{"id":21269,"date":"2019-05-20T17:56:28","date_gmt":"2019-05-20T12:26:28","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21269"},"modified":"2023-02-09T17:43:14","modified_gmt":"2023-02-09T12:13:14","slug":"quant-og-q318-if-x-is-an-integer-greater-than-0","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/quant-og-q318-if-x-is-an-integer-greater-than-0\/","title":{"rendered":"GMAT Quant OG 2020 Question #318 with Solution &#8211; &#8220;If x is an integer greater than 0&#8230;&#8221;"},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">2<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span>\n<h2 id=\"h-pqid-ds49502-01-og-2020-question-no-318\">PQID = DS49502.01 | OG 2020: Question No. 318<\/h2>\n\n\n\n<p>If x is an integer greater than 0, what is the remainder when x is divided by 4?<\/p>\n\n\n\n<ol><li>The remainder is 3 when x + 1 is divided by 4.<\/li><li>The remainder is 0 when 2x is divided by 4.<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Source<\/td><td>OG 2020<\/td><\/tr><tr><td>PQID<\/td><td>DS49502.01<\/td><\/tr><tr><td>Type<\/td><td>Data Sufficiency<\/td><\/tr><tr><td>Topic<\/td><td>Number Properties<\/td><\/tr><tr><td>Sub-Topic<\/td><td>Remainders<\/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-steps-1-2-understand-question-and-draw-inferences\"><strong><u>Steps 1 &amp; 2: Understand Question and Draw Inferences<\/u><\/strong><\/h4>\n\n\n\n<p>In this question, we are given<\/p>\n\n\n\n<ul><li>The number x is an integer, and x &gt; 0<\/li><\/ul>\n\n\n\n<p>We need to determine<\/p>\n\n\n\n<ul><li>The remainder, when x is divided by 4.<\/li><\/ul>\n\n\n\n<p>To find the remainder, when x is divided by 4, we need to know either the exact value of x, or the general expression expressing the number x.<\/p>\n\n\n\n<p>As we do not have any information present in the question statement, let us now analyse the individual statements.<\/p>\n\n\n\n<h4 id=\"h-step-3-analyse-statement-1\"><strong><u>Step 3: Analyse Statement 1<\/u><\/strong><\/h4>\n\n\n\n<p>As per the information given in statement 1, when x + 1 is divided by 4, the remainder is 3.<\/p>\n\n\n\n<ul><li>Hence, we can say x + 1 = 4 \u00d7 k + 3, where k is a non-negative integer.<ul><li>x = 4 \u00d7 k + 2<\/li><li>By comparing the above equation with dividend = divisor \u00d7 quotient + remainder, we can say that the remainder is 2.<\/li><\/ul><\/li><\/ul>\n\n\n\n<p>Therefore, statement 1 is sufficient to answer the question.<\/p>\n\n\n\n<h4 id=\"h-step-4-analyse-statement-2\"><strong><u>Step 4: Analyse Statement 2<\/u><\/strong><\/h4>\n\n\n\n<p>As per the information given in statement 1, when 2x is divided by 4, the remainder is 0.<\/p>\n\n\n\n<ul><li>Therefore, 2x is a multiple of 4.<\/li><li>This can happen in two cases:<ul><li>When x is already a multiple of by 4<ul><li>x = 4 \u00d7 k + 4 = 4(k + 1)<\/li><li>Then 2x will also be divisible by 4.<\/li><\/ul><\/li><li>When x is not a multiple of 4 but x is a multiple of 2.<ul><li>Hence, x = 4 \u00d7 k + 2 = 2(2k +1)<ul><li>And, 2x =4 (2k + 1) which makes 2x a multiple of 4.<\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul>\n\n\n\n<p>Therefore, from this statement the remainder can be either 0 or 2.<\/p>\n\n\n\n<p>Hence, statement 2 is not sufficient to answer the question.<\/p>\n\n\n\n<h4 id=\"h-step-5-combine-both-statements-together-if-needed\"><strong><u>Step 5: Combine Both Statements Together (If Needed)<\/u><\/strong><\/h4>\n\n\n\n<p>Since we can determine the answer from statement 1 individually, this step is not required.<\/p>\n\n\n\n<p>Hence, the correct answer choice is option A.<\/p>\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=\"noreferrer noopener external\" data-wpel-link=\"external\">\u00a0<strong>try out our FREE Trial?<\/strong><\/a> We are the<strong>\u00a0<a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\">most reviewed online GMAT Preparation company in GMATClub<\/a><\/strong>\u00a0with more than 2500 reviews as of January 2023.<\/p><\/blockquote>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-b79134f5-6cc0-4b88-8195-9542b00d4154\"><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>\n\n\n<h2>Takeaways<\/h2>\n\n\n\n<ol type=\"1\"><li>Any integer \u2018p\u2019 when divided by another integer \u2018q\u2019 can be represented in the form: Dividend = Divisor \u00d7 Quotient + Remainder.<ul><li>So, <strong>p = qm + r<\/strong>, where \u2018m\u2019 and \u2018r\u2019 represent the quotient and the remainder, respectively.<\/li><li>Also, r must lie in the range 0 \u2264 r &lt; q.<\/li><\/ul><\/li><\/ol>\n","protected":false},"excerpt":{"rendered":"<p>PQID = DS49502.01 | OG 2020: Question No. 318 If x is an integer greater than 0, what is the remainder when x is divided by 4? The remainder is 3 when x + 1 is divided by 4. The remainder is 0 when 2x is divided by 4. Source OG 2020 PQID DS49502.01 Type [&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":[44,94,60,61,100],"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 Premium plugin v17.1.1 (Yoast SEO v17.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>GMAT Quant OG 2020 Question #318 with Solution - &quot;If x is an integer greater than 0...&quot;<\/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\/quant-og-q318-if-x-is-an-integer-greater-than-0\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GMAT Quant OG 2020 Question #318 with Solution - &quot;If x is an integer greater than 0...&quot;\" \/>\n<meta property=\"og:description\" content=\"PQID = DS49502.01 | OG 2020: Question No. 318 If x is an integer greater than 0, what is the remainder when x is divided by 4? 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