{"id":22881,"date":"2014-02-13T07:00:09","date_gmt":"2014-02-13T14:00:09","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/2014\/02\/gmat-question-of-the-week-data-sufficiency-and-averages-the-explanation-2\/"},"modified":"2014-02-13T07:00:09","modified_gmt":"2014-02-13T14:00:09","slug":"gmat-question-of-the-week-data-sufficiency-and-averages-the-explanation-2","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/gmat-question-of-the-week-data-sufficiency-and-averages-the-explanation-2\/","title":{"rendered":"GMAT Question of the Week: Data Sufficiency and Averages \u2013 The Explanation"},"content":{"rendered":"<div>\n\t\t<a href=\"https:\/\/gmat.kaptest.com\/2014\/02\/13\/gmat-data-sufficiency-and-averages-the-explanation\/\" title=\"GMAT Data Sufficiency\"><img loading=\"lazy\" decoding=\"async\" title=\"GMAT Data Sufficiency\" src=\"https:\/\/gmat.kaptest.com\/wp-content\/uploads\/2014\/02\/hiAverage.jpg\" alt=\"GMAT Data Sufficiency\" width=\"194\" height=\"200\" \/><\/a>\n\t\t<\/div>\n<p>\n\t\t<a href=\"https:\/\/gmat.kaptest.com\/wp-content\/uploads\/2014\/02\/hiAverage.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-3209 alignright\" title=\"GMAT Data Sufficiency\" alt=\"GMAT Data Sufficiency\" src=\"https:\/\/gmat.kaptest.com\/wp-content\/uploads\/2014\/02\/hiAverage.jpg\" width=\"175\" height=\"179\" \/><\/a>If you haven't already, visit our GMAT\u00a0<a href=\"https:\/\/gmat.kaptest.com\/2013\/11\/05\/gmat-question-of-the-week-data-sufficiency-and-averages\/#sthash.bJ136wtz.dpbs\" target=\"_blank\">Data Sufficiency and Averages practice problem<\/a> and give it a try on your own before reading the explanation.<\/p>\n<p>To get this question correct, you must combine your knowledge of fundamental math concepts with use of the <a href=\"https:\/\/www.kaptest.com\/gmat\/kaplan-gmat-prep\/presidents-day?cmp=blog:GMAT_PRES200FLASH_021314\" target=\"_blank\">Kaplan Method<\/a> and strategies for approaching Data Sufficiency and Averages. Here\u2019s a breakdown:<\/p>\n<p>The average formula is<\/p>\n<p><a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=Average&amp;space;=&amp;space;\\frac{sum&amp;space;-of-&amp;space;terms}{number-&amp;space;of-&amp;space;terms}\" target=\"_blank\"><img decoding=\"async\" title=\"Average = \\frac{sum -of- terms}{number- of- terms}\" alt=\"\" src=\"https:\/\/latex.codecogs.com\/gif.latex?Average&amp;space;=&amp;space;\\frac{sum&amp;space;-of-&amp;space;terms}{number-&amp;space;of-&amp;space;terms}\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>The average of <i>m<\/i> and <i>n<\/i> is \u00a0<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=\\frac{\\left&amp;space;(&amp;space;m+n&amp;space;\\right&amp;space;)}{2}\" target=\"_blank\"><img decoding=\"async\" title=\"\\frac{\\left ( m+n \\right )}{2}\" alt=\"\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\left&amp;space;(&amp;space;m+n&amp;space;\\right&amp;space;)}{2}\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>The question stem asks \u00a0\u201cIs \u00a0<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=\\frac{\\left&amp;space;(&amp;space;m+n&amp;space;\\right&amp;space;)}{2}&amp;space;&lt;&amp;space;50\" target=\"_blank\"><img decoding=\"async\" title=\"\\frac{\\left ( m+n \\right )}{2} &lt; 50\" alt=\"\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\left&amp;space;(&amp;space;m+n&amp;space;\\right&amp;space;)}{2}&amp;space;&lt;&amp;space;50\" \/><\/a>?\u201d<\/p>\n<p>&nbsp;<\/p>\n<p>Remember, with a <b>Yes\/No Data Sufficiency<\/b> question, you are looking at the statements and trying to determine whether they provide a <b><i>consistent<\/i><\/b> YES or NO answer to this question. A consistent answer of yes OR no is sufficient. An inconsistent answer (yes <em>and<\/em> no) is insufficient.<\/p>\n<p>&nbsp;<\/p>\n<p><b>Statement (1): Sufficient.<\/b> This statement says that <a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=\\frac{\\left&amp;space;(&amp;space;3m+3n&amp;space;\\right&amp;space;)}{2}&amp;space;=&amp;space;90\" target=\"_blank\"><img decoding=\"async\" title=\"\\frac{\\left ( 3m+3n \\right )}{2} = 90\" alt=\"\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\left&amp;space;(&amp;space;3m+3n&amp;space;\\right&amp;space;)}{2}&amp;space;=&amp;space;90\" \/><\/a><\/p>\n<p>Pull the 3 out of the numerator to get \u00a0<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=\\frac{\\left&amp;space;(&amp;space;3(m+n)&amp;space;\\right&amp;space;)}{2}&amp;space;=&amp;space;90\" target=\"_blank\"><img decoding=\"async\" title=\"\\frac{\\left ( 3(m+n) \\right )}{2} = 90\" alt=\"\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\left&amp;space;(&amp;space;3(m+n)&amp;space;\\right&amp;space;)}{2}&amp;space;=&amp;space;90\" \/><\/a><\/p>\n<p>Multiply both sides by 2 to get \u00a0<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=3\\left&amp;space;(&amp;space;m+n&amp;space;\\right&amp;space;)=180\" target=\"_blank\"><img decoding=\"async\" title=\"3\\left ( m+n \\right )=180\" alt=\"\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\left&amp;space;(&amp;space;m+n&amp;space;\\right&amp;space;)=180\" \/><\/a><\/p>\n<p>Then divide both sides by 3 to get \u00a0<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=m+n&amp;space;=&amp;space;60\" target=\"_blank\"><img decoding=\"async\" title=\"m+n = 60\" alt=\"\" src=\"https:\/\/latex.codecogs.com\/gif.latex?m+n&amp;space;=&amp;space;60\" \/><\/a><\/p>\n<p>So, the average of <i>m<\/i> and <i>n<\/i> is \u00a0\u00a0<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=\\frac{m+n}{2}=&amp;space;\\frac{60}{2}&amp;space;=&amp;space;30\" target=\"_blank\"><img decoding=\"async\" title=\"\\frac{m+n}{2}= \\frac{60}{2} = 30\" alt=\"\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{m+n}{2}=&amp;space;\\frac{60}{2}&amp;space;=&amp;space;30\" \/><\/a>.<\/p>\n<p><strong>The average of <i>m<\/i> and <i>n<\/i> is definitely less than 50<\/strong>, and the answer to the question in the stem is always \u201cyes.\u201d <strong>Statement (1) is sufficient<\/strong>, so you can eliminate (B), (C), and (E).<\/p>\n<p><b>Statement (2): Insufficient.<\/b> This does not allow us to determine the average of m and n, because it does not give us the values or the right relationship between m and n. Eliminate (D).<\/p>\n<p>Answer choice (A) is correct.<\/p>\n<p>&nbsp;<\/p>\n<p>The post <a rel=\"nofollow\" href=\"https:\/\/gmat.kaptest.com\/2014\/02\/13\/gmat-data-sufficiency-and-averages-the-explanation\/\">GMAT Question of the Week: Data Sufficiency and Averages &#8211; The Explanation<\/a> appeared first on <a rel=\"nofollow\" href=\"https:\/\/gmat.kaptest.com\">Kaplan GMAT Blog<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If you haven&#8217;t already, visit our GMAT\u00a0Data Sufficiency and Averages practice problem and give it a try on your own before reading the explanation. To get this question correct, you&#8230;<\/p>\n","protected":false},"author":120,"featured_media":0,"comment_status":"closed","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,558,243,940],"tags":[],"class_list":["post-22881","post","type-post","status-publish","format-standard","hentry","category-gmat","category-kaplan-blog","category-blog","category-gmat-prep-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/22881","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/users\/120"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=22881"}],"version-history":[{"count":0,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/22881\/revisions"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=22881"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=22881"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=22881"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}