{"id":53994,"date":"2024-11-27T13:47:29","date_gmt":"2024-11-27T08:17:29","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=53994"},"modified":"2024-11-27T13:47:30","modified_gmt":"2024-11-27T08:17:30","slug":"time-saving-tactics-outsmart-tricky-quant-questions","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/time-saving-tactics-outsmart-tricky-quant-questions\/","title":{"rendered":"Time-Saving Tactics: Outsmart Tricky Quant Questions"},"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\"> 3<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span>\n<h1 class=\"has-medium-font-size wp-block-heading\" id=\"h-introduction\">Introduction<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Can x\u2074 + x\u00b2 + 1 ever be &lt; 0? Think fast, quant-conqueror!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Got the answer?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If yes, let\u2019s see how this simple question that helps you understand the given expression can help you solve a tricky Quant-based question. If no, don\u2019t worry. As you read further, you will see how you can get to this answer, once you try your hand at the DS question given:<\/p>\n\n\n\n<h1 class=\"has-medium-font-size wp-block-heading\" id=\"h-question\">Question<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">What is the value of x?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Can x\u2074 + x\u00b2 + 1 ever be &lt; 0? Think fast, quant-conqueror!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"539\" height=\"177\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-64.png\" alt=\"\" class=\"wp-image-53995\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-64.png 539w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-64-300x99.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-64-400x131.png 400w\" sizes=\"auto, (max-width: 539px) 100vw, 539px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A.&nbsp;&nbsp;&nbsp; (1) ALONE is sufficient, but (2) alone is not sufficient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B.&nbsp;&nbsp;&nbsp; (2) ALONE is sufficient, but (1) alone is not sufficient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C.&nbsp;&nbsp;&nbsp; TOGETHER are sufficient, but NEITHER ALONE is sufficient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D.&nbsp;&nbsp;&nbsp; EACH ALONE is sufficient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E.&nbsp;&nbsp;&nbsp;&nbsp; NEITHER ALONE NOR TOGETHER is the statements sufficient.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Solution<\/h1>\n\n\n\n<h1 class=\"wp-block-heading\">Statement 1<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Statement 1 seems difficult to simplify.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">However, if you check the LHS, you have:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>x<sup>4<\/sup>&nbsp;which will be \u2265 0 for any value of x<\/li><li>x<sup>2<\/sup>&nbsp;which will be \u2265 0 for any value of x<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">o\u00a0\u00a0 So, when you add two non-negative entities to 1, the sum will be \u2265 1.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"571\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-65.png\" alt=\"\" class=\"wp-image-53996\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-65.png 1021w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-65-300x168.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-65-768x430.png 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-65-400x224.png 400w\" sizes=\"auto, (max-width: 1021px) 100vw, 1021px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Now, if LHS = RHS, it can only be so if LHS = RHS = 1 (<strong>Inference 3<\/strong>)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I guess you know what the next step will be now? Yes, to find the value of x for which LHS = RHS = 1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Just by looking at it, you know that it is possible only for x = 0.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, statement 1 is sufficient to find the value of x.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Statement 2<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">You can now solve statement 2:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"544\" height=\"306\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-66.png\" alt=\"\" class=\"wp-image-53997\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-66.png 544w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-66-300x169.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-66-400x225.png 400w\" sizes=\"auto, (max-width: 544px) 100vw, 544px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">So, as per statement 2, two values are possible for x. Hence, statement 2 is not sufficient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, the&nbsp;<strong>correct answer is A<\/strong>&nbsp;&#8211; (1) ALONE is sufficient, but (2) alone is not sufficient.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Conclusion<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The example we just solved illustrates a fundamental principle of GMAT Quant:\u00a0<em>when faced with complex expressions, your first instinct shouldn&#8217;t be to dive into algebraic manipulation. Instead, step back and analyze what the expression tells you about possible values and relationships- draw inferences.<\/em>\u00a0Remember, in quant problems, looking for these fundamental mathematical properties can save you valuable time and lead you to the correct answer more quickly. Practice identifying these patterns to enhance your problem-solving skills and boost your performance in quantitative sections. <\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Practice Question<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Try this tricky question out:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">What is the value of integer x?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1.&nbsp;&nbsp;&nbsp;&nbsp; x<sup>5<\/sup>&nbsp;+ x<sup>3<\/sup>&nbsp;+ x &gt; 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2.&nbsp;&nbsp;&nbsp;&nbsp; x<sup>2<\/sup>&nbsp;+ 1 = 37<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A.&nbsp;&nbsp;&nbsp; (1) ALONE is sufficient, but (2) alone is not sufficient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B.&nbsp;&nbsp;&nbsp; (2) ALONE is sufficient, but (1) alone is not sufficient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C.&nbsp;&nbsp;&nbsp; TOGETHER are sufficient, but NEITHER ALONE is sufficient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D.&nbsp;&nbsp;&nbsp; EACH ALONE is sufficient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E. NEITHER ALONE NOR TOGETHER is the statements sufficient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Please present your analysis for this question.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/preview.redd.it\/time-saving-tactics-outsmart-tricky-quant-questions-v0-qwdwaqicenwd1.png?width=539&amp;format=png&amp;auto=webp&amp;s=b941d535e3e83676170bfe2733a2a57dca04044f\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\"><\/a><\/p>\n\n\n","protected":false},"excerpt":{"rendered":"<p>Introduction Can x\u2074 + x\u00b2 + 1 ever be &lt; 0? Think fast, quant-conqueror! Got the answer? If yes, let\u2019s see how this simple question that helps you understand the given expression can help you solve a tricky Quant-based question. If no, don\u2019t worry. As you read further, you will see how you can get [&hellip;]<\/p>\n","protected":false},"author":102398,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[92],"tags":[],"class_list":["post-53994","post","type-post","status-publish","format-standard","hentry","category-about-gmat-exam","et-doesnt-have-format-content","et_post_format-et-post-format-standard"],"featured_image_src":null,"author_info":{"display_name":"sujeev","author_link":"https:\/\/e-gmat.com\/blogs\/author\/sujeev\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Time-Saving Tactics: Outsmart Tricky Quant Questions<\/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\/time-saving-tactics-outsmart-tricky-quant-questions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Time-Saving Tactics: Outsmart Tricky Quant Questions\" \/>\n<meta property=\"og:description\" content=\"Introduction Can x\u2074 + x\u00b2 + 1 ever be &lt; 0? 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