{"id":6836,"date":"2020-09-08T14:30:00","date_gmt":"2020-09-08T09:00:00","guid":{"rendered":"https:\/\/online.2iim.com\/cat-exam\/blogs\/?p=6836"},"modified":"2020-09-06T13:40:45","modified_gmt":"2020-09-06T08:10:45","slug":"rules-and-theorems-to-avoid-during-cat-prep","status":"publish","type":"post","link":"https:\/\/online.2iim.com\/cat-exam\/blogs\/cat-gyan\/rules-and-theorems-to-avoid-during-cat-prep\/","title":{"rendered":"Rules and Theorems to Avoid during CAT Prep"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/Rules-and-Theorems-to-Avoid-during-CAT-Prep-1-1-1024x576.png?resize=768%2C432&#038;ssl=1\" alt=\"Rules and Theorems to Avoid during CAT Prep\" class=\"wp-image-6885\" width=\"768\" height=\"432\" srcset=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/Rules-and-Theorems-to-Avoid-during-CAT-Prep-1-1.png?resize=1024%2C576&amp;ssl=1 1024w, https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/Rules-and-Theorems-to-Avoid-during-CAT-Prep-1-1.png?resize=300%2C169&amp;ssl=1 300w, https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/Rules-and-Theorems-to-Avoid-during-CAT-Prep-1-1.png?resize=768%2C432&amp;ssl=1 768w, https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/Rules-and-Theorems-to-Avoid-during-CAT-Prep-1-1.png?resize=1536%2C864&amp;ssl=1 1536w, https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/Rules-and-Theorems-to-Avoid-during-CAT-Prep-1-1.png?w=1920&amp;ssl=1 1920w\" sizes=\"(max-width: 768px) 100vw, 768px\" data-recalc-dims=\"1\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-justify\">In my previous avatar as a research&nbsp;analyst, there was one nugget that the department head gave us that has stuck around with me for a while.&nbsp;As a time-management exercise, he asked all of us to list down a few things that we were doing currently that we would stop doing. The&nbsp;funda&nbsp;is simple \u2013 <em><strong>in a world with finite time, you can do something new only if you stop doing something else<\/strong><\/em>.&nbsp;&nbsp;CAT Preparation can also be structured in similar fashion. In this blog, I am going to give an outline of the rules and theorems that you are better off ignoring. <\/p>\n\n\n\n<p class=\"has-text-align-justify\">I am going to limit this to-don\u2019t&nbsp;list of rules and theorems to academic-sounding stuff, otherwise we will be rehashing the same Amazon to Zomato list that we all know we should avoid.&nbsp;&nbsp;<\/p>\n\n\n\n\n\n<h2 class=\"wp-block-heading\">Euler&nbsp;was a genius \u2013 so stay away from him&nbsp;<\/h2>\n\n\n\n<p class=\"has-text-align-justify\">Euler introduced the concept of a function, devised the notation for&nbsp;trigonometric functions, the letter e for natural logarithmic base and the symbol&nbsp;i&nbsp;for imaginary numbers.&nbsp;Euler\u2019s totient function is a wonderful idea. Having a sense of the number of natural numbers less than N and coprime to it is beautiful. If we want to find the last two digits of 99<sup>81<\/sup>&nbsp;it&nbsp;probably comes of use.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-justify\">But our exam is not the mathematical Olympiad and it has not tested any of Eulerian stuff for decades. The <em><strong>downside<\/strong><\/em> to knowing and learning obscure stuff is two-fold <\/p>\n\n\n\n<ul><li><em>You can end up wasting time in rabbit-holes and <\/em><\/li><li><em>Look for avenues to use and showcase your knowledge&nbsp;<\/em><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/image.png?resize=577%2C197&#038;ssl=1\" alt=\"If all you have is a hammer... \u2013 Analytics Applications for Marketers from  Gordian Knot\" class=\"wp-image-6839\" width=\"577\" height=\"197\" srcset=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/image.png?w=715&amp;ssl=1 715w, https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/image.png?resize=300%2C103&amp;ssl=1 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" data-recalc-dims=\"1\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-justify\">I have seen students use Euler\u2019s totient function correctly for remainder questions. But&nbsp;all of&nbsp;the relevant remainders questions for CAT can be solved without using Euler\u2019s function.&nbsp;The temptation to use Euler\u2019s totient function is so high than far simpler methods get frequently overlooked.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Studying&nbsp;with Fermat&nbsp;is good,&nbsp;but do&nbsp;not&nbsp;go&nbsp;overboard&nbsp;<\/h2>\n\n\n\n<p class=\"has-text-align-justify\">Pierre&nbsp;de Fermat came up with lots of glorious things, the&nbsp;most commonly used&nbsp;of these&nbsp;is perhaps&nbsp;Fermat\u2019s little theorem. Now, Fermat\u2019s little theorem is a neat idea&nbsp;that is like a poor man\u2019s Euler\u2019s totient function. Since it is far simpler and easy to remember stick it in some part of&nbsp;the&nbsp;brain. Stick it in the same part of the brain&nbsp;just before the part where you have stored Wilson\u2019s theorem. Title this&nbsp;part of the brain&nbsp;\u201c<em>unlikely&nbsp;to be tested<\/em>\u201d.&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-justify\">Now the most interesting of Fermat\u2019s creations, rules and theorems is Fermat\u2019s Last Theorem. Now&nbsp;Fermat\u2019s Last Theorem&nbsp;is totally worth&nbsp;digging into. Fermat noted this&nbsp;theorem&nbsp;down&nbsp;on the margins of his notebook, scribbled that he had just got the most wonderful proof for this and died soon after.&nbsp;This remained unsolved for centuries \u2013 prizes were announced, competitions were held, careers were put on hold, wild furious debates were held about whether Fermat really did know the proof.&nbsp;Finally, at long last Andrew Wiles proved it, more than 300 years after Mr. Fermat had written it down.&nbsp;&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"576\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/maxresdefault-1-1.jpg?resize=1024%2C576&#038;ssl=1\" alt=\"rules and theorems - fermat's last theorem\" class=\"wp-image-6868\" srcset=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/maxresdefault-1-1.jpg?resize=1024%2C576&amp;ssl=1 1024w, https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/maxresdefault-1-1.jpg?resize=300%2C169&amp;ssl=1 300w, https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/maxresdefault-1-1.jpg?resize=768%2C432&amp;ssl=1 768w, https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/maxresdefault-1-1.jpg?w=1280&amp;ssl=1 1280w\" sizes=\"(max-width: 1000px) 100vw, 1000px\" data-recalc-dims=\"1\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-justify\">So, why the hell am I asking you to dig into it. Oh, Fermat\u2019s Last Theorem is a wonderful book by&nbsp;a gent&nbsp;called Simon Singh. Reading that would be&nbsp;really delightful&nbsp;prep for VARC.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><em>Fermat\u2019s 2IIM connection, or rather 2IIM\u2019s Fermat connection&nbsp;<\/em><\/h3>\n\n\n\n<p class=\"has-text-align-justify\">In a moment of madness, quite probably in the aftermath of&nbsp;having read something about the last theorem, yours truly&nbsp;(Rajesh&nbsp;Balasubramanian) decided to name the beloved company&nbsp;that owns the 2IIM brand&nbsp;as Fermat Education. So, being&nbsp;closely associated&nbsp;with Fermat is definitely good for your CAT prep \u2013 just <a href=\"https:\/\/learn.2iim.com\/learn\/2IIM-s-Test-Dojo-2020\" target=\"_blank\" rel=\"noreferrer noopener\">take the 2IIM route<\/a> and not the Last Theorem route.&nbsp;&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><em>Chinese Remainder Theorem needs a mention<\/em>&nbsp;<\/h2>\n\n\n\n<p class=\"has-text-align-justify\">From Wikipedia \u2013&nbsp;<em>\u201c<\/em><em>T<\/em><em>he Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime.<\/em><em>\u201d<\/em>&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-justify\">In plain speak, if we know the remainder on dividing N by 5 and&nbsp;on dividing N by 6, we can write N as some 30K + R. How exactly do we do this?&nbsp;More or less by&nbsp;listing possible remainders and seeing where&nbsp;both conditions are satisfied. Put another way, simple old-fashioned&nbsp;method of observing patterns.&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-justify\">For instance, let us say N divided by 5 gives remainder of 3 and N by 6 gives remainder of 1.&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-justify\">We can write N = 5K + 3 and N = 6p + 1.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-justify\">A number of&nbsp;the form 5K + 3 can be of the form 30K +3 or 30K + 8 or 30K + 13 or 30K + 18 or 30K + 23 or 30K + 28.&nbsp;Similarly&nbsp;a number of the form 6p + 1 can be of the form 30K + 1, 30K + 7, 30k + 13, 30K + 19 or 30K + 29.&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-justify\">If you notice 30K + 13 sits in both cases, or our number&nbsp;has to&nbsp;be of the form 30K + 13.&nbsp;If you know how to do this, then all that remains is to say the word \u2018Chinese Remainder Theorem\u2019 every time some question like this appears.&nbsp;It might not help at all, but it does intimidate people around you and that has got to count for something.&nbsp;If you want to sound really in, you should probably say CRT.&nbsp;&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">The other approach would be more algebraic:<\/h4>\n\n\n\n<p class=\"has-text-align-justify\">N = 5K + 3&nbsp;or 6N = 30K + 18&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-justify\">and N = 6p + 1.&nbsp;Or,&nbsp;5N = 30P + 5&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-justify\">Subtracting one equation from another N = 30(K \u2013 N) + 13 = 30q + 13. Again, CRT!&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Verbal can also take you down time-sinks&nbsp;<\/h2>\n\n\n\n<p class=\"has-text-align-justify\">Vocabulary is not&nbsp;tested,&nbsp;grammar rules are not important. We do not need to be able to distinguish between present participle and gerund. Even if you are not able to&nbsp;articulate the technical distinction between&nbsp;the usage of swimming&nbsp;in&nbsp;\u201cI went swimming yesterday\u201d and \u201cSwimming is good exercise\u201d, chances are the exam will go swimmingly well.&nbsp;&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/giphy-9-1.gif?ssl=1\" alt=\"rules and theorems - time-sinks\/loops\" class=\"wp-image-6872\" data-recalc-dims=\"1\"\/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Laundry list of interesting-sounding vague unnecessary stuff&nbsp;plus some pure voodoo&nbsp;<\/h2>\n\n\n\n<p class=\"has-text-align-justify\">Ceva\u2019s&nbsp;theorem, Menelaus Theorem, Ptolemy\u2019s Theorem,&nbsp;Diophantine Equations, Roots of a cubic equation, Cauchy Schwarz inequality,&nbsp;Koningsberg&nbsp;bridge problem, Schrodinger\u2019s&nbsp;Cat&nbsp;and&nbsp;our own&nbsp;beloved Vedic math. And before I forget, CRT!&nbsp;\u2013 this is a nice non-exhaustive list of fancy-sounding irrelevant guff.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-justify\">There&nbsp;will&nbsp; always&nbsp;be the&nbsp;best friend of the niece of the uncle of your second-cousin once removed (by marriage)&nbsp;who swears that these ideas are really important.&nbsp;&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">So, what rules and theorems should we&nbsp;study?<\/h2>\n\n\n\n<p class=\"has-text-align-justify\">Firstly, read the proofs of Angle Bisector Theorem, Perpendicular bisector theorem, triangle inequality, triangle angle property, tangent-secant theorem, why area of a triangle is&nbsp;rs&nbsp;and&nbsp;abc\/4R.&nbsp;Secondly, prove Congruence and Similarity rigorously.&nbsp;&nbsp;Thirdly, learn about the basis for test of divisibility by 4, 9, and 11.&nbsp;Finally, ponder why the&nbsp;formula giving number of factors of a number&nbsp;works. Have your own intuitive explanation for why&nbsp;<sup>(n + r \u2013 1)<\/sup>&nbsp;C&nbsp;<sub>(r \u2013 1)<\/sub>&nbsp;works.&nbsp;&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"400\" height=\"300\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/101497-1.jpg?resize=400%2C300&#038;ssl=1\" alt=\"rules and theorems - professor jerry and student nibbles\" class=\"wp-image-6876\" srcset=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/101497-1.jpg?w=400&amp;ssl=1 400w, https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/101497-1.jpg?resize=300%2C225&amp;ssl=1 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" data-recalc-dims=\"1\" \/><\/figure><\/div>\n\n\n\n<p>In Conclusion, these are the rules and theorems to avoid during your CAT Preparation. If you&#8217;re naturally curious do, check them out at your leisure but for CAT Prep, they are guff. <\/p>\n\n\n\n<h2 class=\"wp-block-heading\">A Final Note <\/h2>\n\n\n\n<p class=\"has-text-align-justify\">On September 5th, we celebrated Teachers\u2019 Day. \ud83d\ude42 <\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-style-large\"><p>Teaching is a wonderful method to&nbsp;consolidate an idea in your own mind.<\/p><\/blockquote>\n\n\n\n<p class=\"has-text-align-justify\">Teaching imposes the pressure of conveying the right idea in an engaging fashion; this makes us search for some juicy analogy. This process of creating analogous frameworks is frightfully useful for getting clarity. Beyond all this is the joy of explaining something to someone else, the pleasure of possibly demystifying something that might have been a pain for the recipient. <\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/art-of-teaching-1.gif?ssl=1\" alt=\"rules and theorems - art of teaching\" class=\"wp-image-6879\" data-recalc-dims=\"1\"\/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-justify\">God knows our Country (and the world) needs as many teachers as it can lay its hands on. We also need teachers to be creative, irreverent, innovative, and free-spirited. We are too conditioned to teaching being strait-jacketed. If ideas need to stick in the brains, they need to be pushed through with loads of passion.&nbsp; Just some thoughts. \ud83d\ude42<\/p>\n\n\n\n<p class=\"has-text-align-justify\">In terms of CAT Preparation, you should definitely be taking Mocks now. Check out this wonderful article about <a href=\"https:\/\/online.2iim.com\/cat-exam\/blogs\/cat-preparation-strategy\/86-days-all-about-handling-mocks-better\/\" target=\"_blank\" rel=\"noreferrer noopener\">Handling Mocks Better with around 86 days to go<\/a>!<\/p>\n\n\n\n\n\n<p class=\"has-text-align-justify\">Cheers, <a href=\"https:\/\/www.who.int\/emergencies\/diseases\/novel-coronavirus-2019\/advice-for-public\" target=\"_blank\" rel=\"noreferrer noopener\">Stay Safe<\/a> and Best Wishes for CAT preparation.&nbsp;<\/p>\n\n\n\n<p><a rel=\"noreferrer noopener\" href=\"https:\/\/www.quora.com\/profile\/Rajesh-Balasubramanian-8\" target=\"_blank\"><em>Rajesh Balasubramanian<\/em><\/a><em> takes the CAT every year and is a 4-time CAT 100 percentiler.&nbsp;He likes few things more than teaching Math and insists to this day that he is a better teacher than exam-taker.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In my previous avatar as a research analyst, there was one nugget that the department head gave us that has stuck around with me for a while. As a time-management exercise, he asked all of us to list down a few things that we were doing currently that we would stop doing. The funda is simple \u2013 in a world with finite time, you can do something new only if you stop doing something else.  CAT Preparation can also be structured in similar fashion. In this blog, I am going to give an outline of the rules and theorems that you are better off ignoring. <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[159,8],"tags":[142,173,344,345,57],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Rules and Theorems to Avoid during CAT Prep - 2IIM CAT Preparation Blog<\/title>\n<meta name=\"description\" content=\"In this blog, we will provide an outline of the rules and theorems that you are better off ignoring in terms of your CAT Preparation. 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