{"id":485,"date":"2020-09-17T07:02:11","date_gmt":"2020-09-17T11:02:11","guid":{"rendered":"https:\/\/gmatbyexample.com\/site\/?p=485"},"modified":"2020-09-27T14:10:49","modified_gmt":"2020-09-27T18:10:49","slug":"solve-gmat-inequalities-comparisons-questions-confidently-with-this-framework","status":"publish","type":"post","link":"https:\/\/gmatbyexample.com\/site\/solve-gmat-inequalities-comparisons-questions-confidently-with-this-framework\/","title":{"rendered":"Solve Gmat Inequalities &#8220;Comparisons&#8221; questions confidently with this framework"},"content":{"rendered":"\n<p>Among the GMAT questions, inequalities make a really tricky set of questions. Whether you get the inequality concept as a Problem Solving (PS) or a Data Sufficiency (DS) question, the standard of the question is usually very high and the potential to make a mistake is high as well. <\/p>\n\n\n\n<p>Often, there is a category of gmat inequalities questions that revolves around the powers of x. Specifically, the question is looking for some sort of comparison between the exponents and fractions of x. For example: x, x<sup>2<\/sup>, x<sup>3<\/sup>, x<sup>4<\/sup>, 1\/x, 1\/x<sup>2<\/sup> and so on. This article focuses on providing an approach to solve these kinds of problems. With practice this framework will become easier to implement. <\/p>\n\n\n\n<p>After you have read through the tutorial and the framework, do not miss out on the <a href=\"#gmat-challenge\">challenge question<\/a>. <\/p>\n\n\n<ul class=\"wp-block-latest-posts__list is-grid columns-3 wp-block-latest-posts\"><li><div class=\"wp-block-latest-posts__featured-image aligncenter\"><img loading=\"lazy\" width=\"150\" height=\"150\" data-src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2022\/08\/pexels-photo-941555-150x150.jpeg\" class=\"attachment-thumbnail size-thumbnail wp-post-image lazyload\" alt=\"photo of a woman thinking\" decoding=\"async\" style=\"--smush-placeholder-width: 150px; --smush-placeholder-aspect-ratio: 150\/150;max-width:75px;max-height:75px;\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" \/><noscript><img loading=\"lazy\" width=\"150\" height=\"150\" src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2022\/08\/pexels-photo-941555-150x150.jpeg\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" alt=\"photo of a woman thinking\" decoding=\"async\" style=\"max-width:75px;max-height:75px;\" \/><\/noscript><\/div><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/gmatbyexample.com\/site\/9-reasons-to-write-an-mba-optional-essay\/\">(2022) 9 Reasons To Write An MBA Optional Essay<\/a><\/li>\n<li><div class=\"wp-block-latest-posts__featured-image aligncenter\"><img loading=\"lazy\" width=\"150\" height=\"150\" data-src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/09\/GMAT_Math-150x150.png\" class=\"attachment-thumbnail size-thumbnail wp-post-image lazyload\" alt=\"GMAT Math\" decoding=\"async\" style=\"--smush-placeholder-width: 150px; --smush-placeholder-aspect-ratio: 150\/150;max-width:75px;max-height:75px;\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" \/><noscript><img loading=\"lazy\" width=\"150\" height=\"150\" src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/09\/GMAT_Math-150x150.png\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" alt=\"GMAT Math\" decoding=\"async\" style=\"max-width:75px;max-height:75px;\" \/><\/noscript><\/div><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/gmatbyexample.com\/site\/2022-what-are-gmat-quant-topics-in-syllabus-for-the-gmat-test\/\">(2022) What Are GMAT Quant Topics in Syllabus For The GMAT Test ?<\/a><\/li>\n<li><div class=\"wp-block-latest-posts__featured-image aligncenter\"><img loading=\"lazy\" width=\"150\" height=\"150\" data-src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2021\/10\/GMAT_Statistics_FEATURED-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail wp-post-image lazyload\" alt=\"GMAT Statistics Practice Examples\" decoding=\"async\" style=\"--smush-placeholder-width: 150px; --smush-placeholder-aspect-ratio: 150\/150;max-width:75px;max-height:75px;\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" \/><noscript><img loading=\"lazy\" width=\"150\" height=\"150\" src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2021\/10\/GMAT_Statistics_FEATURED-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" alt=\"GMAT Statistics Practice Examples\" decoding=\"async\" style=\"max-width:75px;max-height:75px;\" \/><\/noscript><\/div><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/gmatbyexample.com\/site\/gmat-statistics-practice-examples\/\">GMAT Statistics Practice Examples<\/a><\/li>\n<\/ul>\n\n\n<blockquote class=\"wp-block-quote has-text-align-center\"><p><img decoding=\"async\" loading=\"lazy\" width=\"128\" height=\"128\" class=\"wp-image-372 lazyload\" style=\"--smush-placeholder-width: 128px; --smush-placeholder-aspect-ratio: 128\/128;width: 30px;\" data-src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/08\/icons8-idea-128.png\" alt=\"GMAT question\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\"><noscript><img decoding=\"async\" loading=\"lazy\" width=\"128\" height=\"128\" class=\"wp-image-372\" style=\"width: 30px;\" src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/08\/icons8-idea-128.png\" alt=\"GMAT question\"><\/noscript> Remember the ranges: (x&lt;-1, -1&lt;x&lt;0, 0&lt;x&lt;1 &amp; x&gt;1)<\/p><\/blockquote>\n\n\n\n<p>The below video discusses the framework in detail with two solved examples for your practice. We have added some additional links for further <a href=\"http:\/\/gmat-practice\">gmat inequalities practice<\/a> at the end of the post. <\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"GMAT Inequalities: Comparing powers of x - x, x^2, x^3, 1\/x, 1\/x^2, 1\/x^3 etc.\" width=\"640\" height=\"360\" data-src=\"https:\/\/www.youtube.com\/embed\/aJqsq-pBdus?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" class=\"lazyload\" data-load-mode=\"1\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Framework:<\/h3>\n\n\n\n<ol><li>Lay out the four critical ranges <ul><li>x &lt; -1<\/li><li>-1 &lt; x &lt; 0<\/li><li>0 &lt; x &lt; 1<\/li><li>x &gt; 1<\/li><\/ul><\/li><li>Observe which ranges apply to the question. If it is not clearly given, use all<\/li><li>The relationships amongst the terms are always the same within the ranges. To save time on questions, instead of deriving them again and again, practice and remember. <\/li><li>If you do not recall the relationships or are short of time, just take values in the ranges above. <\/li><li>Apply the relationships to solve the question.<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-pullquote is-style-default\" style=\"border-color:#fcb900\"><blockquote class=\"has-text-color has-vivid-cyan-blue-color\"><p><img decoding=\"async\" loading=\"lazy\" width=\"128\" height=\"128\" class=\"wp-image-372 lazyload\" style=\"--smush-placeholder-width: 128px; --smush-placeholder-aspect-ratio: 128\/128;width: 75px;\" data-src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/08\/icons8-idea-128.png\" alt=\"GMAT question\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\"><noscript><img decoding=\"async\" loading=\"lazy\" width=\"128\" height=\"128\" class=\"wp-image-372\" style=\"width: 75px;\" src=\"https:\/\/gmatbyexample.com\/site\/wp-content\/uploads\/2020\/08\/icons8-idea-128.png\" alt=\"GMAT question\"><\/noscript><\/p><p><strong><span style=\"text-decoration: underline;\">Tip<\/span><\/strong>: The relationship amongst the terms such as x, x<sup>2<\/sup>, x<sup>3<\/sup>, x<sup>4<\/sup>, 1\/x, 1\/x<sup>2<\/sup> remains the same between the ranges. Rather than deriving the relationships again and again &#8211; <strong><span style=\"text-decoration: underline;\">Remember them<\/span><\/strong>. <\/p><\/blockquote><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">The final relationship:<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><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<h3 class=\"has-white-color has-luminous-vivid-orange-background-color has-text-color has-background wp-block-heading\" id=\"gmat-challenge\">GMAT Inequalities Challenge Question:<\/h3>\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> > 1\/x<sup>2<\/sup> ?<\/p><p>a) 1\/x > 1\/x<sup>2<\/sup><\/p><p>b) x<sup>2<\/sup> > 7<\/p><p>[su_spoiler title=&#8221;OA&#8221; open=&#8221;no&#8221; style=&#8221;simple&#8221; icon=&#8221;plus&#8221; anchor=&#8221;&#8221; anchor_in_url=&#8221;no&#8221; class=&#8221;&#8221;]D[\/su_spoiler]<\/p><cite>This is a DS question. Standard DS answer choices apply. <a rel=\"noreferrer noopener\" href=\"https:\/\/gmatbyexample.com\/site\/contact-me\/\" target=\"_blank\">Contact us<\/a> if you have questions.<\/cite><\/blockquote><\/figure>\n\n\n\n<p>Read more on <a rel=\"noreferrer noopener\" href=\"https:\/\/gmatbyexample.com\/site\/tag\/gmat-inequalities\/\" target=\"_blank\">Inequalities<\/a><\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"gmat-practice\">GMAT Inequalities: Practice Questions:<\/h4>\n\n\n\n<p>The two questions in the video: <a href=\"https:\/\/gmatclub.com\/forum\/which-of-the-following-could-be-correct-301057.html\" target=\"_blank\" rel=\"noreferrer noopener\">Q1<\/a> and <a href=\"https:\/\/gmatclub.com\/forum\/is-x-2-1-x-239236.html\" target=\"_blank\" rel=\"noreferrer noopener\">Q2<\/a>. <\/p>\n\n\n\n<p>Other practice questions:<\/p>\n\n\n\n<p><a href=\"https:\/\/gmatclub.com\/forum\/if-x-is-positive-which-of-the-following-could-be-correct-ordering-of-71070.html\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/gmatclub.com\/forum\/if-x-is-positive-which-of-the-following-could-be-correct-ordering-of-71070.html<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/gmatclub.com\/forum\/what-is-the-value-of-x-if-x-3-x-243190.html\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/gmatclub.com\/forum\/what-is-the-value-of-x-if-x-3-x-243190.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The comparisons of x, x^2, 1\/x, 1\/x^2 etc are tough. Solve Gmat Inequalities &#8220;Comparisons&#8221; questions confidently &#038; correctly with this framework &#8230;<\/p>\n","protected":false},"author":1,"featured_media":511,"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\/485"}],"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=485"}],"version-history":[{"count":41,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/posts\/485\/revisions"}],"predecessor-version":[{"id":549,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/posts\/485\/revisions\/549"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/media\/511"}],"wp:attachment":[{"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/media?parent=485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/categories?post=485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatbyexample.com\/site\/wp-json\/wp\/v2\/tags?post=485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}