{"id":2200,"date":"2024-05-21T16:44:27","date_gmt":"2024-05-21T11:14:27","guid":{"rendered":"https:\/\/online.wizako.com\/gre-preparation\/blog\/?p=2200"},"modified":"2024-06-07T11:12:53","modified_gmt":"2024-06-07T05:42:53","slug":"quantitative-comparison-absolute-values","status":"publish","type":"post","link":"https:\/\/online.wizako.com\/gre-preparation\/blog\/free-gre-online-preparation\/gre-quant-gre-math\/gre-quant-practice-questions\/quantitative-comparison-absolute-values\/","title":{"rendered":"Quantitative Comparison &#8211; Absolute Values"},"content":{"rendered":"\n<p>A very interesting question testing concepts in absolute values, number line, and the meaning of arithmetic mean of a set of numbers. A good question to understand the meaning of the absolute values of the difference between two numbers.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"question\">Question<\/h4>\n\n\n\n<p>p, q, and r are three points on the real number line where q = $latex \\frac{2pr}{p+r}$.<\/p>\n\n\n\n<p><strong>Quantity A<\/strong>: $latex \\left | \\frac{1}{p} &#8211; \\frac{1}{r}\\right |$<\/p>\n\n\n\n<p><br><strong>Quantity B<\/strong>: $latex \\left | \\frac{1}{q} &#8211; \\frac{1}{p}\\right |$<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Correct Answer<\/summary>\n<p>Choice A &#8211; Quantity A is greater<\/p>\n<\/details>\n\n\n<style><\/style><!-- begin-flying-press-lazy-render -->\n<figure class=\"wp-block-image aligncenter size-full has-custom-border\"><a href=\"https:\/\/wzko.pro\/online\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"256\" src=\"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-content\/uploads\/2024\/02\/GRE-Vocab-4-1.webp\" alt=\"GRE Vocabulary Builder\" class=\"has-border-color has-palette-color-3-border-color wp-image-2786\" srcset=\"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-content\/uploads\/2024\/02\/GRE-Vocab-4-1.webp 1024w, https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-content\/uploads\/2024\/02\/GRE-Vocab-4-1-300x75.webp 300w, https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-content\/uploads\/2024\/02\/GRE-Vocab-4-1-768x192.webp 768w, https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-content\/uploads\/2024\/02\/GRE-Vocab-4-1-360x90.webp 360w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n<!-- end-flying-press-lazy-render -->\n\n\n<h4 class=\"wp-block-heading\" id=\"explanatory-answer\">Explanatory Answer<\/h4>\n\n\n\n<p>Given: q = $latex \\frac{2pr}{p + r}$<\/p>\n\n\n\n<p>Let&#8217;s make sense of this information.<br>Cross multiplying, we get q(p + r) = 2pr<br>i.e., qp + qr = 2pr<\/p>\n\n\n\n<p>Divide the equation by pqr<br>$latex \\frac{1}{r}$ + $latex \\frac{1}{p}$ = $latex \\frac{2}{q}$<\/p>\n\n\n\n<p>Divide the equation by 2<br>$latex \\frac{\\frac{1}{r} + \\frac{1}{p}}{2}$ = $latex \\frac{1}{q}$<\/p>\n\n\n\n<h6 class=\"wp-block-heading\" id=\"what-can-we-infer-from-the-above-equation\">What can we infer from the above equation?<\/h6>\n\n\n\n<p>The same inference that we can draw if someone told us that z = $latex \\frac{x + y}{2}$<br>The inference we will draw is that z is the arithmetic mean (average) of x and y.<\/p>\n\n\n\n<p>Using the same logic, we can infer that $latex \\frac{1}{q}$ is the arithmetic mean (average) of $latex \\frac{1}{p}$ and $latex \\frac{1}{r}$.<\/p>\n\n\n\n<h6 class=\"wp-block-heading\" id=\"a-few-key-insights-from-this-inference\">A few key insights from this inference<\/h6>\n\n\n\n<p>If z is the average of x and y, it is evident that z will lie between x and y on the number line. <\/p>\n\n\n\n<p>By the same logic, $latex \\frac{1}{q}$ will lie between $latex \\frac{1}{p}$ and $latex \\frac{1}{r}$ on the number line. <\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"what-are-we-trying-to-compare\">What are we trying to compare?<\/h4>\n\n\n\n<p>$latex \\left | \\frac{1}{p} &#8211; \\frac{1}{r}\\right |$ and $latex \\left | \\frac{1}{q} &#8211; \\frac{1}{p}\\right |$<\/p>\n\n\n\n<p><strong>If x and y are two points on the number line, what does |x &#8211; y| measure?<\/strong><\/p>\n\n\n\n<p>|x &#8211; y| measures the distance between the two points x and y.<\/p>\n\n\n\n<p>Extending that logic, $latex \\left | \\frac{1}{p} &#8211; \\frac{1}{r}\\right |$ measures the distance between points $latex \\frac{1}{p}$ and $latex \\frac{1}{r}$<\/p>\n\n\n\n<p>Similarly, quantity B measures the distance between points $latex \\frac{1}{p}$ and $latex \\frac{1}{q}$<\/p>\n\n\n\n<p>We deduced that $latex \\frac{1}{q}$ lies between $latex \\frac{1}{p}$ and $latex \\frac{1}{r}$.<\/p>\n\n\n\n<p>Therefore, the distance between $latex \\frac{1}{p}$ and $latex \\frac{1}{r}$ (quantity A) will be greater than the distance between $latex \\frac{1}{p}$ and $latex \\frac{1}{q}$<\/p>\n\n\n\n<p>Hence, Quantity A is greater than Quantity B<\/p>\n\n\n<style><\/style>\n<div class=\"wp-block-group alignfull has-text-color has-background is-layout-flow wp-block-group-is-layout-flow\" style=\"color:#000000;background-color:#ffffff\">\n<div style=\"height:64px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\" style=\"line-height:.9\"><strong>There&#8217;s more where this question came from<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center\" id=\"gre-algebra-practice-questions\" style=\"font-size:clamp(32.969px, 2.061rem + ((1vw - 3.2px) * 2.034), 59px);px;line-height:1.15\"><strong>GRE Algebra Practice Questions<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-buttons is-horizontal is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-03627597 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-50\"><a class=\"wp-block-button__link has-text-color has-background wp-element-button\" href=\"https:\/\/practice-questions.wizako.com\/gre\/quant\/algebra\/linear-equations-quadratic-equations-inequalities-gre-sample-questions-questionbank.shtml\" style=\"border-radius:50px;color:#ffffff;background-color:#000000\" target=\"_blank\" rel=\"noreferrer noopener\">Solve them now<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:64px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>GRE Quantitative Comparison practice question. Absolute values, number line, and arithmetic mean.<\/p>\n","protected":false},"author":1,"featured_media":2215,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_gspb_post_css":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[233],"tags":[342,341],"class_list":["post-2200","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gre-quant-practice-questions","tag-algebra","tag-quantitative-comparison"],"blocksy_meta":[],"_links":{"self":[{"href":"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-json\/wp\/v2\/posts\/2200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-json\/wp\/v2\/comments?post=2200"}],"version-history":[{"count":0,"href":"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-json\/wp\/v2\/posts\/2200\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-json\/wp\/v2\/media\/2215"}],"wp:attachment":[{"href":"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-json\/wp\/v2\/media?parent=2200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-json\/wp\/v2\/categories?post=2200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/online.wizako.com\/gre-preparation\/blog\/wp-json\/wp\/v2\/tags?post=2200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}