<?xml version='1.0' encoding='UTF-8'?><?xml-stylesheet href="http://www.blogger.com/styles/atom.css" type="text/css"?><feed xmlns='http://www.w3.org/2005/Atom' xmlns:openSearch='http://a9.com/-/spec/opensearchrss/1.0/' xmlns:blogger='http://schemas.google.com/blogger/2008' xmlns:georss='http://www.georss.org/georss' xmlns:gd="http://schemas.google.com/g/2005" xmlns:thr='http://purl.org/syndication/thread/1.0'><id>tag:blogger.com,1999:blog-6229672768869848568</id><updated>2025-05-02T23:04:49.251-07:00</updated><category term="algebra"/><category term="cheat sheet"/><category term="exam"/><category term="geometry"/><category term="gmat"/><category term="mba"/><category term="prep"/><title type='text'>Organic Blog</title><subtitle type='html'></subtitle><link rel='http://schemas.google.com/g/2005#feed' type='application/atom+xml' href='http://organicmc.blogspot.com/feeds/posts/default'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6229672768869848568/posts/default?redirect=false'/><link rel='alternate' type='text/html' href='http://organicmc.blogspot.com/'/><link rel='hub' href='http://pubsubhubbub.appspot.com/'/><author><name>MC</name><uri>http://www.blogger.com/profile/04502219692204943427</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><generator version='7.00' uri='http://www.blogger.com'>Blogger</generator><openSearch:totalResults>2</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>25</openSearch:itemsPerPage><entry><id>tag:blogger.com,1999:blog-6229672768869848568.post-6976871531196044224</id><published>2012-07-29T11:34:00.000-07:00</published><updated>2012-07-29T11:42:24.658-07:00</updated><title type='text'>Upgrade to Ice Cream Sandwich - Issues</title><content type='html'>I tried to upgrade my Samsung Galaxy S 2 from Gingerbread to Ice cream sandwich, and I ran into a couple of issues that I thought I should share with people.&lt;br /&gt;
&lt;br /&gt;
I have Bell as the carrier in Canada and I was using Samsung Kies and a USB connection to do the upgrade.&lt;br /&gt;
&lt;br /&gt;
My desktop was a Windows 7 64 bit machine and a laptop with Windows Vista 32 bit.&lt;br /&gt;
&lt;br /&gt;
&lt;b&gt;First problem - Windows 7 64 bit attempt&lt;/b&gt;&lt;br /&gt;
&lt;br /&gt;
I was getting a message in Kies: &quot;Your device does not support software upgrading via Kies&quot;&lt;br /&gt;
&lt;br /&gt;
I called Bell and Samsung, both said I should try taking out battery, hard reset, etc. None of these worked.&lt;br /&gt;
&lt;br /&gt;
The solution to this problem is NOT using Windows 7. I moved to my laptop and I was not getting this message anymore and was able to proceed with upgrade right away.&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;b&gt;Second Problem - Stuck with &quot;Installing Applications&quot; screen&lt;/b&gt;&lt;br /&gt;
&lt;br /&gt;
Once the update is complete, you have to restart your phone. You will get a screen on saying &quot;Installing Applications&quot;. I was stuck here for long time..(1 hour or more).&lt;br /&gt;
&lt;br /&gt;
What I ended up doing is taking out my microsd card and trying it again. I was still getting the same message.&lt;br /&gt;
&lt;br /&gt;
I was still able to use the home screen button to go to Managing Apps section where you can see Running, Downloaded, etc apps. I noticed that for some reason I had very little space (hard disk) on the system drive. It was not using the Phone memory. So I decided to delete some big apps to create space.&lt;br /&gt;
&lt;br /&gt;
Eventually after deleting about 200 mb worth of apps, I restarted and was able to get past the &quot;Installing Applications&quot; screen right away.&lt;br /&gt;
&lt;br /&gt;
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So lesson is to make sure you have System space available before the upgrade. You can either uninstall big apps or move them to your MicroSD card before the upgrade. If you are in the middle of this problem, I recommend playing with the Home screen button during the stuck screen and deleting apps and restarting.&lt;br /&gt;
&lt;br /&gt;
Good luck. Please share your problem and solutions in comments.&lt;br /&gt;
&lt;br /&gt;
Thanks&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;</content><link rel='replies' type='application/atom+xml' href='http://organicmc.blogspot.com/feeds/6976871531196044224/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://organicmc.blogspot.com/2012/07/upgrade-to-ice-cream-sandwich-issues.html#comment-form' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6229672768869848568/posts/default/6976871531196044224'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6229672768869848568/posts/default/6976871531196044224'/><link rel='alternate' type='text/html' href='http://organicmc.blogspot.com/2012/07/upgrade-to-ice-cream-sandwich-issues.html' title='Upgrade to Ice Cream Sandwich - Issues'/><author><name>MC</name><uri>http://www.blogger.com/profile/04502219692204943427</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6229672768869848568.post-8535999641772928572</id><published>2011-07-16T14:47:00.001-07:00</published><updated>2015-07-11T13:49:42.137-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="algebra"/><category scheme="http://www.blogger.com/atom/ns#" term="cheat sheet"/><category scheme="http://www.blogger.com/atom/ns#" term="exam"/><category scheme="http://www.blogger.com/atom/ns#" term="geometry"/><category scheme="http://www.blogger.com/atom/ns#" term="gmat"/><category scheme="http://www.blogger.com/atom/ns#" term="mba"/><category scheme="http://www.blogger.com/atom/ns#" term="prep"/><title type='text'>GMAT Math Cheat (Summary) Sheet</title><content type='html'>&lt;div style=&quot;font-family: Georgia, serif; font-size: 16px;&quot;&gt;
&lt;span class=&quot;Apple-style-span&quot;&gt;Some important topics for you to consider for GMAT:&lt;/span&gt;&lt;/div&gt;
&lt;ul style=&quot;font-size: 16px;&quot; type=&quot;disc&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Zero is integer&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;1 is NOT prime number&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Zero is even number (divisible by 2)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;For number 246.31:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul style=&quot;font-family: Georgia, serif;&quot; type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;6 is units, 4 is tens, 2 hundreds digit&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;3 is tenths, 1 is hundredths digit&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Prime numbers:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul style=&quot;font-family: Georgia, serif;&quot; type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;2 is only even prime number&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;0 and 1 are NOT prime numbers&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;are always positive&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Absolute value&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;: distance between number and 0. e.g.: |-6| = 6&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul style=&quot;font-family: Georgia, serif;&quot; type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;|x+1| &amp;amp;lt;= 4 is same as -4 &amp;amp;lt;= x+1 &amp;amp;lt;= 4 (and vice versa)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Convert -5 &amp;amp;lt;= x &amp;amp;lt;= 3 into absolute, 1) find out length between end points, 3 - (-5) = 8, divide equally: 8/2 = 4, then to convert -5 &amp;amp;lt;= x &amp;amp;lt;= 3 to -4 &amp;amp;lt;= x+1 &amp;amp;lt;= 4 by adding 1 to all sides. therefore |x+1| &amp;amp;lt;= 4&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Odds and Evens&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul style=&quot;font-family: Georgia, serif;&quot; type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;If at least 1 factor of a product is even, then product is even&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;both odd or both even means...both sum and difference are even, otherwise their sums and differences are odd.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Consec even #s: 2n + 2, 2n + 4...&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Consec odd #s: 2n + 1, 2n + 3&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;A number is divisible by:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul style=&quot;font-family: Georgia, serif;&quot; type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;2 if its even&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;3 if sum of its digits is divisible&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;4 if last two digits are divisible by 4&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;5 if last two digits are 0 or 5&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0.0001pt;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;6 if it is divisible by 2 and 3&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;

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&lt;span style=&quot;font-family: Times New Roman, serif;&quot;&gt;&lt;span style=&quot;font-size: 16px;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;ul style=&quot;font-family: Georgia, serif; font-size: 16px; margin-top: 0in;&quot; type=&quot;disc&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0.0001pt;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Fraction: part/whole&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul style=&quot;margin-top: 0in;&quot; type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0.0001pt;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;2 boxes contain 14 shirts, how many in 3 boxes?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;2 (boxes) / 14 shirts = 3 (boxes) / x shirts&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Decimals in fractions&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;0.4 =&amp;nbsp;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;MS Mincho&#39;; font-size: 12pt;&quot;&gt;⅖&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;0.6 =&amp;nbsp;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;MS Mincho&#39;; font-size: 12pt;&quot;&gt;⅗&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;0.66 = ⅔&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;0.8 =&amp;nbsp;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;MS Mincho&#39;; font-size: 12pt;&quot;&gt;⅘&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;14.3 x 0.232 = 3.3176 (1 decimal place times 3 decimal places = 4 decimal places)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Rounding: 9.4 to nearest whole # is 9, 9.5 to nearest whole # is 10&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Ratios:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;part A/ part B, part A + part B = whole&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;The ratio of men to women in a room is 3 to 4 (NOTE that this ratio can also be expressed as 5: 4 and as the fraction, 5/4)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;The number of men and the number of women in the room are not necessarily 3 and 4, but they must be some multiple of 3 and 4 (e.g. 6 men / 8 women, 9 men / 12 women, etc). This notion can be expressed with an &quot;unknown multiplier.&quot; and expressed as &quot;x&quot; in be 3x: 4x or 3x/4x, where x represents the &quot;unknown multiplier.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Eg: Women to Men ratio in room is 3 to 4, if total is 28, how many women?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Whole = part A + part B = 3 + 4 = 7, 28/7 = 4 groups (of 7)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;4 x 3 women = 12 women / 16 men&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Eg 2: Total 300 vehicles, 30% trucks, 20 % diesel including 15 trucks, what % is non truck non diesal?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Compound Interest:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;20 % compounded semi-annually means. Divide interest/# of parts. So, 20% interest/ 2 parts = 10% every six months, After six months it is 10% of 100 and after 1 year it is 10% more of 110&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;answer will be a “little” more than simple compound problems&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Percent increases:&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&amp;nbsp;Year 1: $100, Year 2: $155, Percent increase = Y2-Y1/y1 * 100 = 55/100 *100&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Percent decreases:&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&amp;nbsp;(similar as increase)...see problem #109 on pg 220 of GMAT book&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Average&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Average = total sum of the items/total number of the items&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;The average of 7 numbers is 5. If two numbers are 11 and 14, what is the average of remaining numbers?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;5 = x/7, x (total sum) = 35&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;11 + 14 = 25, 25 + y = 35, y = 10&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Since there are 5 numbers left, average = total sum/total #s then 10/5= 2&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Weighted average&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Applies to many ratio, mixture, percentage problems&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;E.g: Mixture A is 0.3% alcohol, mixture B is 0.5% alcohol, in a 10 lb mixture of A and B with 0.35% alcohol, how much is the weight of A?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Allegation or Scale method (worth learning about this, please google it)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Median:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;SORT Numbers FIRST before choosing&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;if n is odd, the number in middle when sorted&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;If n is even, the two middle numbers/2&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Mode:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Number that occurs the most&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Set of numbers can have more than one node&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Range:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;in a set of numbers 4, 3, 8, 12, 23, 37. Range is 37-3= 34&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Sequences and their Sums:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Sum of all even from 1 - 99 = sum of first 49 evens = n*(n+1) or 49* (50)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;ol start=&quot;1&quot; style=&quot;font-family: Georgia, serif; font-size: 16px;&quot; type=&quot;1&quot;&gt;&lt;ol start=&quot;1&quot; type=&quot;1&quot;&gt;&lt;ol start=&quot;1&quot; type=&quot;1&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;(n = 98/2 = 49)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ol&gt;
&lt;/ol&gt;
&lt;/ol&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Sum of all odds from 1 - 99 (inclusive) = sum of first 50 odds = n*n = 50*50&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Arithmetic sequence:&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&amp;nbsp;a = first term, d = difference between terms, x_n = nth term, then x_n = a + (n-1)d, if x_n = 99 for first even #s, then to find n: 98 = 2 + (n-1)2, 98 = 2 + 2n - 2, n = 98/2 = 49.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt; margin-left: 0.5in; margin-right: 0in; margin-top: 0in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Sum of first 49 sequenced #s (same as all even from 1 - 99, but n = 49 NOT 99!!) = n/2 * (2a + (n-1)d),&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.5in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;for evens Sum = n (n+1)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.5in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;For odds = n*n&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Another way to do this problem:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.5in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Sum of all even numbers from 1 to 199&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.5in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;== 2 + 4 +6+ 8 + ... + 198 == 2 (1 + 2 + 3 + ... 99) = 2 * (99 * 100) / 2 = 9900&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.5in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Sum of all odd numbers from 100 to 300&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.5in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;== 101 + 103 + ... + 299&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.5in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Equally Spaced sets ==&amp;amp;gt; Mean = (101 + 299)/2 = 200&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.5in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;No. of terms = (299 - 101)/2 + 1 = 100&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.5in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Sum of the series = 200 * 100 = 20000&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;My proffered approach (may not be for you):&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;we can simply use AP.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 12pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Sum of all evens from 100 to 301 (inclusive) is: a1 = 100, d = 2, x_n = a1 + (n-1)d = 300, therefore n = 101 Then sub into following formula: formula=(n/2)[2a+(n-1)d]=(101/2)[200+200]=20200&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Geometric sequence&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;in which each subsequent term is multiplied by a certain constant. Compound interest in an example of a geometric sequence.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;The standard formula is: a_n = a1*r ^ (n-1) where a_n is the nth term, “r” is rate and a1 is the first term.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;

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&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;when given the rate of increase and the value of any term, we can find any other term. For example:&lt;br /&gt;
Joe originally put $8 in stock in 2000. If stock triples every year in this time (without Joe adding anymore himself), how much money will he have in 2011?&lt;br /&gt;
r = 3&lt;br /&gt;
a1 = 10&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;a_11 = ?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;ul style=&quot;font-family: Georgia, serif; font-size: 16px;&quot; type=&quot;disc&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Standard Deviation&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;The mean and the median are the same in a normal distribution.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Distance between mean (average) and each of numbers in the set (measure of how spread out numbers are.)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Stand dev forumal is not needed but number looks like 2.4 or 3.0&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;e.g: 14.6 and 9.3 are both more than two standard devs from average 12 (with stand dev at 1.3)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;it is the square root of the Variance. So now you ask, &quot;What is the Variance?&quot;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;The Variance is defined as:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;The average of the squared differences from the Mean.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Standard deviation and confidence intervals.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;About 68% of values drawn from a normal distribution are within one standard deviation σ away from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. This fact is known as the&amp;nbsp;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/68-95-99.7_rule&quot;&gt;&lt;span style=&quot;color: blue; font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;68-95-99.7 rule&lt;/span&gt;&lt;/a&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;, or the empirical rule, or the 3-sigma rule. 50% of the distribution lies within 0.67448 standard deviations of the mean (source: WikiPedia)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;ul style=&quot;font-family: Georgia, serif; font-size: 16px;&quot; type=&quot;disc&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Exponents:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Any number to power 0 is 1&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;X^2 = 100 means x = 10 OR x = -10 DO NOT FORGET the negative!!!!!!&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Radicals:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;3sqrt5 = 5 to power ⅓ (not 3 times but small 3 above sqrt sign)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;3sqrt27 = 27 to power 3 = 3.3.3 = 3&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;sqrtXsqrtY = sqrt XY&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;sqrt (x/y) = sqrt x/ sqrt y&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;sqrt 32 = sqrt 16. sqrt 2 = 4 .sqrt 2&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Remainders:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;for int x and y, qutiont q and remainder r.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;y = xq + r&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;, e.g: For x=8, y = 28, 28 = 8 (3) + 4....3 is quotient and 4 is remainder&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;0 &amp;amp;lt;= r &amp;amp;lt; x&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;small int / big int, quotiont is always 0 and remainder is small int&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;5 / 7 , quotiont is 0 and remainder is 5 since 5 = 7 (0) + 5&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;If for integers a and b, a/b = 74.32, then what is the remainder?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Solution: =&amp;amp;gt; a = 74.32b OR&amp;nbsp;&lt;b&gt;a = 64b + 0.32b&lt;/b&gt;, then 0.32b is remainder where b is an int. Also 0.32b must be an int, find a “b” that makes it true from multiple choice options in a GMAT question.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Algebra:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;ul style=&quot;font-family: Georgia, serif; font-size: 16px;&quot; type=&quot;disc&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Plug in&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;write down the variable and value you choose&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;then for each option see if equation creates same variable&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Eg: if J can drive distance k miles in 50 mins, how many mins, in terms of k, will it take him to driver 10 miles at the same speed&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;if k = 5 miles in 50 mins then, 1 mile = 10 mins&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;then 10 miles will take 100 mins&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;What option given 100 mins when k is 5?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;eg2: if 80% of x is 50% of y and y is 20% of z. What is x in terms of z?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Plug in variable of question (avoid 0 and 1):&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Variables in answer choices&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;percents (of unknown amount) in answer choices&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;fractions or rations (of unspecified amount) in answer choices&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Can also Plug in numbers from answers into question to simplify&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;good for problems like: “today Joe is twice as old as Frank, Steve is 2 years younger than Frank. Four years ago if Joe was 4 times as old as Steve , how old is Joe now?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;If answers are sorted and question is straight forward, eg; What is x?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Start with C, if C is small try bigger, if C is big try smaller A store currently charges the same price for each towel that it sells.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;E.g: If the current price of each bottle were to be increased by $1, 10 fewer of the bottles could be bought for $120 (excluding sales tax). What is the current price of each bottle?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Perfect for &quot;WHAT&amp;nbsp;&lt;b&gt;IS&lt;/b&gt;&amp;nbsp;X&quot; type of question and Answer is given, sub into question and then check given conditions are met.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Must be/could/cannot be problems&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;: almost always plug in&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;if x and y are consec + numbers, which following&amp;nbsp;&lt;i&gt;must be&lt;/i&gt;&amp;nbsp;an even int?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;An equation with a variable with even power may have more than one solution but if variable has odd power there must be only one solution.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Inequalities (&amp;amp;lt;, &amp;amp;gt;): if you multiply or divide both sides of inequality by negative number, direction of inequality symbol changes: -2x &amp;amp;gt; 5, then x &amp;amp;lt; -5/2. also&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;if r &amp;amp;lt; 1, then 1/r &amp;amp;gt; 1, if r &amp;amp;lt; 100, 1/r &amp;amp;gt;1/100&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Rate x Time = distance&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Work problem&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;: figure out total time per hour first. If sam completes work in 3 hrs and Mark in 12, how long both take together? Answer: ⅓ + 1/12 = 1/x (total work per hour together). 1/x = 5/12, x = 12/5 (total time taken for all work)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;can also substitute actual work. eg: total work = 12 widgets.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;0! = 1&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Probability&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;P (ABC) = P(A)*P(B)*P(C)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;P (A OR B) = P(A) + P(B)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;P (not A) = 1 - P(A)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;At least 1 thing will happen: P(at least 1) + P(none) = 1 or another example:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;P (at least 2) + P (0 or 1) = 1, so forth...&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;

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&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Permutations and combinations:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/li&gt;
&lt;ul type=&quot;circle&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Combinations: choose a # of items to fill specific spots each from different source.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Multiply # of choices in each spot&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Permutations:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Single source, order matters (keep duplicates)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;n! (multiply # of choices for each spot, but # of choices get smaller)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Single source, order matters but only for selection (keep duplicates)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;7 teams, permutations for top 3?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;7!/(7-3)! OR n!/(n-r)!&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Single source, order does not matter (remote duplicates)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;We only care about unique permutations&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;#of unique combinations = n!/(n-r)r!&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;6 horses, how many groups could make up first 3 finishers?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;ul type=&quot;square&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;6!/(6-3)!3! = 120/6 = 20&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;It is interesting to also note how this formula is nice and symmetrical:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;In other words choosing 3 balls out of 16, or choosing 13 balls out of 16 have the same number of combinations.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;/ul&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.25in;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Geometry&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Look for drawn to scale to eliminate crazy answers&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Memorize: pie = 3, sqrt 1 = 1, sqrt 2 = 1.4, sqrt 3 = 1.7&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Triangles&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;: one side of triangle can never be longer than sum of lengths of other two sides or less than their difference. Eg: for 6, 8, third side has to be &amp;amp;lt; 14 and &amp;amp;gt; 2 (can not be equal to either)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Area of triagle = ½ base x height&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Right triangles: 3:4:5, 6:8:10,&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Right isosceles: side:side: side*sqrt2.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Wingdings; font-size: 10pt;&quot;&gt;§&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;e.g: 3:3:3sqrt2&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;30:60:90 triangle: side: 2*side: sqrt3*side&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Wingdings; font-size: 10pt;&quot;&gt;§&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;e.g: 1:2:sqrt3 OR 3:6:3*sqrt3&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;45:45:90 triangle: side: 1:1:sqrt2, eg: 4:4:4*sqrt2&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Sum of interior angles of any polygon is 180(n-2), where n is number of sides.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Circles:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Area: pieR*R&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Circumfurence: 2pieR&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Parallelogram:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Area: base*height&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Diagonals of parallelogram bisect each other (i.e. divide each other in halves)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Quadrilateral:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/i&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Area of quadrilater with two sides parellal (trapezoid) = ½ (sum of bases)*height&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Volume of rectangular solid&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;: Area of base * depth (or height)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;(length * width * depth)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Volume of cylinder&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;: Area of circular base * depth&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;pie*R*R * depth&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Surface area&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;: sum of all sides’ areas&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Volume of sphere&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;: 4/3 pie * R*R*R&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 0.75in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: Symbol; font-size: 10pt;&quot;&gt;·&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Any straight line equation&lt;/span&gt;&lt;/i&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;: y = mx + b, where b is y intercept and m is slope of line&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Courier New&#39;; font-size: 10pt;&quot;&gt;o&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Slope (m) = difference in y coords/difference in x coord&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-left: 1.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;= y1-y2/x2-x1 (remember that numerator is Y coords)&lt;br /&gt;
&lt;br /&gt;
&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;General Strategies&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;1.&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Where you have to try every answer choice. HOWEVER, when the only way to get the answer is to try every answer choice, ALWAYS start from E and work up.&lt;br /&gt;
More often than not the answer appears near the bottom and the test writers want you to waste time.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;2.&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Don’t miss key words in problems. READ EVERY PROBLEM CAREFULLY! ( first 10-25 secs should be focused on problem alone. I noticed better results after training myself to do this)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;3.&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Questions with variables in the question. Use PLUG IN or algebra (find your preferred approach)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;4.&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Practice as many questions as you can. I did probably over practice 1000 questions in my study time.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;5.&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Track performance on topics you are weak in and work on those.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&lt;br /&gt;
&lt;br /&gt;
Important Topics that helped me improve my score (may be different for you):&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;ol start=&quot;1&quot; style=&quot;font-family: Georgia, serif; font-size: 16px;&quot; type=&quot;1&quot;&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Number properties&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Sequences (eg: ½ -1/4 + ⅛ - 1/16.... = ?)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Ratios (eg. 31/37 on GMAT test 1)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Remainders&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Permutations and Combinations (they show up once in a while but not too much)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Some geometry&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Probability&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Work/rate problems&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Medians problems&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Percent increase/decreases&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;Weighted average questions&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;LCM and GCF (Least common multiple and greatest common factor)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ol&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Georgia, serif; font-size: 16px; line-height: normal; margin-bottom: 12pt;&quot;&gt;
&lt;span lang=&quot;EN-CA&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&lt;br /&gt;
&lt;i&gt;Disclaimer: Every person is different in their needs for GMAT. This review sheet does not guarantee an improved score for anyone. I advise you create your own summary sheet.&lt;/i&gt;&lt;/span&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://organicmc.blogspot.com/feeds/8535999641772928572/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://organicmc.blogspot.com/2011/07/gmat-math-cheat-summary-sheet.html#comment-form' title='2 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6229672768869848568/posts/default/8535999641772928572'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6229672768869848568/posts/default/8535999641772928572'/><link rel='alternate' type='text/html' href='http://organicmc.blogspot.com/2011/07/gmat-math-cheat-summary-sheet.html' title='GMAT Math Cheat (Summary) Sheet'/><author><name>MC</name><uri>http://www.blogger.com/profile/04502219692204943427</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>2</thr:total></entry></feed>