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	<title>My Guru: Tutoring, Test Prep, &#38; Advice</title>
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	<description>Accelerate your education</description>
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	<itunes:summary>Accelerate your education</itunes:summary>
	<itunes:author>My Guru: Tutoring, Test Prep, &amp; Advice</itunes:author>
	<itunes:explicit>no</itunes:explicit>
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	<itunes:subtitle>Accelerate your education</itunes:subtitle>
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		<title>My Guru: Tutoring, Test Prep, &amp; Advice</title>
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		<title>You Can Improve your LSAT Score</title>
		<link>http://www.myguruedge.com/2012/01/29/you-can-improve-your-lsat-score/</link>
		<comments>http://www.myguruedge.com/2012/01/29/you-can-improve-your-lsat-score/#comments</comments>
		<pubDate>Mon, 30 Jan 2012 02:06:29 +0000</pubDate>
		<dc:creator>myguru</dc:creator>
				<category><![CDATA[LSAT]]></category>
		<category><![CDATA[LSAT Prep]]></category>
		<category><![CDATA[LSAT tutoring]]></category>

		<guid isPermaLink="false">http://www.myguruedge.com/?p=2134</guid>
		<description><![CDATA[With modest preparation, my score jumped almost 10% the second time For those who sit forlornly staring at those admission grids, showing admitted students’ LSAT scores and GPAs, there is hope. I am living proof that you can improve your LSAT score. Yes, the test bills itself as one that requires no preparation. It purports [...]]]></description>
			<content:encoded><![CDATA[<p><strong><em>With modest preparation, my score jumped almost 10% the second time</em></strong></p>
<p>For those who sit forlornly staring at those admission grids, showing admitted students’ LSAT scores and GPAs, there is hope. I am living proof that you can improve your LSAT score.</p>
<p>Yes, the test bills itself as one that requires no preparation. It purports to be simply a review of your existing analytical and critical thinking skills. Anyone who believes that probably won’t do well in American corporate/legal culture. There are tricks to the trade, and insider knowledge to be gained. I’d bet my law school debt that no one on the LSAC committee sends their children to take the LSAT without extensive preparation.</p>
<p>However, I did not have insider information when I first took the test. I went to a state university on the West Coast &#8212; University of Oregon, in laid-back Eugene, where many students imagined a fulfilling life without entry into a top school. I’d always tested well, so I read a couple of exam books and tested myself at my leisure. I was doing pretty good!</p>
<p>I took the LSAT Winter Term of college, while I was interning in Washington, D.C.  I arrived to register early in the morning at the Georgetown campus, and stood in line behind students who apparently all had taken the Kaplan course. They were talking about the exam with the familiarity of obsessed fans, like people talk today about the details of the Kardashian family. It was unnerving to me how confident they all sounded and how much they knew.</p>
<p>Then we started the first section – the analytical section, normally my strong point. I did great on the first problem but then looked up at the clock and panicked. I’d used up much of the time already and I’d have to scramble to get through at least two more problems. I worked feverishly, watching the minutes tick down, when the woman seated in front of me calmly set her pencil down. She set her pencil down!  Time wasn’t even called yet, and she was done? That unnerved me only more, as I frantically filled in a few more bubbles before time ran out. I wasted several minutes into the next section trying to shake off my disappointment over the first one.</p>
<p>On our break, I waited in line for a bathroom stall, while two women talked about how easy the analytical section was. My heart sank as I dragged myself back to my seat with self-flagellating thoughts. And then, I opened the test book to my next section – another analytical section, that was far easier than the first one.  Aha!  There were two sections, so the first must have been the test section!</p>
<p>When it was all over, I did manage to score in the high 80<sup>th</sup> percentile. But I usually scored in the 90<sup>th</sup> percentile on standardized tests, and I aspired to a Top 20 school. So I enrolled in a prep course at San Francisco State. It was four Saturday mornings from 9-1. Each day was devoted to strategies for approaching a different section, and on the last day we took a full, timed LSAT test from a prior year.</p>
<p>The second time I took the LSAT, I went in confidently – I had a plan, I knew what to expect, I knew exactly how to pace myself, I knew <em>not</em> to listen to other people in the bathroom, and I’d trained myself to shake off the prior section as soon as we started a new one. This time, I scored in the high 90<sup>th</sup> percentile. Nine percentage points higher than the first time, which was enough to win admission to a Top 20-ranked law school. I wanted to return to the Northwest, and at the time, the University of Washington Law School, in Seattle, had been climbing the rankings and had just sneaked into the Top 20.</p>
<p>Keep in mind that I’d had little to no prep, and certainly not very useful prep the first time I took the test, so there was room to improve. If you take a good prep course the first time and then want to re-take the test again, you can probably improve your score, but it may not be a dramatic improvement.</p>
<p>The lesson I offer is that you can prepare for the test. There are tricks to be taught, approaches to be learned, meta strategies to the test overall. I’ll be blogging over the next few months sharing tips and insights for the test. During law school, I taught a law school prep course myself. I worked with a friend who’d taught for years with Kaplan. He was one of those geniuses who earned near perfect scores across the range of LSAT, GRE, GMAT, you name it. I will share the Kaplan strategies I learned from him, along with my own techniques. I’m not a freakish test genius like him, but I do fairly well in the LSAT corner of the world.</p>
<p>It’s too bad that the LSAT score is so determinative, but in most law schools, I believe, it remains paramount. It certainly doesn’t measure emotional intelligence, or the range of other skills that go into making productive members of society. But it is what it is, so prepare yourself as best you can – and later I’ll write a blog about admission strategies if you don’t have the stats for a top school.</p>
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		<title>The Revised GRE</title>
		<link>http://www.myguruedge.com/2012/01/27/the-revised-gre/</link>
		<comments>http://www.myguruedge.com/2012/01/27/the-revised-gre/#comments</comments>
		<pubDate>Sat, 28 Jan 2012 04:32:15 +0000</pubDate>
		<dc:creator>myguru</dc:creator>
				<category><![CDATA[GRE]]></category>
		<category><![CDATA[gre test prep]]></category>
		<category><![CDATA[GRE Verbal]]></category>
		<category><![CDATA[Revised GRE]]></category>

		<guid isPermaLink="false">http://www.myguruedge.com/?p=2130</guid>
		<description><![CDATA[The Basics: ETS has released a new version of the GRE. The old GRE had been around for quite some time with very few changes, but it had a number of problems: The quantitative section was too easy &#8211; nearly 6% of all test takers getting a perfect score The verbal section was too hard [...]]]></description>
			<content:encoded><![CDATA[<p><strong>The Basics:</strong></p>
<p><a href="http://ets.org">ETS</a> has released a new version of the <a href="http://www.gre.org">GRE</a>. The old GRE had been around for quite some time with very few changes, but it had a number of problems:</p>
<ol>
<li>The quantitative section was too easy &#8211; nearly 6% of all test takers getting a perfect score</li>
<li>The verbal section was too hard &#8211; a scaled score anywhere between 730 and 800 was a 99th percentile score.</li>
</ol>
<p>Admissions committees must have had a hard time sorting out who&#8217;s perfect quant score was the best, and the verbal section must have seemed like a nearly impossible and somewhat random test of an applicant&#8217;s vocabulary. On top of this there has always been doubt about the correlation between GRE scores and performance in graduate school.</p>
<p>The new version of the test is supposed to be a more well rounded measure of a student&#8217;s critical reasoning ability. It&#8217;s also supposed to be a good measure of academic potential for students entering any field, even an <a href="http://online.wsj.com/article/SB10001424053111903885604576486130608474162.html">MBA program</a>. While only a few MBA programs accepted the old version of the test, many are <a href="http://www.ets.org/gre/news/gre_mba_growth">accepting the Revised GRE.</a></p>
<p><strong>Test Content:</strong></p>
<p><span style="text-decoration: underline;">Writing:</span></p>
<p>The <a href="http://www.ets.org/gre/revised_general/prepare/analytical_writing/">writing portion</a> of the exam remains unchanged</p>
<p><span style="text-decoration: underline;">Verbal:</span></p>
<p>The verbal portion of the exam is almost completely different. With the exception of reading comprehension, the old question types are gone, and even in reading comprehension the changes are significant. The question types are as follows:</p>
<ul>
<li><a href="http://www.ets.org/gre/revised_general/prepare/verbal_reasoning/text_completion">Text Completion</a> &#8211; some text containing between one and three blanks is presented and the student is asked to choose words for the blanks that best complete the text. <a href="http://www.ets.org/gre/revised_general/prepare/verbal_reasoning/text_completion/sample_questions">Examples</a></li>
<li><a href="http://www.ets.org/gre/revised_general/prepare/verbal_reasoning/sentence_equivalence/">Sentence Equivalence</a> &#8211; a sentence with a single blanks is presented and the student must choose two words that will complete the sentence and give it an equivalent meaning. <a href="http://www.ets.org/gre/revised_general/prepare/verbal_reasoning/sentence_equivalence/sample_questions">Examples</a></li>
<li><a href="http://www.ets.org/gre/revised_general/prepare/verbal_reasoning/sentence_equivalence/sample_questions">Reading Comprehension</a> &#8211; this section has several question types (1) Multiple Choice with one answer (2) Multiple Choice with one or more answers (the student must select ALL and ONLY the correct answers) (3) Select in passage (the student must indicate the portion of the passage that contains the answer to the question).<a href="http://www.ets.org/gre/revised_general/prepare/verbal_reasoning/reading_comprehension/sample_questions"> Examples</a></li>
</ul>
<p><span style="text-decoration: underline;">Quantitative:</span></p>
<p>At first glance the quantitative portion of the exam seems much the same as the old exam. However, there are a few important changes: two new question types, harder questions in general, and a CALCULATOR! This last change is huge, and it may be a way to attract many would-be GMAT test takers. The calculator is on screen and has most the basic functions along with a few GRE specific bells and whistles. The question types are as follows:</p>
<ul>
<li><a href="http://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/comparison/">Quantitative Comparison</a> &#8211; a hold-over from the old exam. The student is presented with two quantities labeled (A) and (B). If (A) is greater then the student must select choice A, if (B) is greater, the student must select choice B, if the two quantities are equal, the student must select choice C, if the relationship cannot be determined with the information provided, the student must select choice D. These are definitely the trickiest quantitative questions. <a href="http://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/comparison/sample_questions">Examples</a></li>
<li><a href="http://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/multiple_choice_one/">Multiple Choice</a> &#8211; also a hold-over from the old exam, but with a new <a href="http://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/multiple_choice_more/">twist</a>. There are two distinct types of multiple choice questions: (1) Multiple Choice with one answer (2) Multiple Choice with one or more answers (the student must select ALL and ONLY the correct answers). The second type is rare, accounting for only about 8% of the quantitative section. Examples <a href="http://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/multiple_choice_one/sample_questions">here</a> and <a href="http://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/multiple_choice_more/sample_questions">here</a></li>
<li><a href="http://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/numeric_entry/">Numeric Entry</a> &#8211; these types of questions require the student to enter an actual numerical value &#8211; fraction, decimal, integer, etc. Equivalent forms are correct &#8211; e.g. 1/5 and 0.2 will both receive the same evaluation. The on screen calculator will allow you to transfer a value to the numeric entry box. These questions are also rare, accounting for about 8% of the quantitative section. <a href="http://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/numeric_entry/sample_questions">Examples </a></li>
<li><a href="http://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/data_interpretation/">Data Interpretation</a> &#8211; a hold-over from the old exam. The student is presented with some data in graphical or tabular form and asked a series of multiple choice questions about the data. These questions can include both types of multiple choice as well as numeric entry. <a href="http://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/data_interpretation/sample_questions">Examples </a></li>
</ul>
<p><strong>Scoring</strong>:</p>
<p>The score scale has also changed. Instead of a scale from 200 to 800 in ten point increments for quantitative and verbal along with a combined score, the scale now ranges from 130 to 170 in one point increments with no combined score. The scoring of the writing section is unchanged.</p>
<p>The new scale is a relatively superficial change, but data from the first batch of scores suggests that the new test creates a more normal distribution of students. The quantitative scores are more spread out and not so top-heavy, while the verbal scores don&#8217;t make the exam look impossible hard. The verbal section remains the more difficult of the two for the average student.</p>
<p><strong>MyGuru&#8217;s Perspective:</strong></p>
<p>I took the exam the first day it was offered and managed a 170 on the quantitative (99th percentile) and a 168 on the verbal (98th percentile) without too much work. I finished in plenty of time and overall I felt that the exam was quite a bit easier than the GMAT &#8211; I also managed a 99th percentile score on the GMAT, but not without breaking a sweat. Not all of our GRE specialists have taken the revised version, but those who have share my opinion and all of them scored extremely high. We believe that preparation is essentially the same and most of the changes are insignificant &#8211; solid fundamental skills, knowing what to expect, and a common sense approach along with a few tricks will still produce consistently good scores.<strong></strong></p>
<p>&nbsp;</p>
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		<title>GRE Word of the Day: 1.27.2012</title>
		<link>http://www.myguruedge.com/2012/01/27/gre-word-of-the-day-1-27-2012/</link>
		<comments>http://www.myguruedge.com/2012/01/27/gre-word-of-the-day-1-27-2012/#comments</comments>
		<pubDate>Sat, 28 Jan 2012 03:14:20 +0000</pubDate>
		<dc:creator>myguru</dc:creator>
				<category><![CDATA[GRE]]></category>
		<category><![CDATA[Uncategorized]]></category>
		<category><![CDATA[gre test prep]]></category>
		<category><![CDATA[GRE Verbal]]></category>
		<category><![CDATA[GRE Vocabulary]]></category>

		<guid isPermaLink="false">http://www.myguruedge.com/?p=2119</guid>
		<description><![CDATA[Deleterious &#8211; {adjective} 1. injurious to health: deleterious gases. 2. harmful; injurious: deleterious influences. Synonyms: pernicious, hurtful, destructive; noxious. Antonyms: beneficial Example Sentences: 1. Overwork can be deleterious to one&#8217;s health. 2. Though and improved diet was beneficial, it could not overcome the deleterious effects on the disease.]]></description>
			<content:encoded><![CDATA[<p><strong>Deleterious</strong> &#8211; {adjective}</p>
<div>1. injurious to health: <em>deleterious gases</em>.</div>
<div>2. harmful; injurious: <em>deleterious influences</em>.</div>
<div><span style="text-decoration: underline;">Synonyms:</span></div>
<div>pernicious, hurtful, destructive; noxious.</div>
<div><span style="text-decoration: underline;">Antonyms:</span></div>
<div>beneficial</div>
<div><span style="text-decoration: underline;">Example Sentences:</span></div>
<div>1. Overwork can be <em>deleterious</em> to one&#8217;s health.</div>
<div>2. Though and improved diet was beneficial, it could not overcome the <em>deleterious</em> effects on the disease.</div>
]]></content:encoded>
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		<title>GRE Word of the Day: 1.26.2012</title>
		<link>http://www.myguruedge.com/2012/01/27/gre-word-of-the-day-1-26-2012/</link>
		<comments>http://www.myguruedge.com/2012/01/27/gre-word-of-the-day-1-26-2012/#comments</comments>
		<pubDate>Sat, 28 Jan 2012 03:13:27 +0000</pubDate>
		<dc:creator>myguru</dc:creator>
				<category><![CDATA[GRE]]></category>
		<category><![CDATA[Uncategorized]]></category>
		<category><![CDATA[gre test prep]]></category>
		<category><![CDATA[GRE Verbal]]></category>
		<category><![CDATA[GRE Vocabulary]]></category>

		<guid isPermaLink="false">http://www.myguruedge.com/?p=2110</guid>
		<description><![CDATA[Castigate &#8211; {verb} 1. To criticize or reprimand severely. 2. To punish in order to correct. Related Forms: Castigation {noun} Castigatory {adjective} Synonyms: 1.  scold, reprove. 2.  discipline, chastise, chasten. Example Sentence: &#8220;The child was constantly castigated by his irritable father.&#8221;]]></description>
			<content:encoded><![CDATA[<p><strong>Castigate &#8211; </strong>{verb}</p>
<div>1. To criticize or reprimand severely.</div>
<div>2. To punish in order to correct.</div>
<div><span style="text-decoration: underline;">Related Forms:</span></div>
<div>Castigation {noun}</div>
<div>Castigatory {adjective}</div>
<div><span style="text-decoration: underline;">Synonyms:</span></div>
<div>1.  scold, reprove.</div>
<div>2.  discipline, chastise, chasten.</div>
<div><span style="text-decoration: underline;">Example Sentence:</span></div>
<div>&#8220;The child was constantly <em>castigated </em>by his irritable father.&#8221;</div>
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		<title>GMAT SC Rule of the Day: 1.27.2012</title>
		<link>http://www.myguruedge.com/2012/01/25/gmat-sc-rule-of-the-day-1-25-2012/</link>
		<comments>http://www.myguruedge.com/2012/01/25/gmat-sc-rule-of-the-day-1-25-2012/#comments</comments>
		<pubDate>Wed, 25 Jan 2012 23:10:22 +0000</pubDate>
		<dc:creator>myguru</dc:creator>
				<category><![CDATA[GMAT Blog]]></category>
		<category><![CDATA[Uncategorized]]></category>
		<category><![CDATA[gmat]]></category>
		<category><![CDATA[GMAT prep]]></category>
		<category><![CDATA[Sentence Correction]]></category>
		<category><![CDATA[Subject / Verb Agreement]]></category>

		<guid isPermaLink="false">http://www.myguruedge.com/?p=2115</guid>
		<description><![CDATA[Subject Verb Agreement: Collective Nouns Collective nouns designate large groups of people or things. For example: People: agency, army, band, audience, committee, congress, team Things: baggage, furniture. These nouns are almost always singular on the GMAT. Examples: The agency controls petroleum products regulation. The band plays well. The furniture is old and drab. &#160;]]></description>
			<content:encoded><![CDATA[<p><strong>Subject Verb Agreement: Collective Nouns</strong></p>
<p>Collective nouns designate large groups of people or things. For example:</p>
<p><span style="text-decoration: underline;">People</span>: agency, army, band, audience, committee, congress, team</p>
<p><span style="text-decoration: underline;">Things</span>: baggage, furniture.</p>
<p><strong>These nouns are almost always singular on the GMAT.</strong></p>
<p><span style="text-decoration: underline;">Examples</span>:</p>
<p>The <em>agency controls</em> petroleum products regulation.</p>
<p>The <em>band plays</em> well.</p>
<p>The <em>furniture is</em> old and drab.</p>
<p>&nbsp;</p>
]]></content:encoded>
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		<title>GRE Word of the Day: 1.25.2012</title>
		<link>http://www.myguruedge.com/2012/01/25/gre-word-of-the-day-1-25-2012/</link>
		<comments>http://www.myguruedge.com/2012/01/25/gre-word-of-the-day-1-25-2012/#comments</comments>
		<pubDate>Wed, 25 Jan 2012 22:51:36 +0000</pubDate>
		<dc:creator>myguru</dc:creator>
				<category><![CDATA[GRE]]></category>
		<category><![CDATA[Uncategorized]]></category>
		<category><![CDATA[gre test prep]]></category>
		<category><![CDATA[GRE Verbal]]></category>
		<category><![CDATA[GRE Vocabulary]]></category>

		<guid isPermaLink="false">http://www.myguruedge.com/?p=2107</guid>
		<description><![CDATA[Burgeon &#8211; {verb} 1. To grow or develop quickly; flourish: The town burgeoned into a city. He burgeoned into a fine actor. 2. To begin to grow, as a bud; put forth buds, shoots, etc., as a plant (often followed by out, forth ). Synonyms 1.  bloom, blossom, mushroom, expand. Example Sentence: &#8220;Online reference resources [...]]]></description>
			<content:encoded><![CDATA[<p><strong>Burgeon &#8211; </strong>{verb}</p>
<div>1. To grow or develop quickly; flourish: <em>The town burgeoned into a city. He burgeoned into a fine actor.</em></div>
<div>2. To begin to grow, as a bud; put forth buds, shoots, etc., as a plant (often followed by out, forth ).</div>
<div>Synonyms<br />
1.  bloom, blossom, mushroom, expand.</div>
<div>Example Sentence:</div>
<div>&#8220;Online reference resources <em>burgeon </em>as traditional reference publishers slowly die in a digital world&#8221;</div>
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		<title>GRE Word of the Day: 1.24.2012</title>
		<link>http://www.myguruedge.com/2012/01/24/gre-word-of-the-day-1-24-2012/</link>
		<comments>http://www.myguruedge.com/2012/01/24/gre-word-of-the-day-1-24-2012/#comments</comments>
		<pubDate>Tue, 24 Jan 2012 22:43:01 +0000</pubDate>
		<dc:creator>myguru</dc:creator>
				<category><![CDATA[GRE]]></category>
		<category><![CDATA[gre test prep]]></category>
		<category><![CDATA[Vocab]]></category>

		<guid isPermaLink="false">http://www.myguruedge.com/?p=2105</guid>
		<description><![CDATA[Advocate &#8211; {verb, noun} 1. Verb: To speak or write in favor of; support or urge by argument; recommend publicly: He advocated higher salaries for teachers. 2. Noun: A person who speaks or writes in support or defense of a person, cause, etc. (usually followed by of ): an advocate of peace.]]></description>
			<content:encoded><![CDATA[<p><strong>Advocate &#8211; </strong>{verb, noun}</p>
<p>1. Verb: To speak or write in favor of; support or urge by argument; recommend publicly: <em>He advocated higher salaries for teachers</em>.</p>
<p>2. Noun: A person who speaks or writes in support or defense of a person, cause, etc. (usually followed by of ): <em>an advocate of peace.</em></p>
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		<item>
		<title>How I Gained 260 Points on the GMAT</title>
		<link>http://www.myguruedge.com/2012/01/17/how-i-gained-260-points-on-the-gmat/</link>
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		<pubDate>Wed, 18 Jan 2012 03:26:01 +0000</pubDate>
		<dc:creator>myguru</dc:creator>
				<category><![CDATA[GMAT Blog]]></category>
		<category><![CDATA[GMAT prep]]></category>
		<category><![CDATA[GMAT tutoring]]></category>

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		<description><![CDATA[Five times&#8230;..yes&#8230;..five times&#8230;&#8230;I took the GMAT five times for admission to business school.Was there something wrong with me?For a while, I thought there was but now that I look back&#8230;.Absolutely not. Standardized exams are just one of those things that I&#8217;ve always had to work hard at to score decently.  I should have taken a [...]]]></description>
			<content:encoded><![CDATA[<div><strong><strong><strong>Five times&#8230;..yes&#8230;..five times&#8230;&#8230;</strong></strong></strong>I took the GMAT five times for admission to business school.Was there something wrong with me?For a while, I thought there was but now that I look back&#8230;.Absolutely not.</p>
<p>Standardized exams are just one of those things that I&#8217;ve always had to work hard at to score decently.  I should have taken a hint when I scored about average on the SATs in high school.</p>
<p>My mind just works in mysterious ways and I&#8217;m sure that if the GMAT tested for emotionally charged responses, I&#8217;d score very well.</p>
<p>Regardless, scoring high on the GMAT is definitely possible when you put in the effort to think like a standardized test taker.  This involves various pieces of knowledge, logic, systematic thinking, and a lot of practice.</p>
<p>So&#8230;how does one get there?</p>
<p>For me, it was a long road. 2 years to be exact.  But it was worth it.</p>
<p>For starters, according to the Graduate Management Admissions Council (GMAC), better known as the guys who make the GMAT exam, about 10% of GMAT retakers obtain a significant gain of 100 points or more.</p>
<p>That 10% takes a lot of hard work but with the right attitude, you can accomplish anything!</p>
<p>What exactly was the end result for me?</p>
<p>A 260 point gain! So yes, it&#8217;s doable!</p>
<p>When you think about it, you have a ton of options to increase your score:  self-study, study groups, tutoring, prep courses, and online forums.  Which one is thee right one for you is something only you can answer. It will definitely rely on how committed you are, too!</p>
<p>I&#8217;ll share my experience with you after taking the GMAT each time.</p>
<h4 dir="ltr">1st Attempt</h4>
<p dir="ltr">When I took the GMAT the first time around, I took it cold. No study guides, no prepping, and some knowledge on what the exam was about.</p>
<p dir="ltr">If you had asked me what a data sufficiency question was, I might have given you a deer-in-headlights look! But I bit the bullet and took it. $25o later and a score of a 420, I was a bit short of breath.  The feeling of disappointment lasted for a few days and it gave me the motivation I needed to sign up for a Kaplan prep course.  I had to start somewhere.</p>
<p dir="ltr">I didn&#8217;t dwell on the score so much. I just got back up and knew what I had to do.</p>
<p dir="ltr">Lesson learned?</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">Take a free practice exam on mba.com.  Some prep courses such as Manhattan GMAT give a free diagnostic exam. Go to the library, lock yourself up, and take the whole thing.  Yes, that includes the writing section.  From there, conduct an informal self-assessment and see what your weaknesses are just by looking at the answers you got wrong.  Ask yourself whether it was time management, a lack of knowledge or approach that contributed to the questions you answered incorrectly.</p>
<p dir="ltr">Although there are a variety of factors involved in answering questions incorrectly, this is a start. Make a plan, and follow it.</p>
<p dir="ltr">Whatever you do, don&#8217;t take the GMAT cold, go for lukewarm.</p>
<h4 dir="ltr">2nd Attempt</h4>
<p dir="ltr">Two months later&#8230;&#8230;..a 460.</p>
<p dir="ltr">A 460?!</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">Blargh!</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">A 40 point increase even after taking a prep course?!</p>
<p dir="ltr">Two weeks prior, I had a completed a 6-week Kaplan course at $1,500! I had taken a few of their practice exams and scored okay on some of the exams, definitely nowhere near a 460 though. I was confused.</p>
<p dir="ltr">I was also spending over 30 hours working on practice problems.  I really wasn&#8217;t sure what I was doing wrong.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">But alas, I moved forward.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">At this point, I knew I was in for a challenge and I was determined to do well on the GMAT.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">Lesson learned?</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">Now that I look back, the Kaplan prep course was definitely not for me.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">If you&#8217;re going to take a live class, make sure it goes at a pace that&#8217;s suitable for you.  Also, try and take a glance at some of the resource materials and get a sense of what you&#8217;re looking at.</p>
<p dir="ltr">I know there are a ton of prep courses out there, but if you&#8217;ve made your mind up, ask around and do some research before you spend that type of money.  In my case, I really put in the time and energy but I was missing something and I wasn&#8217;t sure what that was quite yet.</p>
<h4 dir="ltr">3rd attempt</h4>
<p dir="ltr">Bam! A 530.</p>
<p dir="ltr">Okay, I broke the 500 mark but seriously, I was aiming for a top business school and I had my eyes set on MIT Sloan whose average GMAT score was well over 700.  At some points, I think I wanted to break down but I kept strong.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">I spent almost five months studying by myself and using my old Kaplan materials to practice, practice, practice.  I was spending 3-4 hours a day during the week and 6-8 hours during the weekends studying.  It was pretty intense.  I also became aware of other resources such as Beat the GMAT, GMAT Club, and some other websites to read success stories and see where I could improve.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">Lesson learned?</p>
<p dir="ltr">Email other GMAT takers and see what&#8217;s working for them. Don&#8217;t spend TOO much time reading and writing on the forums as this can become a full-time job in itself.</p>
<p dir="ltr">Reach out to a few folks who are studying and have done well on the GMAT and see what are some of their methods.  I definitely learned a few tips that worked for me.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">At this point, I started to see what I needed to improve my score and I figured I needed another prep course. A good one that would work for me. And that&#8217;s exactly what I did.</p>
<h4 dir="ltr">4th attempt</h4>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">A 580!</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">Woohoo!</p>
<p dir="ltr">Okay. I was getting closer.  Although it was only a 50 point increase from my previous score, it was a 160 point increase from my 420.  I didn&#8217;t want to spend time really thinking about getting a higher score. I knew I needed one but I just went back to the drawing board and picked up where I left off.</p>
<p dir="ltr">Before my fourth attempt,  I took an 8-week Manhattan GMAT self-study prep course. I spent less time studying but followed their regimented syllabus which is awesome.  Aside using their materials, I was also participating in the forums a little more but I was only interacting with students who were solving questions.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">I also created my own support group on the Manhattan GMAT website and even set up a study group in my hometown.  Here is where I started to really learn a lot.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">While studying with my study group, I began to realize that I learned best when someone taught me the right way to answer a question.  A lot times, things had to be explained to me in various ways before I could understand some of those moderately difficult math and verbal questions.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">I also became aware that the students in my group were using tutors. Neither of the tutors were affiliated with any major test prep companies, they were general tutors who understood standardized exams.  I was a bit hesitant to hire a tutor since I had spent quite a bit of money already.  At this point, I was running on fumes since I really had devoted a lot of time and energy to the GMAT.  But after seeing positive results come out of other students, I decided to invest one more time.</p>
<p dir="ltr">Lesson learned?</p>
<p dir="ltr">As you move forward, understand your strengths and weaknesses.  How do you learn best? It&#8217;s more than just going over answers over, and over, and over again.  I can&#8217;t tell you how often I went over incorrect answers over and over again only to get them wrong again later.  I wasn&#8217;t truly understanding how to solve the questions.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">It&#8217;s all about your gaining various approaches to answering questions that are commonly asked on the GMAT.  Once you know this, you&#8217;ll start to see a difference.</p>
<h4 dir="ltr">5th attempt</h4>
<p dir="ltr">And the fat lady sang!</p>
<p dir="ltr">A 680!</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">By this point, I had decreased the number of study hours studying to 15 a week and had hired a tutor with whom I was meeting once a week.  It definitely paid off as I started to see a huge difference in my study habits and diagnostic scores on certain online exams.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">All along, what I really needed was someone to guide me through various questions in a way that was easy for me to understand.  Right from the get go, the tutor understood where I faltered and made sure that I COMPLETELY understood WHY I was getting certain answers wrong.</p>
<p dir="ltr">We focused on questions that I guessed on and answers that I answered incorrectly.  I was able to see, for instance, that I was spending way too much time trying to answer difficult questions, when in reality, I should have been trying to answer the question and then making an educated guess if I could not answer it in time.</p>
<p dir="ltr">I also learned various patterns in questions that were frequently asked &#8211; both the verbal and quant sections.  My tutor also showed me various techniques and strategies for answering questions quickly when I was on a time crunch.</p>
<p dir="ltr">I learned new concepts that I had not picked up in prior prep courses.  There are so many ways to solve those math questions, and they&#8217;re endless ways to interpret a passage; my tutor made sure I understood what the question was really asking. I was also staying away from those emotionally charged answers that got me every time.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">Lesson learned?</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">The details go beyond this. What I learned most about my tutoring experience was that she understood my way of thinking.  We went over my exam history and how my weaknesses lied in the verbal section.  Although we spent time on the quant section, we spent more time looking at critical reasoning and reading comprehension.  Together, we built strategies and tactics for dealing with the harder questions.</p>
<p dir="ltr">I could not have done any of this without a tutor.  And had I known this would have been the result when I first started studying for the GMAT, I would have gladly reallocated my funds to hiring a tutor. So before you invest, think about your study habits and learning style.  This will help you out tremendously as you venture on a quest to get a high GMAT score.</p>
<p dir="ltr">Believe me, a higher GMAT score is definitely possible.  A 260 point gain doesn&#8217;t come out of thin air.  It happens when you put in the hard work.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">It will also depend on how much time you spend doing high-quality studying.</p>
<p><strong><strong><br />
</strong></strong></p>
<p dir="ltr">There&#8217;s definitely a psychology to this whole process but if you have dreams, don&#8217;t let the GMAT  get in the way.</p>
<p dir="ltr">Knock it down.</p>
<p dir="ltr">What about you? Do you have any successes? Have you used a tutor?  Your comments are welcome!</p>
<h4 dir="ltr">This was a Guest Post by Oscar Pedroso, Founder of <a href="http://mbawritersblock.com/about/" target="_blank">MBA Writers Block</a></h4>
<p dir="ltr">Here&#8217;s a bit about Oscar and MBA Writers Block:</p>
<p>In October 2011, MBAwritersblock.com was born as a way for me to share my experience of applying to business school.</p>
<p>I spent <em>three years</em> and almost <em>$11,000</em> applying to seven top MBA programs.  I believe no one should ever have to spend that much money to pursue an education in business.  So my first goal is to show you, that with hard work and perseverance, you can tackle the business school writing process by  learning how to write powerful essays.  My second goal is to turn MBAwritersblock.com into a powerful resource for young professionals applying to business school, online and off, so they can apply intelligently and inexpensively.</p>
<p>We encourage you to visit <a href="http://mbawritersblock.com/">http://mbawritersblock.com/</a> and let us know what you think.</p>
</div>
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		<title>GMAT Combinatorics 2.0: Permutations and Combinations</title>
		<link>http://www.myguruedge.com/2011/12/28/gmat-combinatorics-2-0-permutations-and-combinations/</link>
		<comments>http://www.myguruedge.com/2011/12/28/gmat-combinatorics-2-0-permutations-and-combinations/#comments</comments>
		<pubDate>Wed, 28 Dec 2011 21:20:31 +0000</pubDate>
		<dc:creator>myguru</dc:creator>
				<category><![CDATA[GMAT Blog]]></category>
		<category><![CDATA[Combination]]></category>
		<category><![CDATA[Combinatorics]]></category>
		<category><![CDATA[Permutation]]></category>
		<category><![CDATA[Probability]]></category>
		<category><![CDATA[Quant]]></category>

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		<description><![CDATA[If you haven&#8217;t read GMAT Combinatorics 1.0, 1.1, and 1.2, you should do that before you read any further. Even if you&#8217;re familiar with some of the material, you may not be familiar with my approach. Though the subtitle of this posts suggests that I&#8217;m going to discuss permutations and combinations, I&#8217;m never going to [...]]]></description>
			<content:encoded><![CDATA[<p>If you haven&#8217;t read <em>GMAT Combinatorics 1.0, 1.1, and 1.2</em>, you should do that before you read any further. Even if you&#8217;re familiar with some of the material, you may not be familiar with my approach. Though the subtitle of this posts suggests that I&#8217;m going to discuss permutations and combinations, I&#8217;m never going to formally define either one &#8211; that&#8217;s right no formulas. Just careful application of the fundamental counting principle with a couple of modifications.</p>
<p><strong>When Order Matters:</strong></p>
<p>The types of combinatorics problems that you&#8217;re going to encounter on the GMAT can be subdivided into three groups:</p>
<ul>
<li>Simple counting &#8211; A task with sub-tasks involving choices (see 1.0, 1.1, and 1.2)</li>
<li>Permutations &#8211; Ordering or reordering a set or subset of things (we&#8217;ve already done some examples in 1.0, 1.1, and 1.2)</li>
<li>Combinations &#8211; Selecting a subset of things from a larger set.</li>
</ul>
<p>The first two are pretty much taken care of in earlier posts, though we will discuss permutations as a way to illustrate what a combination is. Permutations involve order or assignment and can be done with a simple application of the fundamental principle of counting. Combinations involved selecting a subset without regard to order, and require a simple modification of the fundamental principle of counting.</p>
<p>Here&#8217;s are some typical applications of permutations and combinations.</p>
<p><strong>Permutations:</strong></p>
<ul>
<li>Selecting a president, vice president, and treasurer for a club or organization</li>
<li>Casting a play</li>
<li>Selecting a batting order for a baseball team</li>
<li>Ranking applicants by GMAT score</li>
<li>Arranging books on a shelf</li>
</ul>
<p><strong>Combinations:</strong></p>
<ul>
<li>Selecting a subcommittee</li>
<li>Picking a dodge ball team</li>
<li>Selecting toppings for a pizza</li>
<li>Selecting 50 MBA applicants for acceptance</li>
<li>Poker Hands</li>
</ul>
<p>So, how do we compensate for order. I&#8217;ll illustrate with two examples</p>
<p><strong>Example 1:</strong></p>
<p>This example has two similar problems &#8211; one where order matters and one where it doesn&#8217;t</p>
<p><strong>(A)</strong> High School High&#8217;s Spanish club is holding an election to select the President, Vice President, and Treasurer of their club. If the club has eight members, how many possible outcomes can the election have?</p>
<p><strong>Solution:</strong> Here we are <em>ordering</em> 3 things from a set of 8 things. Each of these three things will be assigned to a particular office, so order matters and we can apply the fundamental counting principle:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=8%20%5Ctimes%207%20%5Ctimes%206%20%3D%20336&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='8 \times 7 \times 6 = 336' title='8 \times 7 \times 6 = 336' class='latex' /></p>
<p style="text-align: left;"><strong>(B) </strong>High School High&#8217;s Latin club will elect a ruling <a href="http://en.wikipedia.org/wiki/First_Triumvirate">triumvirate</a>. If the Latin club has 11 members, how many possible outcomes can the election have?</p>
<p style="text-align: left;"><strong>Solution: </strong>Here we are selecting a subset of three people from a set of eleven people. None of the three people is assigned to a specific office, consequently many elections results are equivalent. Since there are three people in the triumvirate, each one can be listed in 6 ways &#8211; it&#8217;s a simple application of the fundamental principle:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=3%20%5Ctimes%202%20%5Ctimes%201&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='3 \times 2 \times 1' title='3 \times 2 \times 1' class='latex' /></p>
<p style="text-align: left;">In order to compensate we need to divide by the number of ways the selection can be reordered:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%20%5Cfrac%7B11%20%5Ctimes%2010%20%5Ctimes%209%7D%7B3%20%5Ctimes%202%20%5Ctimes%201%7D%20%3D%20165&#038;bg=ffffff&#038;fg=000000&#038;s=2' alt=' \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165' title=' \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165' class='latex' /></p>
<p><strong>A note on calculation</strong> &#8211; This might seem like a difficult computation, especially without access to a calculator, but you can save yourself a lot of work if you cancel bottom terms with top terms. The calculation I actually did looked like this:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%20%5Cfrac%7B11%20%5Ctimes%205%20%5Ctimes%203%7D%7B1%7D%20%3D%20165&#038;bg=ffffff&#038;fg=000000&#038;s=2' alt=' \frac{11 \times 5 \times 3}{1} = 165' title=' \frac{11 \times 5 \times 3}{1} = 165' class='latex' /></p>
<p style="text-align: left;"><strong>To recap:</strong> You <em>must</em> divide by the number of ways your selection of elements can be rearranged when order doesn&#8217;t matter.</p>
<p style="text-align: left;"><strong>Example 2:</strong></p>
<p style="text-align: left;">Again, we&#8217;ll do two similar problems &#8211; one where order matters and one where it doesn&#8217;t</p>
<p style="text-align: left;"><strong>(A) </strong>High School High is putting on a production of Shakepeare&#8217;s play <em>Antony and Cleopatra</em>. Four girls are auditioning for Octavia or Cleopatra. Six boys are auditioning for Octavius Ceasar, Mark Antony, or Lepidus. How many ways can these five parts be cast?</p>
<p style="text-align: left;"><strong>Solution: </strong>Here order matters. We&#8217;re assigning two of the four girls to particular parts, and three of the six boys to particular parts. In, addition the selections are linked and the total number of castings will be the product of the castings for the boys and the castings for the girls. First we&#8217;ll do the boys:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%204%20%5Ctimes%203%20%3D%2012%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' 4 \times 3 = 12 ' title=' 4 \times 3 = 12 ' class='latex' /></p>
<p style="text-align: left;">Now the girls:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%206%20%5Ctimes%205%5Ctimes%204%20%3D%20120%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' 6 \times 5\times 4 = 120 ' title=' 6 \times 5\times 4 = 120 ' class='latex' /></p>
<p style="text-align: left;">Now the boys <em>and</em> the girls:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%20120%20%5Ctimes%2012%20%3D%201440%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' 120 \times 12 = 1440 ' title=' 120 \times 12 = 1440 ' class='latex' /></p>
<p style="text-align: left;"><strong>(B) </strong>At the strike party, the cast orders two pizzas. Due to terrible performances by Antony and Cleopatra, they only have enough money for three toppings for each pizza.  The available toppings are: italian sausage, pepperoni, ham, onion, green pepper, pineapple, mushrooms, ricotta, goat cheese, and parmesan cheese. How many different pairs of pizzas can be ordered?</p>
<p style="text-align: left;"><strong>Solution: </strong>Here order doesn&#8217;t matter &#8211; pepperoni and mushrooms is the same as mushrooms and pepperoni. The three pizzas are linked like the castings for girls and boys above, so the total number will be the product of the ways of selecting each pizza. Each pizza can have one <em>or</em> two <em>or</em> three toppings. Because these three scenarios are mutually exclusive to total number of pizzas will be the sum of these three scenarios. Kinda complicated, so we&#8217;ll take it one step at a time. One pizza &#8211; one topping plus two toppings plus three toppings:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%2010%20%2B%20%5Cfrac%7B10%20%5Ctimes%209%7D%7B2%20%5Ctimes%201%7D%20%2B%20%5Cfrac%7B10%20%5Ctimes%209%20%5Ctimes%208%7D%7B3%20%5Ctimes%202%20%5Ctimes%201%7D%20&#038;bg=ffffff&#038;fg=000000&#038;s=2' alt=' 10 + \frac{10 \times 9}{2 \times 1} + \frac{10 \times 9 \times 8}{3 \times 2 \times 1} ' title=' 10 + \frac{10 \times 9}{2 \times 1} + \frac{10 \times 9 \times 8}{3 \times 2 \times 1} ' class='latex' /></p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=10%20%2B%2045%20%2B%20120%20%3D%20175&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='10 + 45 + 120 = 175' title='10 + 45 + 120 = 175' class='latex' /></p>
<p style="text-align: left;">Since the second pizza will have the same number of variations, the total number of pizzas is</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%20175%20%5Ctimes%20175%20%3D%2030%2C625&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' 175 \times 175 = 30,625' title=' 175 \times 175 = 30,625' class='latex' /></p>
<p style="text-align: center;">
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		<title>GMAT Combinatorics 1.2: Problem Solutions</title>
		<link>http://www.myguruedge.com/2011/12/27/gmat-combinatorics-1-2-problem-solutions/</link>
		<comments>http://www.myguruedge.com/2011/12/27/gmat-combinatorics-1-2-problem-solutions/#comments</comments>
		<pubDate>Wed, 28 Dec 2011 01:03:28 +0000</pubDate>
		<dc:creator>myguru</dc:creator>
				<category><![CDATA[GMAT Blog]]></category>
		<category><![CDATA[Combinatoircs]]></category>
		<category><![CDATA[gmat]]></category>
		<category><![CDATA[Solved Problems]]></category>

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		<description><![CDATA[1. Suppose you perform the following experiment &#8211; You flip a coin 5 times and record the results. How many different outcomes are there? (A result being a 5-character long string of H&#8217;s and T&#8217;s, such as HHTHT) Solution: For every flip of the coin, there are two possible outcomes. Because we flip the coin [...]]]></description>
			<content:encoded><![CDATA[<p><strong>1.</strong> Suppose you perform the following experiment &#8211; You flip a coin 5 times and record the results. How many different outcomes are there? (A result being a 5-character long string of H&#8217;s and T&#8217;s, such as HHTHT)</p>
<p><strong>Solution: </strong>For every flip of the coin, there are two possible outcomes. Because we flip the coin 5 times, according to the fundamental principle of counting the number of possible outcomes is:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=2%20%5Ctimes%202%20%5Ctimes%202%20%5Ctimes%202%20%5Ctimes%202%20%3D%2032&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='2 \times 2 \times 2 \times 2 \times 2 = 32' title='2 \times 2 \times 2 \times 2 \times 2 = 32' class='latex' /></p>
<p style="text-align: left;">Note that this calculation can also be expressed by <img src='http://s.wordpress.com/latex.php?latex=%202%5E5%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' 2^5 ' title=' 2^5 ' class='latex' />. In fact, if you flip a coin <img src='http://s.wordpress.com/latex.php?latex=%20n%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' n ' title=' n ' class='latex' /> times, the number of possible outcomes is <img src='http://s.wordpress.com/latex.php?latex=%202%5En%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' 2^n ' title=' 2^n ' class='latex' />.<strong></strong></p>
<p style="text-align: center;">__________<strong><br />
</strong></p>
<p><strong>2.0</strong> You receive a new debit card in the mail and you are asked to create a new PIN (Personal Identification Number) for your debit card. The PIN must be 4 digits long and each digit must be one of the numbers 0 &#8211; 9. You can use the same digit more than once. How many possible PIN numbers are there?</p>
<p><strong>Solution:</strong> Each number in your PIN can be one of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. One digit must be assigned on each of four places. So, by the fundamental counting principle, the number of outcomes is:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=10%20%5Ctimes%2010%20%5Ctimes%2010%20%5Ctimes%2010%20%3D%2010%2C000%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='10 \times 10 \times 10 \times 10 = 10,000 ' title='10 \times 10 \times 10 \times 10 = 10,000 ' class='latex' /></p>
<p style="text-align: center;">__________</p>
<p><strong>2.1</strong> Same as 2, but now you can use each digit only once.</p>
<p><strong>Solution: </strong>Now that we cannot reuse digits, once we assign a digit to the first place, we will only have 9 options for the second place, then 8 options for the 3rd place and so on. As I mentioned before, this is a permutation &#8211; the ordering or a subset of elements taken from a larger set. But, as you&#8217;ll see in the course of these posts on combinatorics, all the technical jargon and formulas you get in other prep material just reduces to a single principle &#8211; the fundamental principle of counting. The number of possible PIN numbers is now,</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%2010%20%5Ctimes%209%20%5Ctimes%208%20%5Ctimes%207%20%5Ctimes%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' 10 \times 9 \times 8 \times 7 \times ' title=' 10 \times 9 \times 8 \times 7 \times ' class='latex' /> = 5040</p>
<p style="text-align: center;">__________</p>
<p><strong>2.2</strong> Same as 2, but now you can use each digit only once and you cannot begin the PIN with a zero.</p>
<p><strong>Solution: </strong>This is very similar to the last problem with one exception. We only have nine possibilities for the first digit. So the number of possible PIN numbers is</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=9%20%5Ctimes%209%20%5Ctimes%208%20%5Ctimes%207%20%3D%204536%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='9 \times 9 \times 8 \times 7 = 4536 ' title='9 \times 9 \times 8 \times 7 = 4536 ' class='latex' /></p>
<p style="text-align: center;">__________</p>
<p><strong>3.</strong> Sam, Sally, Xanthar, and their parents drive to the park in their Prion (a Prius that has been modified by Xanthar for hydrogen ion technology). If the front of the car has two seats (the drivers seat and the passenger seat), the back seat will hold three people, and the two parents sit in the front and Sam, Sally, and Xanthar sit in the back seat, how many ways can the family be arranged in the car if each seat contains only one passenger.</p>
<p><strong>Solution: </strong>The total arrangements in the car depends on the arrangements of two groups &#8211; the kids and the parents. We will take the product of these two arrangements because they are not mutually exclusive.</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=Kid%20Arrangements%20%3D%203%20%5Ctimes%202%20%5Ctimes%201%20%3D%206&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='Kid Arrangements = 3 \times 2 \times 1 = 6' title='Kid Arrangements = 3 \times 2 \times 1 = 6' class='latex' /></p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=Parent%20Arrangements%20%3D%202%20%5Ctimes%201%20%3D%202&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='Parent Arrangements = 2 \times 1 = 2' title='Parent Arrangements = 2 \times 1 = 2' class='latex' /></p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%20Total%20Arrangements%20%3D%206%20%5Ctimes%202%20%3D%2012&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' Total Arrangements = 6 \times 2 = 12' title=' Total Arrangements = 6 \times 2 = 12' class='latex' /></p>
<p style="text-align: center;">__________</p>
<p><strong>4.0</strong> You roll two die. How many possible outcomes are there?</p>
<p><strong>Solution:</strong> You can think of the outcome of one roll as an ordered pair or numbers <img src='http://s.wordpress.com/latex.php?latex=%28x%2C%20y%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(x, y)' title='(x, y)' class='latex' />. For instance, the ways to roll a sum of seven are <img src='http://s.wordpress.com/latex.php?latex=%281%2C%206%29%2C%20%282%2C%205%29%2C%20%283%2C%204%29%2C%20%284%2C%203%29%2C%20%285%2C%202%29%2C&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(1, 6), (2, 5), (3, 4), (4, 3), (5, 2),' title='(1, 6), (2, 5), (3, 4), (4, 3), (5, 2),' class='latex' /> and <img src='http://s.wordpress.com/latex.php?latex=%286%2C%201%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(6, 1)' title='(6, 1)' class='latex' />. Obviously, there are six options for the first number in the ordered pair, and six options for the second number in the ordered pair. So, according to the fundamental principle of counting the number of outcomes is:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=6%20%5Ctimes%206%20%3D%2036&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='6 \times 6 = 36' title='6 \times 6 = 36' class='latex' /></p>
<p style="text-align: center;">__________</p>
<p><strong>4.1</strong> Same as 4.0. How many ways can you get two even numbers?</p>
<p><strong>Solution:</strong> We can use the same thinking as before. However, this time, because we are only considering even numbers, there are only 3 options for each number. Thus, the number of possibilities is</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=3%20%5Ctimes%203%20%3D%209&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='3 \times 3 = 9' title='3 \times 3 = 9' class='latex' /></p>
<p style="text-align: center;">__________</p>
<p><strong>4.2</strong> Same as 4.0. How many ways can you get two odd numbers?</p>
<p><strong>Solution: </strong>This is the exact same problem as the one above. See the solution to 4.1.</p>
<p style="text-align: center;">__________</p>
<p><strong>4.3</strong> Same as 4.0. How many ways can you get one even and one odd number?</p>
<p><strong>Solution:</strong> This may seem somewhat complicated as we don&#8217;t know in what order the even number and odd number appear in our ordered pair. However, if you were paying attention when you read my original <a href="http://www.myguruedge.com/2011/12/26/gmat-combinatorics-part-1/">combinatorics post</a>, you might be thinking about the &#8216;complement method.&#8217; In fact, it&#8217;s perfect for this problem. On any given roll, one of three things will happen:</p>
<ul>
<li>You&#8217;ll get two odds</li>
<li>You&#8217;ll get two evens</li>
<li>You&#8217;ll get an even and an odd</li>
</ul>
<p>We already know the number of ways in which the first two outcomes can happen, and we know the total number of outcomes. So, we can use the complement method:</p>
<p style="text-align: center;">Even &amp; Odd = Total &#8211; Two Odds &#8211; Two Evens</p>
<p style="text-align: center;">Even &amp; Odd = 36 &#8211; 9 &#8211; 9 = 18</p>
<p style="text-align: center;">__________</p>
<p><strong>4.4</strong> Same as 4.0. Now take the sum of the two upward facing numbers. How many ways can the sum be an even number?</p>
<p><strong>Solution: </strong>We can only get and even sum in two ways:</p>
<ul>
<li>Even + Even = Even</li>
<li>Odd + Odd = Even</li>
</ul>
<p>Using the problems we already solved above, we know that there are nine ways to roll two evens and nine ways to roll two odds. Since these are mutually exclusive events we add to get the total number of outcomes, which is 18.</p>
<p style="text-align: center;">__________</p>
<p><strong>4.5</strong> Same as 4.0. Now take the product of the two upward facing numbers. How many ways can the product be an even number?</p>
<p><strong>Solution: </strong>We proceed as above. We get an even product in one of two ways</p>
<ul>
<li>Even X Even = Even</li>
<li>Even X Odd = Odd X Even = Even</li>
</ul>
<p>The number of ways the first even can happen is nine and the number of ways the second event can happen is 18. Since they are mutually exclusive, we add, and get 27.</p>
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