{"id":28642,"date":"2025-06-20T14:11:48","date_gmt":"2025-06-20T14:11:48","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=28642"},"modified":"2025-06-20T14:57:59","modified_gmt":"2025-06-20T14:57:59","slug":"here-are-some-clues-to-a-mystery-number","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/here-are-some-clues-to-a-mystery-number\/","title":{"rendered":"Here are some clues to a mystery number."},"content":{"rendered":"\n<p>Here are some clues to a mystery number. \u2022 The GCF of 18. 36, and me is 2. I am a multiple of 5. I am greater than 18 and less than 30. What is the mystery number? \u2022 The mystery number is <\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct mystery number is <strong>20<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To find the mystery number, each clue must be carefully examined and all conditions met:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Clue 1: &#8220;The GCF of 18, 36, and me is 2&#8221;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Begin by listing the factors of 18: 1, 2, 3, 6, 9, 18<\/li>\n\n\n\n<li>Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36<\/li>\n\n\n\n<li>The number must share only <strong>2<\/strong> as the greatest common factor with both 18 and 36.<\/li>\n<\/ul>\n\n\n\n<p>This implies that the mystery number must be even, but cannot have any other common factors with 18 and 36 except for 2.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Clue 2: &#8220;I am a multiple of 5&#8221;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiples of 5 between 18 and 30 are: 20 and 25<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Clue 3: &#8220;I am greater than 18 and less than 30&#8221;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This narrows the possibilities to the numbers: 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29<\/li>\n<\/ul>\n\n\n\n<p>Now combine the clues:<\/p>\n\n\n\n<p>From clue 2 and 3, only <strong>20 and 25<\/strong> are multiples of 5 and lie between 18 and 30.<\/p>\n\n\n\n<p>Now test each of these with the GCF clue:<\/p>\n\n\n\n<p><strong>Test 20:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>GCF of 18 and 20 = 2<\/li>\n\n\n\n<li>GCF of 36 and 20 = 4<\/li>\n\n\n\n<li>But this fails, because 4 is not acceptable<\/li>\n<\/ul>\n\n\n\n<p>Wait, this shows a contradiction, so re-evaluate:<\/p>\n\n\n\n<p>Actually:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Factors of 18: 1, 2, 3, 6, 9, 18<\/li>\n\n\n\n<li>Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36<\/li>\n\n\n\n<li>Factors of 20: 1, 2, 4, 5, 10, 20<\/li>\n\n\n\n<li>Common factors of 18, 36, and 20 = <strong>Only 1 and 2<\/strong>, and <strong>2 is the greatest<\/strong><\/li>\n<\/ul>\n\n\n\n<p>So <strong>GCF(18, 36, 20) = 2<\/strong> \u2014 this satisfies the clue.<\/p>\n\n\n\n<p><strong>Test 25:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>GCF(18, 25) = 1<\/li>\n\n\n\n<li>GCF(36, 25) = 1<\/li>\n\n\n\n<li>So the overall GCF would be 1 \u2014 this does <strong>not<\/strong> meet the clue<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the only number that fits <strong>all three<\/strong> clues is:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>The mystery number is 20.<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-236.jpeg\" alt=\"\" class=\"wp-image-28652\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-236.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-236-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-236-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Here are some clues to a mystery number. \u2022 The GCF of 18. 36, and me is 2. I am a multiple of 5. I am greater than 18 and less than 30. What is the mystery number? \u2022 The mystery number is The Correct Answer and Explanation is: The correct mystery number is 20. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-28642","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28642","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=28642"}],"version-history":[{"count":2,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28642\/revisions"}],"predecessor-version":[{"id":28741,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28642\/revisions\/28741"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=28642"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=28642"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=28642"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}