{"id":2022,"date":"2024-03-05T15:26:42","date_gmt":"2024-03-05T15:26:42","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=2022"},"modified":"2024-03-05T15:26:42","modified_gmt":"2024-03-05T15:26:42","slug":"suppose-x-y-z-are-three-positive-integers-such-that-x-yz-and-xyz-which-one-of-the-following-values-of-s-yields-more-than-one-solution-to-the-equation-xyzs","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/suppose-x-y-z-are-three-positive-integers-such-that-x-yz-and-xyz-which-one-of-the-following-values-of-s-yields-more-than-one-solution-to-the-equation-xyzs\/","title":{"rendered":"Suppose x, y, z are three positive integers such that x < yz and xyz = Which one of the following values of S yields more than one solution to the equation x+y+z=S?"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;13&#8243; option2=&#8221;4&#8243; option3=&#8221;15&#8243; option4=&#8221;16&#8243; correct=&#8221;option2&#8243;]<!--more--><\/p>\n<p>The correct answer is (b).<\/p>\n<p>Suppose $x, y, z$ are three positive integers such that $x &lt; yz$ and $xyz = 13$. We can factor $13$ as $13 = 1 \\cdot 13 = 3 \\cdot 4 = 6 \\cdot 2$. Therefore, we can choose $x, y, z$ to be any of the following ordered triples:<\/p>\n<ul>\n<li>$(1, 13)$<\/li>\n<li>$(3, 4)$<\/li>\n<li>$(6, 2)$<\/li>\n<\/ul>\n<p>Since there are three possible solutions, $S = 13$ yields more than one solution to the equation $x + y + z = S$.<\/p>\n<p>For the other options, we can see that there is only one solution to the equation $x + y + z = S$ for each value of $S$.<\/p>\n<ul>\n<li>For $S = 4$, the only solution is $(1, 1, 2)$.<\/li>\n<li>For $S = 15$, the only solution is $(3, 5, 3)$.<\/li>\n<li>For $S = 16$, the only solution is $(4, 4, 4)$.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;13&#8243; option2=&#8221;4&#8243; option3=&#8221;15&#8243; option4=&#8221;16&#8243; correct=&#8221;option2&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[75],"tags":[],"class_list":["post-2022","post","type-post","status-publish","format-standard","hentry","category-number-theory","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 x, y, z are three positive integers such that x &lt; yz and xyz = Which one of the following values of S yields more than one solution to the equation x+y+z=S?<\/title>\n<meta name=\"description\" content=\"Suppose $x, y, z$ are three positive integers such that $x &lt; yz$ and $xyz = 13$. We can factor $13$ as $13 = 1 cdot 13 = 3 cdot 4 = 6 cdot 2$. Therefore, we can choose $x, y, z$ to be any of the following ordered triples:\" \/>\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-x-y-z-are-three-positive-integers-such-that-x-yz-and-xyz-which-one-of-the-following-values-of-s-yields-more-than-one-solution-to-the-equation-xyzs\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Suppose x, y, z are three positive integers such that x &lt; yz and xyz = Which one of the following values of S yields more than one solution to the equation x+y+z=S?\" \/>\n<meta property=\"og:description\" content=\"Suppose $x, y, z$ are three positive integers such that $x &lt; yz$ and $xyz = 13$. We can factor $13$ as $13 = 1 cdot 13 = 3 cdot 4 = 6 cdot 2$. Therefore, we can choose $x, y, z$ to be any of the following ordered triples:\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/suppose-x-y-z-are-three-positive-integers-such-that-x-yz-and-xyz-which-one-of-the-following-values-of-s-yields-more-than-one-solution-to-the-equation-xyzs\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-03-05T15:26:42+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":"Suppose x, y, z are three positive integers such that x < yz and xyz = Which one of the following values of S yields more than one solution to the equation x+y+z=S?","description":"Suppose $x, y, z$ are three positive integers such that $x &lt; yz$ and $xyz = 13$. We can factor $13$ as $13 = 1 cdot 13 = 3 cdot 4 = 6 cdot 2$. Therefore, we can choose $x, y, z$ to be any of the following ordered triples:","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-x-y-z-are-three-positive-integers-such-that-x-yz-and-xyz-which-one-of-the-following-values-of-s-yields-more-than-one-solution-to-the-equation-xyzs\/","og_locale":"en_US","og_type":"article","og_title":"Suppose x, y, z are three positive integers such that x < yz and xyz = Which one of the following values of S yields more than one solution to the equation x+y+z=S?","og_description":"Suppose $x, y, z$ are three positive integers such that $x &lt; yz$ and $xyz = 13$. We can factor $13$ as $13 = 1 cdot 13 = 3 cdot 4 = 6 cdot 2$. Therefore, we can choose $x, y, z$ to be any of the following ordered triples:","og_url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-x-y-z-are-three-positive-integers-such-that-x-yz-and-xyz-which-one-of-the-following-values-of-s-yields-more-than-one-solution-to-the-equation-xyzs\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-03-05T15:26:42+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\/suppose-x-y-z-are-three-positive-integers-such-that-x-yz-and-xyz-which-one-of-the-following-values-of-s-yields-more-than-one-solution-to-the-equation-xyzs\/","url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-x-y-z-are-three-positive-integers-such-that-x-yz-and-xyz-which-one-of-the-following-values-of-s-yields-more-than-one-solution-to-the-equation-xyzs\/","name":"Suppose x, y, z are three positive integers such that x < yz and xyz = Which one of the following values of S yields more than one solution to the equation x+y+z=S?","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-03-05T15:26:42+00:00","dateModified":"2024-03-05T15:26:42+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Suppose $x, y, z$ are three positive integers such that $x &lt; yz$ and $xyz = 13$. We can factor $13$ as $13 = 1 \\cdot 13 = 3 \\cdot 4 = 6 \\cdot 2$. 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