{"id":90247,"date":"2025-06-01T10:23:51","date_gmt":"2025-06-01T10:23:51","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90247"},"modified":"2025-06-01T10:23:51","modified_gmt":"2025-06-01T10:23:51","slug":"an-international-conference-is-attended-by-65-people-they-all-speak-a","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/an-international-conference-is-attended-by-65-people-they-all-speak-a\/","title":{"rendered":"An international conference is attended by 65 people. They all speak a"},"content":{"rendered":"<p>An international conference is attended by 65 people. They all speak at least one of English, French and German language. Suppose 15 speak English and French, 13 speak English and German, 12 speak French and German and 5 speak all the three languages. A total of 30 people can speak German and 30 can speak French. What is the number of people who can speak only English?<\/p>\n<p>[amp_mcq option1=&#8221;17&#8243; option2=&#8221;20&#8243; option3=&#8221;22&#8243; option4=&#8221;40&#8243; correct=&#8221;option1&#8243;]<\/p>\n<div class=\"psc-box-pyq-exam-year-detail\">\n<div class=\"pyq-exam\">\n<div class=\"psc-heading\">This question was previously asked in<\/div>\n<div class=\"psc-title line-ellipsis\">UPSC CAPF &#8211; 2018<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-capf-2018.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-capf-2018\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nThe number of people who can speak only English is 17.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\n&#8211; Let E, F, and G be the sets of people who speak English, French, and German, respectively.<br \/>\n&#8211; Total people |E U F U G| = 65 (since all speak at least one language).<br \/>\n&#8211; We are given: |E \u2229 F| = 15, |E \u2229 G| = 13, |F \u2229 G| = 12, |E \u2229 F \u2229 G| = 5.<br \/>\n&#8211; We are also given: |G| = 30, |F| = 30.<br \/>\n&#8211; We can find the number of people speaking exactly two languages:<br \/>\n    &#8211; |E \u2229 F only| = |E \u2229 F| &#8211; |E \u2229 F \u2229 G| = 15 &#8211; 5 = 10<br \/>\n    &#8211; |E \u2229 G only| = |E \u2229 G| &#8211; |E \u2229 F \u2229 G| = 13 &#8211; 5 = 8<br \/>\n    &#8211; |F \u2229 G only| = |F \u2229 G| &#8211; |E \u2229 F \u2229 G| = 12 &#8211; 5 = 7<br \/>\n&#8211; We can find the number of people speaking only one language using the given total for F and G:<br \/>\n    &#8211; |G| = |G only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G|<br \/>\n      30 = |G only| + 8 + 7 + 5 => 30 = |G only| + 20 => |G only| = 10.<br \/>\n    &#8211; |F| = |F only| + |E \u2229 F only| + |F \u2229 G only| + |E \u2229 F \u2229 G|<br \/>\n      30 = |F only| + 10 + 7 + 5 => 30 = |F only| + 22 => |F only| = 8.<br \/>\n&#8211; The total number of people is the sum of those speaking only one language, exactly two languages, and all three:<br \/>\n    &#8211; |E U F U G| = |E only| + |F only| + |G only| + |E \u2229 F only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G|<br \/>\n    &#8211; 65 = |E only| + 8 + 10 + 10 + 8 + 7 + 5<br \/>\n    &#8211; 65 = |E only| + 48<br \/>\n    &#8211; |E only| = 65 &#8211; 48 = 17.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nThis problem can be effectively solved using a Venn diagram to visualize the different sections representing speakers of one, two, or three languages. The Principle of Inclusion-Exclusion is the formal mathematical basis for these calculations.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>An international conference is attended by 65 people. They all speak at least one of English, French and German language. Suppose 15 speak English and French, 13 speak English and German, 12 speak French and German and 5 speak all the three languages. A total of 30 people can speak German and 30 can speak &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"An international conference is attended by 65 people. They all speak a\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/an-international-conference-is-attended-by-65-people-they-all-speak-a\/#more-90247\">Detailed Solution<span class=\"screen-reader-text\">An international conference is attended by 65 people. They all speak a<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1114,1102],"class_list":["post-90247","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1114","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>An international conference is attended by 65 people. They all speak a<\/title>\n<meta name=\"description\" content=\"The number of people who can speak only English is 17. - Let E, F, and G be the sets of people who speak English, French, and German, respectively. - Total people |E U F U G| = 65 (since all speak at least one language). - We are given: |E \u2229 F| = 15, |E \u2229 G| = 13, |F \u2229 G| = 12, |E \u2229 F \u2229 G| = 5. - We are also given: |G| = 30, |F| = 30. - We can find the number of people speaking exactly two languages: - |E \u2229 F only| = |E \u2229 F| - |E \u2229 F \u2229 G| = 15 - 5 = 10 - |E \u2229 G only| = |E \u2229 G| - |E \u2229 F \u2229 G| = 13 - 5 = 8 - |F \u2229 G only| = |F \u2229 G| - |E \u2229 F \u2229 G| = 12 - 5 = 7 - We can find the number of people speaking only one language using the given total for F and G: - |G| = |G only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G| 30 = |G only| + 8 + 7 + 5 =&gt; 30 = |G only| + 20 =&gt; |G only| = 10. - |F| = |F only| + |E \u2229 F only| + |F \u2229 G only| + |E \u2229 F \u2229 G| 30 = |F only| + 10 + 7 + 5 =&gt; 30 = |F only| + 22 =&gt; |F only| = 8. - The total number of people is the sum of those speaking only one language, exactly two languages, and all three: - |E U F U G| = |E only| + |F only| + |G only| + |E \u2229 F only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G| - 65 = |E only| + 8 + 10 + 10 + 8 + 7 + 5 - 65 = |E only| + 48 - |E only| = 65 - 48 = 17.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/an-international-conference-is-attended-by-65-people-they-all-speak-a\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"An international conference is attended by 65 people. They all speak a\" \/>\n<meta property=\"og:description\" content=\"The number of people who can speak only English is 17. - Let E, F, and G be the sets of people who speak English, French, and German, respectively. - Total people |E U F U G| = 65 (since all speak at least one language). - We are given: |E \u2229 F| = 15, |E \u2229 G| = 13, |F \u2229 G| = 12, |E \u2229 F \u2229 G| = 5. - We are also given: |G| = 30, |F| = 30. - We can find the number of people speaking exactly two languages: - |E \u2229 F only| = |E \u2229 F| - |E \u2229 F \u2229 G| = 15 - 5 = 10 - |E \u2229 G only| = |E \u2229 G| - |E \u2229 F \u2229 G| = 13 - 5 = 8 - |F \u2229 G only| = |F \u2229 G| - |E \u2229 F \u2229 G| = 12 - 5 = 7 - We can find the number of people speaking only one language using the given total for F and G: - |G| = |G only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G| 30 = |G only| + 8 + 7 + 5 =&gt; 30 = |G only| + 20 =&gt; |G only| = 10. - |F| = |F only| + |E \u2229 F only| + |F \u2229 G only| + |E \u2229 F \u2229 G| 30 = |F only| + 10 + 7 + 5 =&gt; 30 = |F only| + 22 =&gt; |F only| = 8. - The total number of people is the sum of those speaking only one language, exactly two languages, and all three: - |E U F U G| = |E only| + |F only| + |G only| + |E \u2229 F only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G| - 65 = |E only| + 8 + 10 + 10 + 8 + 7 + 5 - 65 = |E only| + 48 - |E only| = 65 - 48 = 17.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/an-international-conference-is-attended-by-65-people-they-all-speak-a\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:23:51+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"An international conference is attended by 65 people. They all speak a","description":"The number of people who can speak only English is 17. - Let E, F, and G be the sets of people who speak English, French, and German, respectively. - Total people |E U F U G| = 65 (since all speak at least one language). - We are given: |E \u2229 F| = 15, |E \u2229 G| = 13, |F \u2229 G| = 12, |E \u2229 F \u2229 G| = 5. - We are also given: |G| = 30, |F| = 30. - We can find the number of people speaking exactly two languages: - |E \u2229 F only| = |E \u2229 F| - |E \u2229 F \u2229 G| = 15 - 5 = 10 - |E \u2229 G only| = |E \u2229 G| - |E \u2229 F \u2229 G| = 13 - 5 = 8 - |F \u2229 G only| = |F \u2229 G| - |E \u2229 F \u2229 G| = 12 - 5 = 7 - We can find the number of people speaking only one language using the given total for F and G: - |G| = |G only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G| 30 = |G only| + 8 + 7 + 5 => 30 = |G only| + 20 => |G only| = 10. - |F| = |F only| + |E \u2229 F only| + |F \u2229 G only| + |E \u2229 F \u2229 G| 30 = |F only| + 10 + 7 + 5 => 30 = |F only| + 22 => |F only| = 8. - The total number of people is the sum of those speaking only one language, exactly two languages, and all three: - |E U F U G| = |E only| + |F only| + |G only| + |E \u2229 F only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G| - 65 = |E only| + 8 + 10 + 10 + 8 + 7 + 5 - 65 = |E only| + 48 - |E only| = 65 - 48 = 17.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/an-international-conference-is-attended-by-65-people-they-all-speak-a\/","og_locale":"en_US","og_type":"article","og_title":"An international conference is attended by 65 people. They all speak a","og_description":"The number of people who can speak only English is 17. - Let E, F, and G be the sets of people who speak English, French, and German, respectively. - Total people |E U F U G| = 65 (since all speak at least one language). - We are given: |E \u2229 F| = 15, |E \u2229 G| = 13, |F \u2229 G| = 12, |E \u2229 F \u2229 G| = 5. - We are also given: |G| = 30, |F| = 30. - We can find the number of people speaking exactly two languages: - |E \u2229 F only| = |E \u2229 F| - |E \u2229 F \u2229 G| = 15 - 5 = 10 - |E \u2229 G only| = |E \u2229 G| - |E \u2229 F \u2229 G| = 13 - 5 = 8 - |F \u2229 G only| = |F \u2229 G| - |E \u2229 F \u2229 G| = 12 - 5 = 7 - We can find the number of people speaking only one language using the given total for F and G: - |G| = |G only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G| 30 = |G only| + 8 + 7 + 5 => 30 = |G only| + 20 => |G only| = 10. - |F| = |F only| + |E \u2229 F only| + |F \u2229 G only| + |E \u2229 F \u2229 G| 30 = |F only| + 10 + 7 + 5 => 30 = |F only| + 22 => |F only| = 8. - The total number of people is the sum of those speaking only one language, exactly two languages, and all three: - |E U F U G| = |E only| + |F only| + |G only| + |E \u2229 F only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G| - 65 = |E only| + 8 + 10 + 10 + 8 + 7 + 5 - 65 = |E only| + 48 - |E only| = 65 - 48 = 17.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/an-international-conference-is-attended-by-65-people-they-all-speak-a\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:23:51+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/an-international-conference-is-attended-by-65-people-they-all-speak-a\/","url":"https:\/\/exam.pscnotes.com\/mcq\/an-international-conference-is-attended-by-65-people-they-all-speak-a\/","name":"An international conference is attended by 65 people. They all speak a","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:23:51+00:00","dateModified":"2025-06-01T10:23:51+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The number of people who can speak only English is 17. - Let E, F, and G be the sets of people who speak English, French, and German, respectively. - Total people |E U F U G| = 65 (since all speak at least one language). - We are given: |E \u2229 F| = 15, |E \u2229 G| = 13, |F \u2229 G| = 12, |E \u2229 F \u2229 G| = 5. - We are also given: |G| = 30, |F| = 30. - We can find the number of people speaking exactly two languages: - |E \u2229 F only| = |E \u2229 F| - |E \u2229 F \u2229 G| = 15 - 5 = 10 - |E \u2229 G only| = |E \u2229 G| - |E \u2229 F \u2229 G| = 13 - 5 = 8 - |F \u2229 G only| = |F \u2229 G| - |E \u2229 F \u2229 G| = 12 - 5 = 7 - We can find the number of people speaking only one language using the given total for F and G: - |G| = |G only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G| 30 = |G only| + 8 + 7 + 5 => 30 = |G only| + 20 => |G only| = 10. - |F| = |F only| + |E \u2229 F only| + |F \u2229 G only| + |E \u2229 F \u2229 G| 30 = |F only| + 10 + 7 + 5 => 30 = |F only| + 22 => |F only| = 8. - The total number of people is the sum of those speaking only one language, exactly two languages, and all three: - |E U F U G| = |E only| + |F only| + |G only| + |E \u2229 F only| + |E \u2229 G only| + |F \u2229 G only| + |E \u2229 F \u2229 G| - 65 = |E only| + 8 + 10 + 10 + 8 + 7 + 5 - 65 = |E only| + 48 - |E only| = 65 - 48 = 17.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/an-international-conference-is-attended-by-65-people-they-all-speak-a\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/an-international-conference-is-attended-by-65-people-they-all-speak-a\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/an-international-conference-is-attended-by-65-people-they-all-speak-a\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"An international conference is attended by 65 people. They all speak a"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90247","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=90247"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90247\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90247"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90247"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90247"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}