{"id":21339,"date":"2019-05-21T01:21:53","date_gmt":"2019-05-20T19:51:53","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21339"},"modified":"2023-06-02T10:31:19","modified_gmt":"2023-06-02T05:01:19","slug":"if-x-y-and-k-are-positive-and-x-is-less-than-y-then-x-k-y-k-is-ogqr-2020-question-80-with-solution","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/if-x-y-and-k-are-positive-and-x-is-less-than-y-then-x-k-y-k-is-ogqr-2020-question-80-with-solution\/","title":{"rendered":"If x, y, and k are positive and x is less than y, then (x + k) \/ (y + k)\u00a0 is &#8211; OGQR 2020 Question #80 with Solution"},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">&lt; 1<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span>\n<h2 id=\"h-ogqr-2020-question-no-80\">OGQR 2020: Question No. 80<\/h2>\n\n\n\n<p>If x, y, and k are positive and x is less than y, then (x + k) \/ (y + k) is<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Source<\/td><td>OGQR 2020<\/td><\/tr><tr><td>Type<\/td><td>Problem Solving<\/td><\/tr><tr><td>Topic<\/td><td>Algebra<\/td><\/tr><tr><td>Sub-Topic<\/td><td>Ratio \/ Inequality<\/td><\/tr><tr><td>Difficulty<\/td><td>Medium<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 id=\"h-solution\">Solution<\/h3>\n\n\n\n<h4 id=\"h-given\"><strong><u>Given<\/u><\/strong><\/h4>\n\n\n\n<p>In this question, we are given<\/p>\n\n\n\n<ul><li>The numbers x, y, and k are positive.<\/li><li>Also, x is less than y.<\/li><\/ul>\n\n\n\n<h4 id=\"h-to-find\"><strong><u>To Find<\/u><\/strong><\/h4>\n\n\n\n<p>We need to determine<\/p>\n\n\n\n<ul><li>The possible range of (x+ k) \/ (y+ k).<\/li><\/ul>\n\n\n\n<h4 id=\"h-approach-working\"><strong><u>Approach &amp; Working<\/u><\/strong><\/h4>\n\n\n\n<p>We know that<\/p>\n\n\n\n<ul><li>x &lt; y<\/li><\/ul>\n\n\n\n<p>Or, xk &lt; yk   [Since k is a positive number, multiplication does not change the sign of inequality.]<\/p>\n\n\n\n<p>Or, xk + xy &lt; yk + xy     [Adding xy on both sides]<\/p>\n\n\n\n<p>Or, x (y + k) &lt; y (x + k)    [Taking x and y common on each side]<\/p>\n\n\n\n<p>Or,&nbsp; x \/y&lt;&nbsp;(x+ k) \/ (y+ k).     [Since y and (y + k) are positive numbers, division does not change the sign of inequality.]<\/p>\n\n\n\n<p>Hence, the correct answer is option B.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2><strong>Takeaways:<\/strong><\/h2>\n\n\n\n<ol type=\"1\"><li>Multiplying\/dividing both sides of an inequality by a positive number does not change the sign of the inequality.<ol><li>Example: If x &lt; y, then 2x &lt; 2y.<\/li><\/ol><\/li><li>Multiplying\/dividing both sides of an inequality by a negative number reverses the sign of the inequality.<ol><li>Example: If x &lt; y, then -2x &gt; -2y.<\/li><\/ol><\/li><\/ol>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>Did you know a 700+ GMAT Score can increase your chances to get into your dream business school? We can help you achieve that. Why don\u2019t you<a href=\"https:\/\/e-gmat.com\/ft-gmat\/?channel=blogsin_article&amp;utm_source=blogs&amp;utm_medium=in_article&amp;utm_campaign=free_trial&amp;utm_term=blogs_in_article_lekhika\" target=\"_blank\" rel=\"noopener noreferrer external\" data-wpel-link=\"external\">&nbsp;<strong>try out our FREE Trial?<\/strong><\/a><strong>&nbsp;<\/strong>We are the<strong>&nbsp;<a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" target=\"_blank\" rel=\"noopener noreferrer external\" data-wpel-link=\"external\">most reviewed online GMAT Preparation company in GMATClub<\/a><\/strong> with more than 1950 reviews as of November 2020.<\/p><\/blockquote>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-c5941e00-4e2c-4789-a0c3-03b48388b431\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium ub-button-flex-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-block-btn\">Sign up for a Free Trial<\/span>\n    <\/div><\/a><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>OGQR 2020: Question No. 80 If x, y, and k are positive and x is less than y, then (x + k) \/ (y + k) is Source OGQR 2020 Type Problem Solving Topic Algebra Sub-Topic Ratio \/ Inequality Difficulty Medium Solution Given In this question, we are given The numbers x, y, and k [&hellip;]<\/p>\n","protected":false},"author":102413,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","ub_ctt_via":""},"categories":[103,44,94,60,100],"tags":[],"featured_image_src":null,"author_info":{"display_name":"Ashutosh","author_link":"https:\/\/e-gmat.com\/blogs\/author\/ashutoshe-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.1 - 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