{"id":21701,"date":"2016-02-17T22:08:24","date_gmt":"2016-02-17T22:08:24","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=21701"},"modified":"2026-03-25T11:21:39","modified_gmt":"2026-03-25T16:21:39","slug":"venn-diagrams","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/venn-diagrams\/","title":{"rendered":"Venn Diagrams"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_JJRkDxA2xz0\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_JJRkDxA2xz0\" data-source-videoID=\"JJRkDxA2xz0\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Venn Diagrams Video\" height=\"720\" width=\"1280\" class=\"size-full\" data-matomo-title = \"Venn Diagrams\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_JJRkDxA2xz0:hover {cursor:pointer;} img#videoThumbnailImage_JJRkDxA2xz0 {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/05\/Venn-diagram-thumb.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_JJRkDxA2xz0\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_JJRkDxA2xz0\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Venn Diagrams\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_JJRkDxA2xz0\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_JJRkDxA2xz0\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_JJRkDxA2xz0\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video lesson on Venn diagrams!<\/p>\n<p>Venn diagrams are super helpful, because they help us understand the relationships between large groups or sets of different things. Venn diagrams were developed during the 1702 and have been used more and more ever since.<\/p>\n<p>Here&#8217;s how they work. Imagine we have a set of things called &#8220;A&#8221;. Set A has a lot of different fonts for the letter A (go figure, right?). Some of those fonts can be used on the letter B. Imagine there is a set B, as well. Set B contains a bunch of fonts for the letter B.<\/p>\n<p>As you can imagine, there are many fans that can be used both on the letters A and B. What do you do about them? Well, our Venn diagram provides an option. We can make set A and set B overlap, creating a third set within both of them. Let&#8217;s try a more practical example.<\/p>\n<p>Imagine set A is set of numbers between 1 and 20 divisible by 2. That includes 2, 4, 6, etc. Now, imagine another set exists. All the numbers between 1 and 20 divisible by 3. That&#8217;s set B. What do we do about those numbers between 1 and 20 that are divisible by both 2 and 3?<\/p>\n<p>Well, let&#8217;s diagram it. We can see that by overlapping sets A and B, we create a third set that is part of both. We can see that by overlapping sets A and B we create a whole new third subset. Venn diagrams are really helpful for helping us understand how sets interact with one another, and there&#8217;s no limit to how many sets can interact.<\/p>\n<p>Take for example, this. This is a Venn diagram of four different sets. They all interact, and they create nine new subsets. Crazy, right?<\/p>\n<p>I hope that helps. Thanks so much for watching this video lesson. Until next time, happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Venn_Diagram_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Venn Diagram Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe following Venn diagram shows the number of students enrolled in Chemistry, Physics, or both. How many more students are exclusively enrolled in Chemistry, compared to exclusively enrolled in Physics?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-64810 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/Image-1.png\" alt=\"Venn Diagram of students enrolled in science courses\" width=\"315\" height=\"223\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/Image-1.png 1086w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/Image-1-300x212.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/Image-1-1024x725.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/Image-1-768x544.png 768w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">Six more students<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">Nine more students<\/div><div class=\"PQ\"  id=\"PQ-1-3\">Thirty-two more students<\/div><div class=\"PQ\"  id=\"PQ-1-4\">Forty-one more students<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Forty-one students are enrolled in Chemistry exclusively, and thirty-two students are enrolled in Physics exclusively. The difference can be calculated by subtracting 32 from 41.<\/p>\n<p style=\"text-align: center\">\\(41-32=9\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe following Venn diagram shows the number of students enrolled in Chemistry, Physics, or both. Based on the information provided, what is the total number of students?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-64810 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/Image-1.png\" alt=\"Venn Diagram of students enrolled in science courses\" width=\"315\" height=\"223\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/Image-1.png 1086w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/Image-1-300x212.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/Image-1-1024x725.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/Image-1-768x544.png 768w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">59 students<\/div><div class=\"PQ\"  id=\"PQ-2-2\">64 students<\/div><div class=\"PQ\"  id=\"PQ-2-3\">73 students<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-4\">79 students<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>41 students are exclusively enrolled in Chemistry, and 32 students are exclusively enrolled in Physics.<\/p>\n<p style=\"text-align: center\">\\(41+32=73\\text{ students}\\)<\/p>\n<p>6 students are enrolled in both classes, so 6 should be added to 73.<\/p>\n<p style=\"text-align: center\">\\(6+73=79\\text{ total students}\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nAccording to the Venn diagram, which pets would not be kept indoors? <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70487 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-Diagram-of-indoor-pets-versus-outdoor-pets.png\" alt=\"Venn Diagram of indoor pets versus outdoor pets\" width=\"315\" height=\"228\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-Diagram-of-indoor-pets-versus-outdoor-pets.png 1061w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-Diagram-of-indoor-pets-versus-outdoor-pets-300x217.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-Diagram-of-indoor-pets-versus-outdoor-pets-1024x742.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-Diagram-of-indoor-pets-versus-outdoor-pets-768x557.png 768w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">Cat, dog, and turtle<\/div><div class=\"PQ\"  id=\"PQ-3-2\">Hamster, spider, and iguana<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">Horse, goat, and pig<\/div><div class=\"PQ\"  id=\"PQ-3-4\">Spider, horse, and pig<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The pets that would not be kept indoors are listed on the far right portion of the Venn diagram. This portion lists horse, goat, and pig as being exclusively outdoor pets.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nAccording to the Venn diagram, which pets are considered indoor and outdoor pets?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70487 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-Diagram-of-indoor-pets-versus-outdoor-pets.png\" alt=\"Venn Diagram of indoor pets versus outdoor pets\" width=\"315\" height=\"228\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-Diagram-of-indoor-pets-versus-outdoor-pets.png 1061w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-Diagram-of-indoor-pets-versus-outdoor-pets-300x217.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-Diagram-of-indoor-pets-versus-outdoor-pets-1024x742.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-Diagram-of-indoor-pets-versus-outdoor-pets-768x557.png 768w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">Cats, Horses, and Dogs<\/div><div class=\"PQ\"  id=\"PQ-4-2\">Cats, Spiders, and Dogs<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-3\">Cats, Dogs, and Turtles<\/div><div class=\"PQ\"  id=\"PQ-4-4\">Iguanas, and Pigs<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The overlapping middle portion of the Venn diagram shows animals that are considered <em>both<\/em> indoor and outdoor pets. The pets in this middle section are cats, dogs, and turtles.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nCompare the number of factors of sixteen, to the number of factors of twenty-four. How many more factors does twenty-four have?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70490 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-factors-of-16-and-24.png\" alt=\"Venn diagram of factors of 16 and 24\" width=\"315\" height=\"222\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-factors-of-16-and-24.png 1086w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-factors-of-16-and-24-300x211.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-factors-of-16-and-24-1024x720.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-factors-of-16-and-24-768x540.png 768w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">Six more<\/div><div class=\"PQ\"  id=\"PQ-5-2\">Five more<\/div><div class=\"PQ\"  id=\"PQ-5-3\">Four more<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-4\">Three more<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The number 24 has eight factors: 1, 2, 3, 4, 6, 8, 12, 24. <\/p>\n<p>The number 16 has five factors: 1, 2, 4, 8, 16.<\/p>\n<p>Therefore, the number 24 has three more factors than 16. <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #6:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nAccording to the Venn diagram, how many factors are <em>exclusive<\/em> to twenty-four?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70490 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-factors-of-16-and-24.png\" alt=\"Venn diagram of factors of 16 and 24\" width=\"315\" height=\"222\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-factors-of-16-and-24.png 1086w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-factors-of-16-and-24-300x211.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-factors-of-16-and-24-1024x720.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-factors-of-16-and-24-768x540.png 768w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-6-1\">Four factors<\/div><div class=\"PQ\"  id=\"PQ-6-2\">One factor<\/div><div class=\"PQ\"  id=\"PQ-6-3\">Eight factors<\/div><div class=\"PQ\"  id=\"PQ-6-4\">Two factors<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-6\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-6\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-6-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The factors that are exclusive to 24 are 3, 6, 12, and 24. The other factors of 24 (1, 2, 4, and 8) are shared with 16.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-6-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-6-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #7:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe Venn diagram below will display the factors of thirty, twenty, and twenty-six when filled out. Which factors will be listed in the section between 20 and 30, with no overlap with 26?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70493 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Blank-venn-diagram-with-30-20-and-26-being-the-categories.png\" alt=\"Blank venn diagram with 30, 20, and 26 being the categories\" width=\"246\" height=\"211\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Blank-venn-diagram-with-30-20-and-26-being-the-categories.png 851w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Blank-venn-diagram-with-30-20-and-26-being-the-categories-300x257.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Blank-venn-diagram-with-30-20-and-26-being-the-categories-768x658.png 768w\" sizes=\"auto, (max-width: 246px) 100vw, 246px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-7-1\">1, 3, and 5<\/div><div class=\"PQ\"  id=\"PQ-7-2\">1, 4, and 5 <\/div><div class=\"PQ correct_answer\"  id=\"PQ-7-3\">5 and 10<\/div><div class=\"PQ\"  id=\"PQ-7-4\">2, 5, and 8<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-7\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-7\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-7-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The factors of 20: 1, 2, 4, 5, 10, and 20.<\/p>\n<p>The factors of 26: 1, 2, 13, and 26.<\/p>\n<p>The factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30.<\/p>\n<p>The factors that 20 and 30 have in common are 1, 2, 5, and 10. However, 1 and 2 are also shared with 26, so these will not be in the section shared only by 20 and 30. The only factors shared by 20 and 30 but not 26 will be 5 and 10.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70496 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-the-factors-of-30-20-and-26.png\" alt=\"Venn diagram of the factors of 30, 20, and 26\" width=\"236\" height=\"203\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-the-factors-of-30-20-and-26.png 851w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-the-factors-of-30-20-and-26-300x257.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-the-factors-of-30-20-and-26-768x658.png 768w\" sizes=\"auto, (max-width: 236px) 100vw, 236px\" \/><\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-7-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-7-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #8:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich factors are exclusive to the number thirty? Which section of the Venn diagram will these factors be placed?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70493 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Blank-venn-diagram-with-30-20-and-26-being-the-categories.png\" alt=\"Blank venn diagram with 30, 20, and 26 being the categories\" width=\"246\" height=\"211\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Blank-venn-diagram-with-30-20-and-26-being-the-categories.png 851w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Blank-venn-diagram-with-30-20-and-26-being-the-categories-300x257.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Blank-venn-diagram-with-30-20-and-26-being-the-categories-768x658.png 768w\" sizes=\"auto, (max-width: 246px) 100vw, 246px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-8-1\">3, 6, and 20. They will be placed in the top right section of the Venn diagram. <\/div><div class=\"PQ correct_answer\"  id=\"PQ-8-2\">3, 6, and 15. They will be placed in the top left section of the Venn diagram. <\/div><div class=\"PQ\"  id=\"PQ-8-3\">16, and 26. They will be placed in the top right section of the Venn diagram. <\/div><div class=\"PQ\"  id=\"PQ-8-4\">1 and 2. They will be placed in the top left section of the Venn diagram. <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-8\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-8\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-8-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The top left section of the Venn diagram is for factors that are exclusive to thirty. The factors 3, 6, and 15 are not factors of 20 or 26, so they will not be contained in any overlapping region.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70496 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-the-factors-of-30-20-and-26.png\" alt=\"Venn diagram of the factors of 30, 20, and 26\" width=\"236\" height=\"203\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-the-factors-of-30-20-and-26.png 851w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-the-factors-of-30-20-and-26-300x257.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-the-factors-of-30-20-and-26-768x658.png 768w\" sizes=\"auto, (max-width: 236px) 100vw, 236px\" \/><\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-8-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-8-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #9:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nIf each sport requires a separate jersey, how many jerseys will need to be ordered so that the students can play all of the sports they are registered for?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-70505 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-students-playing-basketball-and-or-soccer.png\" alt=\"Venn diagram of students playing basketball and or soccer\" width=\"315\" height=\"234\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-students-playing-basketball-and-or-soccer.png 1009w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-students-playing-basketball-and-or-soccer-300x223.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-students-playing-basketball-and-or-soccer-768x572.png 768w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-9-1\">13 jerseys<\/div><div class=\"PQ\"  id=\"PQ-9-2\">14 jerseys<\/div><div class=\"PQ\"  id=\"PQ-9-3\">15 jerseys<\/div><div class=\"PQ\"  id=\"PQ-9-4\">16 jerseys<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-9\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-9\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-9-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>There are seven students registered for basketball, and six students registered for soccer. This means that a total of 13 jerseys need to be ordered for the students. <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-9-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-9-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #10:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nHow many more students are registered for basketball than soccer?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-70505 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-students-playing-basketball-and-or-soccer.png\" alt=\"Venn diagram of students playing basketball and or soccer\" width=\"315\" height=\"234\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-students-playing-basketball-and-or-soccer.png 1009w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-students-playing-basketball-and-or-soccer-300x223.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Venn-diagram-of-students-playing-basketball-and-or-soccer-768x572.png 768w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-10-1\">Four more<\/div><div class=\"PQ\"  id=\"PQ-10-2\">Three more<\/div><div class=\"PQ\"  id=\"PQ-10-3\">Two more<\/div><div class=\"PQ correct_answer\"  id=\"PQ-10-4\">One more<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-10\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-10\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-10-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>There are seven students registered for basketball, and six students registered for soccer. This means that basketball has one more student than soccer.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-10-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-10-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-21701","1":"page","2":"type-page","3":"status-publish","5":"page_category-charts-graphs","6":"page_category-math-advertising-group","7":"page_category-video-pages-for-study-course-sidebar-ad","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21701","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=21701"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21701\/revisions"}],"predecessor-version":[{"id":256867,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21701\/revisions\/256867"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=21701"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}