{"id":90248,"date":"2025-06-01T10:23:52","date_gmt":"2025-06-01T10:23:52","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90248"},"modified":"2025-06-01T10:23:52","modified_gmt":"2025-06-01T10:23:52","slug":"suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1\/","title":{"rendered":"Suppose 72 = m x n, where m and n are positive integers such that 1 <"},"content":{"rendered":"<p>Suppose 72 = m x n, where m and n are positive integers such that 1 < m < n. How many possible values of m are there?\n\n[amp_mcq option1=\"5\" option2=\"6\" option3=\"10\" option4=\"12\" correct=\"option1\"]\n\n\n\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\">\nThere are 5 possible values for m.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\n&#8211; We are given that 72 = m x n, where m and n are positive integers such that 1 < m < n.\n- We need to find pairs of factors (m, n) of 72 that satisfy the condition 1 < m < n.\n- First, list pairs of factors (m, n) of 72 such that m <= n:\n    - 72 = 1 x 72  (m=1, n=72)\n    - 72 = 2 x 36  (m=2, n=36)\n    - 72 = 3 x 24  (m=3, n=24)\n    - 72 = 4 x 18  (m=4, n=18)\n    - 72 = 6 x 12  (m=6, n=12)\n    - 72 = 8 x 9   (m=8, n=9)\n- Now, apply the condition 1 < m < n:\n    - (1, 72): m=1. Fails 1 < m.\n    - (2, 36): m=2. Satisfies 1 < 2 < 36. m=2 is a possible value.\n    - (3, 24): m=3. Satisfies 1 < 3 < 24. m=3 is a possible value.\n    - (4, 18): m=4. Satisfies 1 < 4 < 18. m=4 is a possible value.\n    - (6, 12): m=6. Satisfies 1 < 6 < 12. m=6 is a possible value.\n    - (8, 9): m=8. Satisfies 1 < 8 < 9. m=8 is a possible value.\n- The possible values for m are the first elements of the valid pairs: 2, 3, 4, 6, 8.\n- There are 5 possible values for m.\n<\/section>\n<section id=\"pyq-additional-information\">\nTo find all pairs of factors (m, n) of a number N, list all factors of N. Then pair them up such that their product is N. For the condition m < n, ensure m is the smaller factor in each pair (or check against sqrt(N)). For 72, sqrt(72) is between 8 and 9. Pairs with m <= sqrt(72) are (1,72), (2,36), (3,24), (4,18), (6,12), (8,9).\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>Suppose 72 = m x n, where m and n are positive integers such that 1 < m < n. How many possible values of m are there? [amp_mcq option1=\"5\" option2=\"6\" option3=\"10\" option4=\"12\" correct=\"option1\"] This question was previously asked in UPSC CAPF &#8211; 2018 Download PDFAttempt Online There are 5 possible values for m. &#8211; ... \n\n<p class=\"read-more-container\"><a title=\"Suppose 72 = m x n, where m and n are positive integers such that 1 \" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1\/#more-90248\">Detailed Solution<span class=\"screen-reader-text\">Suppose 72 = m x n, where m and n are positive integers such that 1 <<\/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-90248","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>Suppose 72 = m x n, where m and n are positive integers such that 1<\/title>\n<meta name=\"description\" content=\"There are 5 possible values for m. - We are given that 72 = m x n, where m and n are positive integers such that 1 &lt; m &lt; n. - We need to find pairs of factors (m, n) of 72 that satisfy the condition 1 &lt; m &lt; n. - First, list pairs of factors (m, n) of 72 such that m &lt;= n: - 72 = 1 x 72 (m=1, n=72) - 72 = 2 x 36 (m=2, n=36) - 72 = 3 x 24 (m=3, n=24) - 72 = 4 x 18 (m=4, n=18) - 72 = 6 x 12 (m=6, n=12) - 72 = 8 x 9 (m=8, n=9) - Now, apply the condition 1 &lt; m &lt; n: - (1, 72): m=1. Fails 1 &lt; m. - (2, 36): m=2. Satisfies 1 &lt; 2 &lt; 36. m=2 is a possible value. - (3, 24): m=3. Satisfies 1 &lt; 3 &lt; 24. m=3 is a possible value. - (4, 18): m=4. Satisfies 1 &lt; 4 &lt; 18. m=4 is a possible value. - (6, 12): m=6. Satisfies 1 &lt; 6 &lt; 12. m=6 is a possible value. - (8, 9): m=8. Satisfies 1 &lt; 8 &lt; 9. m=8 is a possible value. - The possible values for m are the first elements of the valid pairs: 2, 3, 4, 6, 8. - There are 5 possible values for m.\" \/>\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\/suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Suppose 72 = m x n, where m and n are positive integers such that 1\" \/>\n<meta property=\"og:description\" content=\"There are 5 possible values for m. - We are given that 72 = m x n, where m and n are positive integers such that 1 &lt; m &lt; n. - We need to find pairs of factors (m, n) of 72 that satisfy the condition 1 &lt; m &lt; n. - First, list pairs of factors (m, n) of 72 such that m &lt;= n: - 72 = 1 x 72 (m=1, n=72) - 72 = 2 x 36 (m=2, n=36) - 72 = 3 x 24 (m=3, n=24) - 72 = 4 x 18 (m=4, n=18) - 72 = 6 x 12 (m=6, n=12) - 72 = 8 x 9 (m=8, n=9) - Now, apply the condition 1 &lt; m &lt; n: - (1, 72): m=1. Fails 1 &lt; m. - (2, 36): m=2. Satisfies 1 &lt; 2 &lt; 36. m=2 is a possible value. - (3, 24): m=3. Satisfies 1 &lt; 3 &lt; 24. m=3 is a possible value. - (4, 18): m=4. Satisfies 1 &lt; 4 &lt; 18. m=4 is a possible value. - (6, 12): m=6. Satisfies 1 &lt; 6 &lt; 12. m=6 is a possible value. - (8, 9): m=8. Satisfies 1 &lt; 8 &lt; 9. m=8 is a possible value. - The possible values for m are the first elements of the valid pairs: 2, 3, 4, 6, 8. - There are 5 possible values for m.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:23:52+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<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Suppose 72 = m x n, where m and n are positive integers such that 1","description":"There are 5 possible values for m. - We are given that 72 = m x n, where m and n are positive integers such that 1 &lt; m &lt; n. - We need to find pairs of factors (m, n) of 72 that satisfy the condition 1 &lt; m &lt; n. - First, list pairs of factors (m, n) of 72 such that m &lt;= n: - 72 = 1 x 72 (m=1, n=72) - 72 = 2 x 36 (m=2, n=36) - 72 = 3 x 24 (m=3, n=24) - 72 = 4 x 18 (m=4, n=18) - 72 = 6 x 12 (m=6, n=12) - 72 = 8 x 9 (m=8, n=9) - Now, apply the condition 1 &lt; m &lt; n: - (1, 72): m=1. Fails 1 &lt; m. - (2, 36): m=2. Satisfies 1 &lt; 2 &lt; 36. m=2 is a possible value. - (3, 24): m=3. Satisfies 1 &lt; 3 &lt; 24. m=3 is a possible value. - (4, 18): m=4. Satisfies 1 &lt; 4 &lt; 18. m=4 is a possible value. - (6, 12): m=6. Satisfies 1 &lt; 6 &lt; 12. m=6 is a possible value. - (8, 9): m=8. Satisfies 1 &lt; 8 &lt; 9. m=8 is a possible value. - The possible values for m are the first elements of the valid pairs: 2, 3, 4, 6, 8. - There are 5 possible values for m.","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\/suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1\/","og_locale":"en_US","og_type":"article","og_title":"Suppose 72 = m x n, where m and n are positive integers such that 1","og_description":"There are 5 possible values for m. - We are given that 72 = m x n, where m and n are positive integers such that 1 &lt; m &lt; n. - We need to find pairs of factors (m, n) of 72 that satisfy the condition 1 &lt; m &lt; n. - First, list pairs of factors (m, n) of 72 such that m &lt;= n: - 72 = 1 x 72 (m=1, n=72) - 72 = 2 x 36 (m=2, n=36) - 72 = 3 x 24 (m=3, n=24) - 72 = 4 x 18 (m=4, n=18) - 72 = 6 x 12 (m=6, n=12) - 72 = 8 x 9 (m=8, n=9) - Now, apply the condition 1 &lt; m &lt; n: - (1, 72): m=1. Fails 1 &lt; m. - (2, 36): m=2. Satisfies 1 &lt; 2 &lt; 36. m=2 is a possible value. - (3, 24): m=3. Satisfies 1 &lt; 3 &lt; 24. m=3 is a possible value. - (4, 18): m=4. Satisfies 1 &lt; 4 &lt; 18. m=4 is a possible value. - (6, 12): m=6. Satisfies 1 &lt; 6 &lt; 12. m=6 is a possible value. - (8, 9): m=8. Satisfies 1 &lt; 8 &lt; 9. m=8 is a possible value. - The possible values for m are the first elements of the valid pairs: 2, 3, 4, 6, 8. - There are 5 possible values for m.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:23:52+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1\/","url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1\/","name":"Suppose 72 = m x n, where m and n are positive integers such that 1","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:23:52+00:00","dateModified":"2025-06-01T10:23:52+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"There are 5 possible values for m. - We are given that 72 = m x n, where m and n are positive integers such that 1 &lt; m &lt; n. - We need to find pairs of factors (m, n) of 72 that satisfy the condition 1 &lt; m &lt; n. - First, list pairs of factors (m, n) of 72 such that m &lt;= n: - 72 = 1 x 72 (m=1, n=72) - 72 = 2 x 36 (m=2, n=36) - 72 = 3 x 24 (m=3, n=24) - 72 = 4 x 18 (m=4, n=18) - 72 = 6 x 12 (m=6, n=12) - 72 = 8 x 9 (m=8, n=9) - Now, apply the condition 1 &lt; m &lt; n: - (1, 72): m=1. Fails 1 &lt; m. - (2, 36): m=2. Satisfies 1 &lt; 2 &lt; 36. m=2 is a possible value. - (3, 24): m=3. Satisfies 1 &lt; 3 &lt; 24. m=3 is a possible value. - (4, 18): m=4. Satisfies 1 &lt; 4 &lt; 18. m=4 is a possible value. - (6, 12): m=6. Satisfies 1 &lt; 6 &lt; 12. m=6 is a possible value. - (8, 9): m=8. Satisfies 1 &lt; 8 &lt; 9. m=8 is a possible value. - The possible values for m are the first elements of the valid pairs: 2, 3, 4, 6, 8. - There are 5 possible values for m.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-72-m-x-n-where-m-and-n-are-positive-integers-such-that-1\/#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":"Suppose 72 = m x n, where m and n are positive integers such that 1"}]},{"@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\/90248","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=90248"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90248\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90248"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90248"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90248"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}