{"id":21047,"date":"2019-05-13T16:58:49","date_gmt":"2019-05-13T11:28:49","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21047"},"modified":"2023-02-09T19:43:13","modified_gmt":"2023-02-09T14:13:13","slug":"if-a-and-b-are-integers-is-a5-4b-og-2020-question-316-with-solution","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/if-a-and-b-are-integers-is-a5-4b-og-2020-question-316-with-solution\/","title":{"rendered":"If a and b are integers, is a5 < 4b? - OG 2020 Question #316 with Solution"},"content":{"rendered":"<span class=\"span-reading-time 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 class=\"wp-block-heading\" id=\"h-pqid-ds38502-01-og-2020-question-no-316\">PQID = DS38502.01 | OG 2020: Question No. 316<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If a and b are integers, is a<sup>5<\/sup> &lt; 4<sup>b<\/sup>?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>a<sup>3<\/sup> = \u201327<\/li><li>b<sup>2<\/sup> = 16<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Source<\/strong><\/td><td><strong>OG 2020<\/strong><\/td><\/tr><tr><td>PQID<\/td><td>DS38502.01<\/td><\/tr><tr><td>Type<\/td><td>Data Sufficiency<\/td><\/tr><tr><td>Topic<\/td><td>Algebra<\/td><\/tr><tr><td>Sub-Topic<\/td><td>Exponents<\/td><\/tr><tr><td>Difficulty<\/td><td>Medium<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-solution\">Solution<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\" 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 class=\"wp-block-paragraph\">In this question, we are given<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>The numbers a and b are integers.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">We need to determine<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Whether a<sup>5<\/sup> &lt; 4<sup>b<\/sup> or not.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">For this, we need more information about the integers a and b. Hence, let us analyse the individual statements.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-step-3-analyse-statement-1\"><strong><u>Step 3: Analyse Statement 1<\/u><\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">As per the information given in statement 1, a<sup>3<\/sup> = -27<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>If a<sup>3<\/sup> = -27, then a = -3, which is a negative number<\/li><li>Therefore, a<sup>5<\/sup> will be equal to (-3)<sup>5<\/sup>, which is also a negative number.<\/li><li>However, for any integer value of b, 4<sup>b<\/sup> will be always positive.\n<ul>\n<li>Therefore, a<sup>5<\/sup> &lt; 4<sup>b<\/sup><\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, statement 1 is sufficient to answer the question.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-step-4-analyse-statement-2\"><strong><u>Step 4: Analyse Statement 2<\/u><\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">As per the information given in statement 2, b<sup>2<\/sup> = 16<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>From this statement, we can say that b can be either 4 or -4.<\/li><li>However, we do not get any relevant information about the value of a.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, statement 2 is not sufficient to answer the question.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" 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 class=\"wp-block-paragraph\">Since we can determine the answer from statement 1 individually, this step is not required.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, the correct answer choice is option A.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Takeaways:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If x^2 = a^2, then the value of x can be either +a or \u2013a.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Take a free GMAT mock to understand your baseline score and start your GMAT prep with our free trial. 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a3 = \u201327 b2 = 16 Source OG 2020 PQID DS38502.01 Type Data Sufficiency Topic Algebra Sub-Topic Exponents Difficulty Medium Solution Steps 1 &amp; 2: Understand Question and Draw Inferences In this question, we are given [&hellip;]<\/p>\n","protected":false},"author":79663,"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":"","footnotes":""},"categories":[103,44,94,60,100],"tags":[],"class_list":["post-21047","post","type-post","status-publish","format-standard","hentry","category-algebra","category-gmat-official-guide-solutions","category-gmat-prep","category-gmat-quant","category-quant-official-guide-solutions","et-doesnt-have-format-content","et_post_format-et-post-format-standard"],"featured_image_src":null,"author_info":{"display_name":"Juhi Gupta","author_link":"https:\/\/e-gmat.com\/blogs\/author\/juhie-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>If a and b are integers, is a5 &lt; 4b? 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