{"id":5414,"date":"2015-04-30T08:11:24","date_gmt":"2015-04-30T15:11:24","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=5414"},"modified":"2019-01-30T11:56:01","modified_gmt":"2019-01-30T06:26:01","slug":"3-mistakes-of-lcm-gcd-questions-q5","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/3-mistakes-of-lcm-gcd-questions-q5\/","title":{"rendered":"3 mistakes of LCM-GCD questions – Q5"},"content":{"rendered":"A <\/span> 2<\/span> min read <\/span><\/span>

Question 5<\/h2>\n

Q5: If A and B are positive integers greater than 1 such that the GCD of A and B is 1, then which of the following must be true<\/span>?<\/em><\/strong><\/p>\n

 <\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 I.\u00a0 <\/em><\/strong>A and B are prime numbers.<\/em><\/strong><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 II.\u00a0 <\/em><\/strong>A and B are consecutive numbers.<\/em><\/strong><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0 III.\u00a0\u00a0 <\/em><\/strong>A and B do not have a common prime factor<\/em><\/strong><\/p>\n

\u00a0\u00a0 \u00a0\u00a0 IV.\u00a0 <\/em><\/strong>The product AB has two prime factors<\/em><\/strong><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0 V.\u00a0 <\/em><\/strong>A and B have the opposite even-odd nature<\/em><\/strong><\/p>\n

 <\/p>\n

    \n
  1. \u00a0I & II only<\/em><\/strong><\/li>\n
  2. III only<\/em><\/strong><\/li>\n
  3. I, V only<\/em><\/strong><\/li>\n
  4. I, II, III, V only<\/em><\/strong><\/li>\n
  5. I, II, III, IV & V<\/em><\/strong><\/li>\n<\/ol>\n

    Correct Answer<\/h3>\n

    B<\/p>\n

    Solution<\/h3>\n

    Given<\/strong><\/span><\/p>\n

    We are given two positive integers A & B which are greater than 1. We are also given that GCD(A, B) = 1. We are asked to find the options which must be true<\/p>\n

     <\/p>\n

    Approach<\/strong><\/span><\/p>\n

     <\/p>\n

    We know that if two positive integers have their GCD as 1, they do not have any common prime factor.\u00a0 We will use this understanding to find out the must be true<\/span><\/strong> statements out of the statements given<\/p>\n

     <\/p>\n

    Working Out<\/strong><\/span><\/p>\n

    Let\u2019s evaluate the statements given in the option:<\/p>\n

     <\/p>\n

    I.<\/strong>\u00a0 A & B are prime numbers<\/strong> \u2013 May not be true.GCD of two numbers is 1 when they don\u2019t have any common prime factor. These numbers need not necessarily be primes. For example 4, 9 have their GCD = 1 but they are not prime numbers.<\/p>\n

     <\/p>\n

    II.<\/strong>\u00a0 A and B are consecutive numbers<\/strong>– May not be true. Two numbers having their GCD = 1 need not necessarily be consecutive numbers.<\/p>\n

     <\/p>\n

    III.<\/strong>\u00a0\u00a0 A & B do not have a common prime factor<\/strong>– Must be true. Numbers who have their GCD = 1 do not have any common prime factor.<\/p>\n

     <\/p>\n

    IV.\u00a0<\/strong> The product AB has two prime factors<\/strong>– May not be true. Number A and number B can have more than 1 different prime numbers as their factors. Thus, the product of A & B may have more than 2 prime factors<\/p>\n

     <\/p>\n

    V<\/strong>.\u00a0\u00a0A & B have the opposite even-odd nature<\/strong>\u2013 May not be true. Let us consider A = 7 and B = 9. In this case, both A and B are odd numbers greater than 1 and their GCD is 1. Hence, it is not necessarily true that A & B have the opposite even-odd nature.<\/p>\n

     <\/p>\n

    Answer: Option (B)<\/strong><\/p>\n


    \n<\/strong><\/p>\n

     <\/p>\n


    \n<\/strong><\/p>\n

     <\/p>\n","protected":false},"excerpt":{"rendered":"

    Question 5 Q5: If A and B are positive integers greater than 1 such that the GCD of A and B is 1, then which of the following must be true?   \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 I.\u00a0 A and B are prime numbers. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 II.\u00a0 A and B are consecutive numbers. \u00a0\u00a0\u00a0\u00a0\u00a0 III.\u00a0\u00a0 A and B do not […]<\/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":"\n3 mistakes of LCM-GCD questions - Q5<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/e-gmat.com\/blogs\/3-mistakes-of-lcm-gcd-questions-q5\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"3 mistakes of LCM-GCD questions - Q5\" \/>\n<meta property=\"og:description\" content=\"Question 5 Q5: If A and B are positive integers greater than 1 such that the GCD of A and B is 1, then which of the following must be true?   \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 I.\u00a0 A and B are prime numbers. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 II.\u00a0 A and B are consecutive numbers. \u00a0\u00a0\u00a0\u00a0\u00a0 III.\u00a0\u00a0 A and B do not […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/e-gmat.com\/blogs\/3-mistakes-of-lcm-gcd-questions-q5\/\" \/>\n<meta property=\"og:site_name\" content=\"e-GMAT Blog | Best GMAT blog on the planet\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/E-Gmat-499275643430980\" \/>\n<meta property=\"article:published_time\" content=\"2015-04-30T15:11:24+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-01-30T06:26:01+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@e_GMAT\" \/>\n<meta name=\"twitter:site\" content=\"@e_GMAT\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Krishna Chaitanya\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/e-gmat.com\/blogs\/#organization\",\"name\":\"e-GMAT\",\"url\":\"https:\/\/e-gmat.com\/blogs\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/E-Gmat-499275643430980\",\"https:\/\/www.linkedin.com\/in\/rajat-sadana-ba459a\/\",\"https:\/\/www.youtube.com\/user\/eGMATconcepts\",\"https:\/\/twitter.com\/e_GMAT\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/e-gmat.com\/blogs\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/04\/logo-full.png\",\"contentUrl\":\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/04\/logo-full.png\",\"width\":908,\"height\":802,\"caption\":\"e-GMAT\"},\"image\":{\"@id\":\"https:\/\/e-gmat.com\/blogs\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/e-gmat.com\/blogs\/#website\",\"url\":\"https:\/\/e-gmat.com\/blogs\/\",\"name\":\"e-GMAT Blog | Best GMAT blog on the planet\",\"description\":\"Prepare for your GMAT and MBA journey\",\"publisher\":{\"@id\":\"https:\/\/e-gmat.com\/blogs\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/e-gmat.com\/blogs\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/e-gmat.com\/blogs\/3-mistakes-of-lcm-gcd-questions-q5\/#webpage\",\"url\":\"https:\/\/e-gmat.com\/blogs\/3-mistakes-of-lcm-gcd-questions-q5\/\",\"name\":\"3 mistakes of LCM-GCD questions - 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