{"id":5392,"date":"2015-04-30T08:08:40","date_gmt":"2015-04-30T15:08:40","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=5392"},"modified":"2015-04-30T21:00:01","modified_gmt":"2015-05-01T04:00:01","slug":"3-mistakes-of-lcm-gcd-questions-q4","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/3-mistakes-of-lcm-gcd-questions-q4\/","title":{"rendered":"3 mistakes of LCM-GCD Questions: Q4"},"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><h2>Question 4<\/h2>\n<p><strong><em>Q4: Which of the following CANNOT be the greatest common divisor of two positive integers x and y?<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong><em>(A)\u00a0 <\/em><\/strong><strong><em>1<\/em><\/strong><\/p>\n<p><strong><em>(B)\u00a0 <\/em><\/strong><strong><em>x<\/em><\/strong><\/p>\n<p><strong><em>(C)\u00a0 <\/em><\/strong><strong><em>y<\/em><\/strong><\/p>\n<p><strong><em>(D) <\/em><\/strong><strong><em>x -y<\/em><\/strong><\/p>\n<p><strong><em>(E)\u00a0 <\/em><\/strong><strong><em>x + y<\/em><\/strong><\/p>\n<h3 style=\"text-align: left;\">Correct Answer<\/h3>\n<p>E<\/p>\n<h3 style=\"text-align: left;\">Solution<\/h3>\n<p><span style=\"text-decoration: underline;\"><strong>Given<\/strong><\/span><\/p>\n<p>We are given two positive integers x and y and are asked to find the GCD(x, y)<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Approach<\/strong><\/span><\/p>\n<p>We know that<\/p>\n<p>&nbsp;<\/p>\n<p align=\"center\"><strong><em>1 &lt; = GCD of a set of integers &lt; = Magnitude of the smallest integer of the set<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>We will use the above constraints on GCD to find the possible values which can\u2019t be the GCD(x, y)<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Working Out<\/strong><\/span><\/p>\n<p>In this the question the range of GCD(x, y) can be written as<\/p>\n<p>&nbsp;<\/p>\n<p align=\"center\"><strong><em>1 &lt; = GCD(x, y) &lt; = Smaller of (x, y)<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Let\u2019s evaluate the options one by one:<\/p>\n<p>&nbsp;<\/p>\n<p>(A)\u00a0 <strong>1<\/strong> \u2013 GCD can be equal to 1 if x, y don\u2019t have any common prime factor<\/p>\n<p>(B)\u00a0 <strong>x<\/strong>&#8211; GCD can be equal to x if x is the smaller integer and is a factor of y<\/p>\n<p>(C)\u00a0 <strong>y<\/strong>&#8211; GCD can be equal to y if y is the smaller integer and is a factor of x<\/p>\n<p>(D) <strong>x-y<\/strong> \u2013 GCD can be equal to the difference of x and y provided it is less than the magnitude of the smaller \u00a0integer<\/p>\n<p>(E)\u00a0 <strong>x + y<\/strong> \u2013 since x and y are given to be positive integers, the sum (x + y) will definitely be greater than the integers x and y and we know that GCD can\u2019t be greater than the magnitude of the smallest integer. Hence x + y cannot be the GCD.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Answer: Option (E)<\/strong><\/p>\n<p><strong><br \/>\n<\/strong><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Question 4 Q4: Which of the following CANNOT be the greatest common divisor of two positive integers x and y? &nbsp; (A)\u00a0 1 (B)\u00a0 x (C)\u00a0 y (D) x -y (E)\u00a0 x + y Correct Answer E Solution Given We are given two positive integers x and y and are asked to find the GCD(x, [&hellip;]<\/p>\n","protected":false},"author":7,"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":[1],"tags":[],"featured_image_src":null,"author_info":{"display_name":"Krishna Chaitanya","author_link":"https:\/\/e-gmat.com\/blogs\/author\/krishnae-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.1 - 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