{"id":53881,"date":"2024-11-11T12:14:58","date_gmt":"2024-11-11T06:44:58","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=53881"},"modified":"2024-11-11T12:14:59","modified_gmt":"2024-11-11T06:44:59","slug":"never-miss-a-gmat-probability-question-again-the-matrix-method-that-top-scorers-use","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/never-miss-a-gmat-probability-question-again-the-matrix-method-that-top-scorers-use\/","title":{"rendered":"Never Miss a GMAT Probability Question Again: The Matrix Method That Top Scorers Use"},"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<p class=\"wp-block-paragraph\">&#8220;I knew how to solve it, but I messed up the counting!&#8221;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is the most common regret we hear from GMAT test-takers about probability questions. Not concepts, not formulas &#8211; just simple counting. Even 700+ scorers admit to double-counting cases or missing possibilities entirely. But what if counting cases could be as simple as filling boxes in a grid? <strong>What if you could solve any GMAT probability question with zero chance of missing or double-counting cases<\/strong>?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Let&#8217;s Master This Method Step by Step<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Warm-up Question<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If x is chosen from {1,2} and y is chosen from {3,4}, how many different pairs (x,y) will give an even product?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Take a moment to solve this before reading further. Got your answer? Let&#8217;s solve it using a method that will forever change how you tackle such questions.<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li><strong>The Matrix Method Solution<\/strong><\/li><\/ol>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\"><li>1. First, create a simple matrix:<ul><li>Put x values (1,2) as column headers<\/li><li>Put y values (3,4) as row headers<\/li><\/ul><\/li><\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"375\" height=\"392\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-12.png\" alt=\"\" class=\"wp-image-53883\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-12.png 375w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-12-287x300.png 287w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-12-272x284.png 272w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\"><li>2. Fill in the matrix:<ul><li>Multiply each x with each y<\/li><li>Mark &#8216;E&#8217; where you get even products<\/li><\/ul><\/li><\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"384\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-13.png\" alt=\"\" class=\"wp-image-53886\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-13.png 360w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-13-281x300.png 281w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-13-266x284.png 266w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\"><li>3. Count the results:<ul><li>Count all E&#8217;s: we have 3 cases<\/li><li>These represent the pairs (1,4), (2,3), and (2,4)<\/li><\/ul><\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Here is the process summary:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"728\" height=\"548\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-14.png\" alt=\"\" class=\"wp-image-53887\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-14.png 728w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-14-300x226.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-14-377x284.png 377w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-14-400x301.png 400w\" sizes=\"auto, (max-width: 728px) 100vw, 728px\" \/><\/figure>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Official GMAT Example<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Let\u2019s try our hand at this Medium Level question.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"A\"><li>1\/6<\/li><li>1\/3<\/li><li>1\/2<\/li><li>2\/3<\/li><li>5\/6<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step-by-Step Solution<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Create the matrix:<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"703\" height=\"540\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-15.png\" alt=\"\" class=\"wp-image-53888\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-15.png 703w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-15-300x230.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-15-370x284.png 370w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/11\/image-15-400x307.png 400w\" sizes=\"auto, (max-width: 703px) 100vw, 703px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">2. Count favorable outcomes:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211;> Count E&#8217;s: 8 cases where the product is even<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3. Calculate total outcomes:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211;> Total pairs possible = 4 \u00d7 3 = 12<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">4. Calculate probability:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211;> Probability = 8\/12 = 2\/3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211;> <strong>Answer: D<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Common Trap Alert! <\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Many students select Choice E, i.e., 5\/6 because they count<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>both (2,6) and (6,2) as possible outcomes<\/strong><\/li><li><strong>both (4,6) and (6,4) as possible outcomes<\/strong>.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Remember: x can only be chosen from the first set and y from the second set. <strong>The matrix automatically prevents this mistake!<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. <strong>Alternate Approach: The Listing Method<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Many students prefer listing out cases systematically. While this method can work, it requires extra care to avoid missing cases. Here&#8217;s how to do it carefully:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step-by-Step Solution<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\"><li>Fix x = 1, list all products:<ul><li>1 \u00d7 5 = 5 (odd)<\/li><li>1 \u00d7 6 = 6 (even) \u2713<\/li><li>1 \u00d7 7 = 7 (odd) Cases so far: 1<\/li><\/ul><\/li><li>Fix x = 2, list all products:<ul><li>2 \u00d7 5 = 10 (even) \u2713<\/li><li>2 \u00d7 6 = 12 (even) \u2713<\/li><li>2 \u00d7 7 = 14 (even) \u2713 Cases so far: 4<\/li><\/ul><\/li><li>Fix x = 3, list all products:<ul><li>3 \u00d7 5 = 15 (odd)<\/li><li>3 \u00d7 6 = 18 (even) \u2713<\/li><li>3 \u00d7 7 = 21 (odd) Cases so far: 5<\/li><\/ul><\/li><li>Fix x = 4, list all products:<ul><li>4 \u00d7 5 = 20 (even) \u2713<\/li><li>4 \u00d7 6 = 24 (even) \u2713<\/li><li>4 \u00d7 7 = 28 (even) \u2713 Total even cases: 8<\/li><\/ul><\/li><li>Calculate probability:<ul><li>Total possible outcomes = 4 \u00d7 3 = 12<\/li><li>Probability = 8\/12 = 2\/3<\/li><li><strong>Answer: D<\/strong><\/li><\/ul><\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Why Students Often Get This Wrong<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\"><li>Random listing instead of fixing one variable<\/li><li>Missing cases like 4 \u00d7 7 = 28 (it&#8217;s less obvious that it&#8217;s even)<\/li><li>Forgetting to count the total possible outcomes<\/li><li>Double-counting some cases, such as (6,2) because of random listing.<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">While this method works, it&#8217;s more prone to errors than the matrix method. <strong>Use it only if you&#8217;re very comfortable with systematic listing.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Remember: In the GMAT, it&#8217;s not just about getting the right answer\u2014it&#8217;s about getting it right consistently under time pressure. <strong><em><u>Choose your method wisely!<\/u><\/em><\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Key Takeaways for the Matrix Method<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Draw a matrix whenever you need to count pairs<\/li><li>Each box = exactly one possible outcome<\/li><li>Can&#8217;t miss cases &#8211; every possibility has its own box<\/li><li>Can&#8217;t count twice &#8211; each box is counted exactly once<\/li><li>Remember: x and y are from specific sets &#8211; don&#8217;t swap positions<\/li><\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Pro Tips <\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Accuracy Boost<\/strong>: In our experience, this method has reduced counting errors by nearly 100%. <\/li><li><strong>Quick Check<\/strong>: After marking E&#8217;s, quickly scan each row. Any pattern you notice can help verify your counting.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Want to master this method? Head to the comments section below for a hard practice question that will help cement your learning.<\/p>\n\n\n","protected":false},"excerpt":{"rendered":"<p>&#8220;I knew how to solve it, but I messed up the counting!&#8221; This is the most common regret we hear from GMAT test-takers about probability questions. Not concepts, not formulas &#8211; just simple counting. Even 700+ scorers admit to double-counting cases or missing possibilities entirely. But what if counting cases could be as simple as [&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-53881","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>Never Miss a GMAT Probability Question Again: The Matrix Method That Top Scorers Use<\/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\/never-miss-a-gmat-probability-question-again-the-matrix-method-that-top-scorers-use\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Never Miss a GMAT Probability Question Again: The Matrix Method That Top Scorers Use\" \/>\n<meta property=\"og:description\" content=\"&#8220;I knew how to solve it, but I messed up the counting!&#8221; This is the most common regret we hear from GMAT test-takers about probability questions. 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\/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Never Miss a GMAT Probability Question Again: The Matrix Method That Top Scorers Use","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/e-gmat.com\/blogs\/never-miss-a-gmat-probability-question-again-the-matrix-method-that-top-scorers-use\/","og_locale":"en_US","og_type":"article","og_title":"Never Miss a GMAT Probability Question Again: The Matrix Method That Top Scorers Use","og_description":"&#8220;I knew how to solve it, but I messed up the counting!&#8221; This is the most common regret we hear from GMAT test-takers about probability questions. Not concepts, not formulas &#8211; just simple counting. Even 700+ scorers admit to double-counting cases or missing possibilities entirely. 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