{"id":595,"date":"2020-10-25T05:42:11","date_gmt":"2020-10-25T09:42:11","guid":{"rendered":"https:\/\/gmatbyexample.com\/site\/?p=595"},"modified":"2020-10-25T06:13:51","modified_gmt":"2020-10-25T10:13:51","slug":"gmat-inequalities-problems-challenge-problem-i-2-explanation","status":"publish","type":"post","link":"https:\/\/gmatbyexample.com\/site\/gmat-inequalities-problems-challenge-problem-i-2-explanation\/","title":{"rendered":"GMAT Inequalities Problems: Challenge Problem I.2 explanation"},"content":{"rendered":"\n<p>As most GMAT Test takers already know, this is a very specific type GMAT Inequalities problems that they often come across while practicing GMAT Math. Quite frequently, test takers either get this type of GMAT Inequalities problems incorrect (thus loosing points) or spend too much time on them resulting in time wastage. <\/p>\n\n\n\n<figure class=\"wp-block-pullquote has-background is-style-solid-color\" style=\"background-color:#eef0e4\"><blockquote class=\"has-text-color has-black-color\"><p>QI2. Is 1\/x<sup>4<\/sup>&nbsp;&gt; 1\/x<sup>2<\/sup>&nbsp;?<\/p><p>a) 1\/x &gt; 1\/x<sup>2<\/sup><\/p><p>b) x<sup>2<\/sup>&nbsp;&gt; 7<\/p><\/blockquote><\/figure>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"alignright size-thumbnail\"><a href=\"https:\/\/www.youtube.com\/channel\/UCkC-Xqxt9dW5py8YKl9lWEQ\/\"><img decoding=\"async\" loading=\"lazy\" width=\"150\" height=\"150\" data-src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/Screen-Shot-2020-10-25-at-6.01.17-AM-edited-150x150.png\" alt=\"Subscribe to GMATByExample Videos\" class=\"wp-image-643 lazyload\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" style=\"--smush-placeholder-width: 150px; --smush-placeholder-aspect-ratio: 150\/150;\" \/><noscript><img decoding=\"async\" loading=\"lazy\" width=\"150\" height=\"150\" src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/Screen-Shot-2020-10-25-at-6.01.17-AM-edited-150x150.png\" alt=\"Subscribe to GMATByExample Videos\" class=\"wp-image-643\"\/><\/noscript><\/a><\/figure><\/div>\n\n\n\n<p>Hence, to make it quick and easy to solve these type of problems, we have developed a <a href=\"https:\/\/gmatbyexample.com\/site\/solve-gmat-inequalities-comparisons-questions-confidently-with-this-framework\/\">GMAT Inequalities Comparison Framework<\/a>. However, the framework does come with a caveat &#8211; you must remember the range table or must atleast be able to draw the table quickly. This is certainly possible with a little bit of practice. <\/p>\n\n\n\n<p>Since the details of the basic framework for solving this type of question is covered in the article <a rel=\"noreferrer noopener\" href=\"https:\/\/gmatbyexample.com\/site\/solve-gmat-inequalities-comparisons-questions-confidently-with-this-framework\/\" target=\"_blank\">GMAT Comparisons Framework<\/a>, in this article, we will skip the basics and solve this question using the framework only.  <\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The comparisons framework<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" loading=\"lazy\" width=\"787\" height=\"463\" data-src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/09\/inequalities_correct.png\" alt=\"\" class=\"wp-image-543 lazyload\" data-srcset=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/09\/inequalities_correct.png 787w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/09\/inequalities_correct-300x176.png 300w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/09\/inequalities_correct-768x452.png 768w\" data-sizes=\"(max-width: 787px) 100vw, 787px\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" style=\"--smush-placeholder-width: 787px; --smush-placeholder-aspect-ratio: 787\/463;\" \/><noscript><img decoding=\"async\" loading=\"lazy\" width=\"787\" height=\"463\" src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/09\/inequalities_correct.png\" alt=\"\" class=\"wp-image-543\" srcset=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/09\/inequalities_correct.png 787w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/09\/inequalities_correct-300x176.png 300w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/09\/inequalities_correct-768x452.png 768w\" sizes=\"(max-width: 787px) 100vw, 787px\" \/><\/noscript><\/figure>\n\n\n\n<p>Let&#8217;s start with the question statement and see in which of these ranges would the statement be true:<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#ecf7fd\"><strong>Is 1\/x<sup>4<\/sup>&nbsp;&gt; 1\/x<sup>2<\/sup> ?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" loading=\"lazy\" width=\"787\" height=\"463\" data-src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-7.png\" alt=\"\" class=\"wp-image-598 lazyload\" data-srcset=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-7.png 787w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-7-300x176.png 300w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-7-768x452.png 768w\" data-sizes=\"(max-width: 787px) 100vw, 787px\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" style=\"--smush-placeholder-width: 787px; --smush-placeholder-aspect-ratio: 787\/463;\" \/><noscript><img decoding=\"async\" loading=\"lazy\" width=\"787\" height=\"463\" src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-7.png\" alt=\"\" class=\"wp-image-598\" srcset=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-7.png 787w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-7-300x176.png 300w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-7-768x452.png 768w\" sizes=\"(max-width: 787px) 100vw, 787px\" \/><\/noscript><\/figure>\n\n\n\n<p>As you can see from the ranges, for the question statement to be true, x must lie between -1 and 1. We could have arrived at the same conclusion after algebra, but that would have been time consuming and also prone to mistakes. <\/p>\n\n\n\n<p>So the question statement truly becomes:<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#ecf7fd\"><strong>Is 1\/x<sup>4<\/sup>\u00a0> 1\/x<sup>2<\/sup> ?<\/strong> is same as <strong><em>Is -1 &lt; x &lt; 1 ? <\/em><\/strong><\/p>\n\n\n\n<p>Now look at statement (a)<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#ecf7fd\"><strong>a) 1\/x &gt; 1\/x<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p>Lets look at the ranges where this is true:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" loading=\"lazy\" width=\"787\" height=\"152\" data-src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-9.png\" alt=\"\" class=\"wp-image-600 lazyload\" data-srcset=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-9.png 787w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-9-300x58.png 300w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-9-768x148.png 768w\" data-sizes=\"(max-width: 787px) 100vw, 787px\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" style=\"--smush-placeholder-width: 787px; --smush-placeholder-aspect-ratio: 787\/152;\" \/><noscript><img decoding=\"async\" loading=\"lazy\" width=\"787\" height=\"152\" src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-9.png\" alt=\"\" class=\"wp-image-600\" srcset=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-9.png 787w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-9-300x58.png 300w, https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/10\/image-9-768x148.png 768w\" sizes=\"(max-width: 787px) 100vw, 787px\" \/><\/noscript><\/figure>\n\n\n\n<p>As you can see in the diagram, this is only possible when x>1. So given that 1\/x > 1\/x<sup>2<\/sup>, we are given that x>1. Hence x cannot be between -1 and 1. So this answers <strong><span style=\"text-decoration: underline;\">a clear &#8220;NO&#8221;<\/span><\/strong> to the asked question in the question statement. <\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#d8eccf\">Hence,  statement (a) is SUFFICIENT.<\/p>\n\n\n\n<p>Lets look at statement (b)<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#ecf7fd\"><strong>b) x<sup>2<\/sup> > 7<\/strong><\/p>\n\n\n\n<p>Using a little bit of algebra, we get<\/p>\n\n\n\n<p>x2 &#8211; 7 > 0 => (x-\u23b77)(x+\u23b77) > 0<\/p>\n\n\n\n<p>This gives us:<\/p>\n\n\n\n<p>either x>\u23b77 OR x&lt;-\u23b77 . This clearly means that x is NOT in the range -1&lt;x&lt;1. Hence, this gives <strong><span style=\"text-decoration: underline;\">a clear &#8220;NO&#8221;<\/span><\/strong> to the asked question. <\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#d8eccf\">Hence,  statement (a) is SUFFICIENT.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solve GMAT Inequalities Problem Using Algebra<\/h2>\n\n\n\n<p>[Coming Soon][su_quote]Coming soon![\/su_quote]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>You must understand this framework of solving GMAT Inequalities problems like &#8220;1\/x^4 > 1\/x^2&#8221; within 2 minutes. Now you can ace these problems<\/p>\n","protected":false},"author":1,"featured_media":637,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,48],"tags":[59,58,61,60,62],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/posts\/595"}],"collection":[{"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/comments?post=595"}],"version-history":[{"count":10,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/posts\/595\/revisions"}],"predecessor-version":[{"id":688,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/posts\/595\/revisions\/688"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/media\/637"}],"wp:attachment":[{"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/media?parent=595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/categories?post=595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/tags?post=595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}