1 correto. Portanto, o racioc\u00ednio correto seria o seguinte:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><em>&#8220;<\/em><strong><em>Ao selecionar uma das pessoas que tem restri\u00e7\u00e3o de posicionamento na mesa, ela cria um referencial, havendo uma \u00fanica possibilidade de ela tomar assento na mesa<\/em><\/strong><em>. A segunda pessoa com restri\u00e7\u00e3o, <\/em><strong><em>uma vez j\u00e1 fixado esse referencial<\/em><\/strong><em>, teria ent\u00e3o tr\u00eas possibilidades de tomar assento \u00e0 mesa. Portanto, as duas pessoas com restri\u00e7\u00e3o de posicionamento teriam <\/em><strong>1 \u00d7 3 = 3 <em>possibilidade<\/em>s de <em>posicionamento<\/em><\/strong><em>. Como as outras quatro pessoas podem se sentar em qualquer local, ent\u00e3o tem-se <\/em><strong>3<\/strong>\u00d74! = <strong>3<\/strong> \u00d7 24 = <strong>72<em> possibilidades<\/em><\/strong><em> de essas pessoas tomarem assento \u00e0 mesa.&#8221;<\/em><\/p>\n\n\n\n<p class=\"has-text-align-center has-pale-cyan-blue-background-color has-background wp-block-paragraph\"><strong>Outra forma de resolver o problema<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Primeiramente, vamos <strong><u>desconsiderar<\/u><\/strong> a restri\u00e7\u00e3o de que duas pessoas n\u00e3o podem sentar lado a lado. Nesse caso, o <strong><u>n\u00famero de possibilidades em que 6 pessoas podem se reunir em uma mesa redonda<\/u><\/strong> \u00e9 a Permuta\u00e7\u00e3o Circular de 6:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"404\" height=\"58\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221300\/image-697.png\" alt=\"\" class=\"wp-image-843771\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221300\/image-697.png 404w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221300\/image-697-300x43.png 300w\" sizes=\"auto, (max-width: 404px) 100vw, 404px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Desses 120 casos, <strong><u>devemos subtrair os casos em que as duas pessoas sentam juntas<\/u><\/strong>. Considere a seguinte disposi\u00e7\u00e3o em que fixamos as pessoas A e B que n\u00e3o poderiam sentar juntas:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"247\" height=\"234\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221312\/image-699.png\" alt=\"\" class=\"wp-image-843773\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">O n\u00famero de possibilidades de as 6 pessoas sentarem com a disposi\u00e7\u00e3o &#8220;A-B&#8221; \u00e9 a permuta\u00e7\u00e3o circular de 5 elementos:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"396\" height=\"66\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221400\/image-701.png\" alt=\"\" class=\"wp-image-843775\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221400\/image-701.png 396w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221400\/image-701-300x50.png 300w\" sizes=\"auto, (max-width: 396px) 100vw, 396px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Veja essa nova disposi\u00e7\u00e3o em que A e B sentam juntas: &#8220;B-A&#8221;.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"282\" height=\"260\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221417\/image-703.png\" alt=\"\" class=\"wp-image-843777\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">O n\u00famero de possibilidades de as 6 pessoas sentarem com a disposi\u00e7\u00e3o &#8220;B-A&#8221; tamb\u00e9m \u00e9 a permuta\u00e7\u00e3o circular de 5 elementos:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"381\" height=\"60\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221429\/image-705.png\" alt=\"\" class=\"wp-image-843779\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221429\/image-705.png 381w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221429\/image-705-300x47.png 300w\" sizes=\"auto, (max-width: 381px) 100vw, 381px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Logo, <strong>descontando todos os casos em que as duas pessoas n\u00e3o podem sentar juntas<\/strong>, ficamos com as 72 possibilidades j\u00e1 obtidas:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"538\" height=\"65\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221450\/image-707.png\" alt=\"\" class=\"wp-image-843781\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221450\/image-707.png 538w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221450\/image-707-300x36.png 300w\" sizes=\"auto, (max-width: 538px) 100vw, 538px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Em resumo, a resposta correta \u00e9:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"263\" height=\"61\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221503\/image-709.png\" alt=\"\" class=\"wp-image-843783\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Logo, a quantidade de maneiras distintas de essas seis pessoas sentarem em torno dessa mesa \u00e9 <strong>inferior<\/strong> a 400.<\/p>\n\n\n\n<p class=\"has-text-align-center has-pale-cyan-blue-background-color has-background wp-block-paragraph\"><strong>Considera\u00e7\u00f5es Finais<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Espero que a explana\u00e7\u00e3o acima sirva como um bom embasamento para aqueles que desejam pleitear a mudan\u00e7a do gabarito. At\u00e9 a pr\u00f3xima!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.estrategiaconcursos.com.br\/professor\/eduardo-mocellin-2280\/\"><strong>Prof. Eduardo Mocellin<\/strong><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Instagram<\/strong>:&nbsp;<a href=\"https:\/\/www.instagram.com\/edu.mocellin\"><strong>@edu.mocellin<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fala, pessoal! Sou o Eduardo Mocellin, professor de Matem\u00e1tica e de Racioc\u00ednio L\u00f3gico do Estrat\u00e9gia Concursos. Neste artigo, disponibilizo um embasamento para que o candidato elabore um recurso para uma quest\u00e3o da prova da PCDF de 2021 para o cargo de Escriv\u00e3o. Antes de analisarmos a quest\u00e3o, convido voc\u00ea a me seguir no Instagram: @edu.mocellin [&hellip;]<\/p>\n","protected":false},"author":2051,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"post_tipo":"article","footnotes":""},"categories":[1],"tags":[],"tax_estado":[219970],"class_list":["post-843763","post","type-post","status-publish","format-standard","hentry","category-cursos-e-concursos","tax_estado-df"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.7 (Yoast SEO v27.7) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>RECURSO PCDF (Escriv\u00e3o): Matem\u00e1tica e Racioc\u00ednio L\u00f3gico<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blog-estrategia.mystagingwebsite.com\/recurso-pcdf-escrivao-matematica-e-raciocinio-logico\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"RECURSO PCDF (Escriv\u00e3o): Matem\u00e1tica e Racioc\u00ednio L\u00f3gico\" \/>\n<meta property=\"og:description\" content=\"Fala, pessoal! Sou o Eduardo Mocellin, professor de Matem\u00e1tica e de Racioc\u00ednio L\u00f3gico do Estrat\u00e9gia Concursos. Neste artigo, disponibilizo um embasamento para que o candidato elabore um recurso para uma quest\u00e3o da prova da PCDF de 2021 para o cargo de Escriv\u00e3o. Antes de analisarmos a quest\u00e3o, convido voc\u00ea a me seguir no Instagram: @edu.mocellin [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blog-estrategia.mystagingwebsite.com\/recurso-pcdf-escrivao-matematica-e-raciocinio-logico\/\" \/>\n<meta property=\"og:site_name\" content=\"Estrat\u00e9gia Concursos\" \/>\n<meta property=\"article:published_time\" content=\"2021-08-24T01:23:29+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-08-25T14:53:35+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/08\/23221056\/image-691.png\" \/>\n\t<meta property=\"og:image:width\" content=\"872\" \/>\n\t<meta property=\"og:image:height\" content=\"326\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Eduardo Mocellin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@EstratConcursos\" \/>\n<meta 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