{"id":89803,"date":"2025-06-01T10:12:58","date_gmt":"2025-06-01T10:12:58","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89803"},"modified":"2025-06-01T10:12:58","modified_gmt":"2025-06-01T10:12:58","slug":"if-x-is-a-positive-integer-such-that-2x-12-is-perfectly-divisible-by","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-x-is-a-positive-integer-such-that-2x-12-is-perfectly-divisible-by\/","title":{"rendered":"If x is a positive integer such that 2x + 12 is perfectly divisible by"},"content":{"rendered":"

If x is a positive integer such that 2x + 12 is perfectly divisible by x, then the number of possible values of x is :<\/p>\n

[amp_mcq option1=”2″ option2=”5″ option3=”6″ option4=”12″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2014<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nFor 2x + 12 to be perfectly divisible by the positive integer x, x must be a positive divisor of 12.
\n<\/section>\n
\nThe expression (2x + 12) is perfectly divisible by x if the division (2x + 12) \/ x results in an integer.
\n(2x + 12) \/ x = (2x \/ x) + (12 \/ x) = 2 + 12\/x.
\nSince 2 is an integer, for the entire expression (2 + 12\/x) to be an integer, 12\/x must be an integer.
\nThis means x must be a divisor of 12.
\nSince x is a positive integer, we need to find all positive divisors of 12.
\nThe positive divisors of 12 are the numbers that divide 12 without leaving a remainder: 1, 2, 3, 4, 6, and 12.
\nThere are 6 such positive integers.
\n<\/section>\n
\nWe can verify each divisor:
\nIf x=1, 2(1)+12 = 14, 14\/1 = 14 (integer)
\nIf x=2, 2(2)+12 = 16, 16\/2 = 8 (integer)
\nIf x=3, 2(3)+12 = 18, 18\/3 = 6 (integer)
\nIf x=4, 2(4)+12 = 20, 20\/4 = 5 (integer)
\nIf x=6, 2(6)+12 = 24, 24\/6 = 4 (integer)
\nIf x=12, 2(12)+12 = 36, 36\/12 = 3 (integer)
\nAll 6 values are valid.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

If x is a positive integer such that 2x + 12 is perfectly divisible by x, then the number of possible values of x is : [amp_mcq option1=”2″ option2=”5″ option3=”6″ option4=”12″ correct=”option3″] This question was previously asked in UPSC CAPF – 2014 Download PDFAttempt Online For 2x + 12 to be perfectly divisible by the … <\/p>\n

Detailed SolutionIf x is a positive integer such that 2x + 12 is perfectly divisible by<\/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-89803","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1468","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nIf x is a positive integer such that 2x + 12 is perfectly divisible by<\/title>\n<meta name=\"description\" content=\"For 2x + 12 to be perfectly divisible by the positive integer x, x must be a positive divisor of 12. The expression (2x + 12) is perfectly divisible by x if the division (2x + 12) \/ x results in an integer. (2x + 12) \/ x = (2x \/ x) + (12 \/ x) = 2 + 12\/x. Since 2 is an integer, for the entire expression (2 + 12\/x) to be an integer, 12\/x must be an integer. This means x must be a divisor of 12. Since x is a positive integer, we need to find all positive divisors of 12. The positive divisors of 12 are the numbers that divide 12 without leaving a remainder: 1, 2, 3, 4, 6, and 12. There are 6 such positive integers.\" \/>\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-x-is-a-positive-integer-such-that-2x-12-is-perfectly-divisible-by\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If x is a positive integer such that 2x + 12 is perfectly divisible by\" \/>\n<meta property=\"og:description\" content=\"For 2x + 12 to be perfectly divisible by the positive integer x, x must be a positive divisor of 12. The expression (2x + 12) is perfectly divisible by x if the division (2x + 12) \/ x results in an integer. (2x + 12) \/ x = (2x \/ x) + (12 \/ x) = 2 + 12\/x. Since 2 is an integer, for the entire expression (2 + 12\/x) to be an integer, 12\/x must be an integer. This means x must be a divisor of 12. Since x is a positive integer, we need to find all positive divisors of 12. The positive divisors of 12 are the numbers that divide 12 without leaving a remainder: 1, 2, 3, 4, 6, and 12. There are 6 such positive integers.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-x-is-a-positive-integer-such-that-2x-12-is-perfectly-divisible-by\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:12:58+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 x is a positive integer such that 2x + 12 is perfectly divisible by","description":"For 2x + 12 to be perfectly divisible by the positive integer x, x must be a positive divisor of 12. The expression (2x + 12) is perfectly divisible by x if the division (2x + 12) \/ x results in an integer. (2x + 12) \/ x = (2x \/ x) + (12 \/ x) = 2 + 12\/x. Since 2 is an integer, for the entire expression (2 + 12\/x) to be an integer, 12\/x must be an integer. This means x must be a divisor of 12. Since x is a positive integer, we need to find all positive divisors of 12. The positive divisors of 12 are the numbers that divide 12 without leaving a remainder: 1, 2, 3, 4, 6, and 12. There are 6 such positive integers.","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-x-is-a-positive-integer-such-that-2x-12-is-perfectly-divisible-by\/","og_locale":"en_US","og_type":"article","og_title":"If x is a positive integer such that 2x + 12 is perfectly divisible by","og_description":"For 2x + 12 to be perfectly divisible by the positive integer x, x must be a positive divisor of 12. The expression (2x + 12) is perfectly divisible by x if the division (2x + 12) \/ x results in an integer. (2x + 12) \/ x = (2x \/ x) + (12 \/ x) = 2 + 12\/x. Since 2 is an integer, for the entire expression (2 + 12\/x) to be an integer, 12\/x must be an integer. This means x must be a divisor of 12. Since x is a positive integer, we need to find all positive divisors of 12. The positive divisors of 12 are the numbers that divide 12 without leaving a remainder: 1, 2, 3, 4, 6, and 12. There are 6 such positive integers.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-x-is-a-positive-integer-such-that-2x-12-is-perfectly-divisible-by\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:12:58+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-x-is-a-positive-integer-such-that-2x-12-is-perfectly-divisible-by\/","url":"https:\/\/exam.pscnotes.com\/mcq\/if-x-is-a-positive-integer-such-that-2x-12-is-perfectly-divisible-by\/","name":"If x is a positive integer such that 2x + 12 is perfectly divisible by","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:12:58+00:00","dateModified":"2025-06-01T10:12:58+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"For 2x + 12 to be perfectly divisible by the positive integer x, x must be a positive divisor of 12. The expression (2x + 12) is perfectly divisible by x if the division (2x + 12) \/ x results in an integer. (2x + 12) \/ x = (2x \/ x) + (12 \/ x) = 2 + 12\/x. Since 2 is an integer, for the entire expression (2 + 12\/x) to be an integer, 12\/x must be an integer. This means x must be a divisor of 12. Since x is a positive integer, we need to find all positive divisors of 12. The positive divisors of 12 are the numbers that divide 12 without leaving a remainder: 1, 2, 3, 4, 6, and 12. There are 6 such positive integers.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/if-x-is-a-positive-integer-such-that-2x-12-is-perfectly-divisible-by\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/if-x-is-a-positive-integer-such-that-2x-12-is-perfectly-divisible-by\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/if-x-is-a-positive-integer-such-that-2x-12-is-perfectly-divisible-by\/#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 x is a positive integer such that 2x + 12 is perfectly divisible by"}]},{"@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\/89803","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=89803"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89803\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=89803"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=89803"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=89803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}