{"id":89785,"date":"2025-06-01T10:12:38","date_gmt":"2025-06-01T10:12:38","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89785"},"modified":"2025-06-01T10:12:38","modified_gmt":"2025-06-01T10:12:38","slug":"if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3\/","title":{"rendered":"If three times of the first of the three consecutive odd integers is 3"},"content":{"rendered":"<p>If three times of the first of the three consecutive odd integers is 3 more than twice the third integer, what is the third integer ?<\/p>\n<p>[amp_mcq option1=&#8221;15&#8243; option2=&#8221;11&#8243; option3=&#8221;9&#8243; option4=&#8221;5&#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; 2014<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-capf-2014.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-capf-2014\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nLet the three consecutive odd integers be represented as \\(x\\), \\(x+2\\), and \\(x+4\\), where \\(x\\) is the first odd integer. The problem states that three times the first integer is 3 more than twice the third integer. We can write this as an equation: \\(3x = 2(x+4) + 3\\).<br \/>\nSolving the equation:<br \/>\n\\(3x = 2x + 8 + 3\\)<br \/>\n\\(3x = 2x + 11\\)<br \/>\n\\(3x &#8211; 2x = 11\\)<br \/>\n\\(x = 11\\)<br \/>\nThe first integer is 11. The three consecutive odd integers are 11, 13, and 15. The third integer is 15.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\nConsecutive odd integers differ by 2. Setting up the algebraic equation correctly based on the given relationship is crucial to finding the value of the first integer.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nWe can verify the answer: Three times the first integer (11) is 3 * 11 = 33. Twice the third integer (15) is 2 * 15 = 30. 30 + 3 = 33. The condition is satisfied.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>If three times of the first of the three consecutive odd integers is 3 more than twice the third integer, what is the third integer ? [amp_mcq option1=&#8221;15&#8243; option2=&#8221;11&#8243; option3=&#8221;9&#8243; option4=&#8221;5&#8243; correct=&#8221;option1&#8243;] This question was previously asked in UPSC CAPF &#8211; 2014 Download PDFAttempt Online Let the three consecutive odd integers be represented as \\(x\\), &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"If three times of the first of the three consecutive odd integers is 3\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3\/#more-89785\">Detailed Solution<span class=\"screen-reader-text\">If three times of the first of the three consecutive odd integers is 3<\/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":[1468,1102],"class_list":["post-89785","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1468","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>If three times of the first of the three consecutive odd integers is 3<\/title>\n<meta name=\"description\" content=\"Let the three consecutive odd integers be represented as (x), (x+2), and (x+4), where (x) is the first odd integer. The problem states that three times the first integer is 3 more than twice the third integer. We can write this as an equation: (3x = 2(x+4) + 3). Solving the equation: (3x = 2x + 8 + 3) (3x = 2x + 11) (3x - 2x = 11) (x = 11) The first integer is 11. The three consecutive odd integers are 11, 13, and 15. The third integer is 15. Consecutive odd integers differ by 2. Setting up the algebraic equation correctly based on the given relationship is crucial to finding the value of the first integer.\" \/>\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\/if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If three times of the first of the three consecutive odd integers is 3\" \/>\n<meta property=\"og:description\" content=\"Let the three consecutive odd integers be represented as (x), (x+2), and (x+4), where (x) is the first odd integer. The problem states that three times the first integer is 3 more than twice the third integer. We can write this as an equation: (3x = 2(x+4) + 3). Solving the equation: (3x = 2x + 8 + 3) (3x = 2x + 11) (3x - 2x = 11) (x = 11) The first integer is 11. The three consecutive odd integers are 11, 13, and 15. The third integer is 15. Consecutive odd integers differ by 2. Setting up the algebraic equation correctly based on the given relationship is crucial to finding the value of the first integer.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:12:38+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=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"If three times of the first of the three consecutive odd integers is 3","description":"Let the three consecutive odd integers be represented as (x), (x+2), and (x+4), where (x) is the first odd integer. The problem states that three times the first integer is 3 more than twice the third integer. We can write this as an equation: (3x = 2(x+4) + 3). Solving the equation: (3x = 2x + 8 + 3) (3x = 2x + 11) (3x - 2x = 11) (x = 11) The first integer is 11. The three consecutive odd integers are 11, 13, and 15. The third integer is 15. Consecutive odd integers differ by 2. Setting up the algebraic equation correctly based on the given relationship is crucial to finding the value of the first integer.","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\/if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3\/","og_locale":"en_US","og_type":"article","og_title":"If three times of the first of the three consecutive odd integers is 3","og_description":"Let the three consecutive odd integers be represented as (x), (x+2), and (x+4), where (x) is the first odd integer. The problem states that three times the first integer is 3 more than twice the third integer. We can write this as an equation: (3x = 2(x+4) + 3). Solving the equation: (3x = 2x + 8 + 3) (3x = 2x + 11) (3x - 2x = 11) (x = 11) The first integer is 11. The three consecutive odd integers are 11, 13, and 15. The third integer is 15. Consecutive odd integers differ by 2. Setting up the algebraic equation correctly based on the given relationship is crucial to finding the value of the first integer.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:12:38+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3\/","url":"https:\/\/exam.pscnotes.com\/mcq\/if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3\/","name":"If three times of the first of the three consecutive odd integers is 3","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:12:38+00:00","dateModified":"2025-06-01T10:12:38+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let the three consecutive odd integers be represented as \\(x\\), \\(x+2\\), and \\(x+4\\), where \\(x\\) is the first odd integer. The problem states that three times the first integer is 3 more than twice the third integer. We can write this as an equation: \\(3x = 2(x+4) + 3\\). Solving the equation: \\(3x = 2x + 8 + 3\\) \\(3x = 2x + 11\\) \\(3x - 2x = 11\\) \\(x = 11\\) The first integer is 11. The three consecutive odd integers are 11, 13, and 15. The third integer is 15. Consecutive odd integers differ by 2. Setting up the algebraic equation correctly based on the given relationship is crucial to finding the value of the first integer.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/if-three-times-of-the-first-of-the-three-consecutive-odd-integers-is-3\/#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":"If three times of the first of the three consecutive odd integers is 3"}]},{"@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\/89785","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=89785"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89785\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=89785"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=89785"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=89785"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}