<?xml version="1.0" encoding="UTF-8"?><rss version="2.0" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:wfw="http://wellformedweb.org/CommentAPI/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:sy="http://purl.org/rss/1.0/modules/syndication/" xmlns:slash="http://purl.org/rss/1.0/modules/slash/" > <channel> <title>Remainders – GRE</title> <atom:link href="https://www.manhattanprep.com/gre/blog/tag/remainders/feed/" rel="self" type="application/rss+xml" /> <link>https://www.manhattanprep.com/gre</link> <description>GRE Prep | Best GRE Test Preparation | Manhattan Prep GRE</description> <lastBuildDate>Fri, 30 Aug 2019 16:40:29 +0000</lastBuildDate> <language>en-US</language> <sy:updatePeriod> hourly </sy:updatePeriod> <sy:updateFrequency> 1 </sy:updateFrequency> <generator>https://wordpress.org/?v=6.3.2</generator> <item> <title>GRE Math for People Who Hate Math: Remainder Problems</title> <link>https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-remainder-problems/</link> <dc:creator><![CDATA[Chelsey Cooley]]></dc:creator> <pubDate>Wed, 18 Oct 2017 16:13:32 +0000</pubDate> <category><![CDATA[Challenge Problems]]></category> <category><![CDATA[Current Studiers]]></category> <category><![CDATA[GRE Prep]]></category> <category><![CDATA[GRE Quant]]></category> <category><![CDATA[GRE Strategies]]></category> <category><![CDATA[How To Study]]></category> <category><![CDATA[Life Hacks]]></category> <category><![CDATA[Math]]></category> <category><![CDATA[Study Tips]]></category> <category><![CDATA[Taking the GRE]]></category> <category><![CDATA[GRE Math for People Who Hate Math]]></category> <category><![CDATA[Remainder Problems]]></category> <category><![CDATA[Remainders]]></category> <guid isPermaLink="false">https://www.manhattanprep.com/gre/?p=10874</guid> <description><![CDATA[<p>You can attend the first session of any of our online or in-person GRE courses absolutely free. Crazy, right? Check out our upcoming courses here. The secret to understanding GRE remainder problems is in the word remainder itself. Suppose you bake a dozen brownies, and while you’re at work, your roommate eats ten of them. […]</p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-remainder-problems/">GRE Math for People Who Hate Math: Remainder Problems</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gre">GRE</a>.</p> ]]></description> <content:encoded><![CDATA[<p><img decoding="async" fetchpriority="high" class="alignnone size-full wp-image-10907" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/gre-math-people-who-hate-math-remainder-problems-chelsey-cooley.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Remainder Problems by Chelsey Cooley" width="1200" height="628" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/gre-math-people-who-hate-math-remainder-problems-chelsey-cooley.png 1200w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/gre-math-people-who-hate-math-remainder-problems-chelsey-cooley-300x157.png 300w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/gre-math-people-who-hate-math-remainder-problems-chelsey-cooley-768x402.png 768w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/gre-math-people-who-hate-math-remainder-problems-chelsey-cooley-1024x536.png 1024w" sizes="(max-width: 1200px) 100vw, 1200px" /></p> <p><b><i>You can attend the first session of any of our online or in-person GRE courses absolutely free. Crazy, right? </i></b><a id="bloglink" href="https://www.manhattanprep.com/gre/classes/" target="_blank" rel="noopener"><b><i>Check out our upcoming courses here</i></b></a><b><i>.</i></b></p> <hr /> <p><b><i></i></b><span style="font-weight: 400;">The secret to understanding GRE remainder problems is in the word </span><i><span style="font-weight: 400;">remainder </span></i><span style="font-weight: 400;">itself. Suppose you bake a dozen brownies, and while you’re at work, your roommate eats ten of them. The two brownies left over are the </span><i><span style="font-weight: 400;">remainder</span></i><span style="font-weight: 400;"> of the batch. The mathematical term </span><i><span style="font-weight: 400;">remainder</span></i><span style="font-weight: 400;"> refers to the same thing: what’s left over after something is taken away. </span><span id="more-10874"></span></p> <p><span style="font-weight: 400;">Here are those brownies again:</span></p> <p><img decoding="async" class="alignnone size-full wp-image-10875" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/gre-10-4-brownies-1.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Remainder Problems by Chelsey Cooley" width="750" height="67" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/gre-10-4-brownies-1.png 750w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/gre-10-4-brownies-1-300x27.png 300w" sizes="(max-width: 750px) 100vw, 750px" /></p> <p><span style="font-weight: 400;">And here’s a piece of a GRE Quant problem:</span></p> <p style="padding-left: 30px;"><i><span style="font-weight: 400;">What is the remainder when 12 is divided by 5?</span></i></p> <p><span style="font-weight: 400;">The word “divided” in there makes you want to start doing division. But if you divide 12 by 5, you end up with 2.4. So what? That 2.4 won’t help you answer the question you’re being asked.</span></p> <p><span style="font-weight: 400;">When you first learned about division as a kid, you may have learned that dividing is the same as splitting a larger group up into smaller groups. When you divided 12 by 5, you learned to picture twelve brownies being split into groups of 5 brownies each.</span></p> <p><img decoding="async" class="alignnone size-full wp-image-10876" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/gre-10-4-brownies-2.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Remainder Problems by Chelsey Cooley" width="472" height="225" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/gre-10-4-brownies-2.png 472w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/gre-10-4-brownies-2-300x143.png 300w" sizes="(max-width: 472px) 100vw, 472px" /></p> <p><span style="font-weight: 400;">You didn’t even know about decimals yet, so you didn’t know that the real answer was 2.4. You did know that there were two full groups, so the answer was bigger than 2 but smaller than 3. You also knew that there were two brownies left over. Those two brownies were the remainder. </span></p> <p><span style="font-weight: 400;">This might seem like kid stuff—and that’s because it is! In order to handle remainder problems, you want to think about division in a </span><i><span style="font-weight: 400;">less</span></i><span style="font-weight: 400;"> sophisticated way than you’re used to. Imagine splitting a large number of brownies into smaller groups of a certain size. When you can’t make any more groups, you’re finished. Look at the extra brownies that are left over: that’s your remainder.</span></p> <p style="padding-left: 30px;"><b>Bonus question for GRE Quant gurus</b><span style="font-weight: 400;">: On the GRE, it’s useful to know that the remainder is always </span><i><span style="font-weight: 400;">smaller</span></i><span style="font-weight: 400;"> than the number you’re dividing by. For instance, if you divide 43,894,784,412 by 7, the remainder will definitely be smaller than 7. Why is that true?</span></p> <p><span style="font-weight: 400;">Suppose that instead of a dozen brownies, we had exactly 503 brownies. (Too many brownies? Nah.)</span></p> <p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-10877" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-3.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Remainder Problems by Chelsey Cooley" width="569" height="140" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-3.png 569w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-3-300x74.png 300w" sizes="(max-width: 569px) 100vw, 569px" /></p> <p><span style="font-weight: 400;">And let’s suppose that instead of dividing by 5, we’re dividing by 7. Now we’ve got a GRE problem that looks like this:</span></p> <p style="padding-left: 30px;"><i><span style="font-weight: 400;">What is the remainder when 503 is divided by 7?</span></i></p> <p><span style="font-weight: 400;">If you had a ridiculous amount of time on your hands, you could start splitting the 503 brownies into groups of 7, one group at a time. When you finished, you could check how many brownies were left over. That number would be the remainder.</span></p> <p><span style="font-weight: 400;">Let’s take a shortcut, though. Instead of counting one group at a time, let’s count ten groups at a time. In other words, we’re going to remove 70 brownies at once, not just 7.</span></p> <p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-10878" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-4.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Remainder Problems by Chelsey Cooley" width="566" height="405" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-4.png 566w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-4-300x215.png 300w" sizes="(max-width: 566px) 100vw, 566px" /></p> <p><span style="font-weight: 400;">We’ve got 13 brownies left over. That doesn’t mean the remainder is 13, though. We could actually remove one last group of 7, leaving us with just 6 brownies:</span></p> <p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-10879" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-5.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Remainder Problems by Chelsey Cooley" width="393" height="119" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-5.png 393w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-5-300x91.png 300w" sizes="(max-width: 393px) 100vw, 393px" /></p> <p><span style="font-weight: 400;">The remainder when we divide 503 by 7 is 6. </span></p> <p><span style="font-weight: 400;">We need a way to take this shortcut without visualizing brownies (as fun as that is). Here it is. We wanted to find the remainder when we divided 503 by 7. In order to do so, </span><i><span style="font-weight: 400;">think of a number smaller than 503 that can be divided evenly into groups of 7</span></i><span style="font-weight: 400;">. For instance, we might think of 490, because 490 = 70 x 7. We can remove the first 490 brownies, and we’re left with 503 — 490 = 13. </span></p> <p><span style="font-weight: 400;">Then, if necessary, repeat the process: think of a number smaller than 13 that can be divided evenly into groups of 7. Here, the only number that works is 7. Remove the next 7 brownies, and you’re left with 6. </span></p> <p><span style="font-weight: 400;">Try it on this problem:</span></p> <p style="padding-left: 30px;"><i><span style="font-weight: 400;">What is the remainder when you divide 77,218 by 7?</span></i></p> <p><span style="font-weight: 400;">Here’s my approach. 77,000 is divisible by 7. So, I can subtract it right away. Now, I’m only looking for the remainder when 218 is divided by 7. I know that 210 is divisible by 7, so I’ll subtract that as well: 218 – 210 = 8. 8 isn’t the remainder, though. I can still remove one final group of 7 brownies, leaving me with exactly 1 left over. The remainder is 1. </span></p> <p style="padding-left: 30px;"><b>Bonus question for GRE Quant gurus</b><span style="font-weight: 400;">: Suppose that the remainder when </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is divided by 7 is 4. What’s the remainder when </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> + 14 is divided by 7? How about when </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> + 100 is divided by 7? </span></p> <p><span style="font-weight: 400;">Finally, let’s go in the opposite direction. In the problems above, you needed to find the remainder. What if you already </span><i><span style="font-weight: 400;">knew</span></i><span style="font-weight: 400;"> the remainder? Suppose that I told you that I baked a certain number of brownies—at least 10 of them. When I divided those brownies into groups of 10, I ended up with 2 left over. What do you know about how many brownies I have?</span></p> <p><span style="font-weight: 400;">In other words, </span></p> <p style="padding-left: 30px;"><i><span style="font-weight: 400;">The remainder when x is divided by 10 is 2.</span></i></p> <p><span style="font-weight: 400;">Let’s start by finding the smallest number of brownies I might have had. I already told you that I removed groups of 10 brownies and had 2 left over. What if I only removed </span><i><span style="font-weight: 400;">one</span></i><span style="font-weight: 400;"> group of 10?</span></p> <p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-10880" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-6.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Remainder Problems by Chelsey Cooley" width="659" height="119" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-6.png 659w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-6-300x54.png 300w" sizes="(max-width: 659px) 100vw, 659px" /></p> <p><span style="font-weight: 400;">Then you know that I started with 10 + 2, or 12.</span></p> <p><span style="font-weight: 400;">What if I removed </span><i><span style="font-weight: 400;">two</span></i><span style="font-weight: 400;"> groups of 10?</span></p> <p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-10881" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-7.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Remainder Problems by Chelsey Cooley" width="659" height="175" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-7.png 659w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/10/brownies-7-300x80.png 300w" sizes="(max-width: 659px) 100vw, 659px" /></p> <p><span style="font-weight: 400;">Then you know that I started with 2 x 10 + 2, or 22. </span></p> <p><span style="font-weight: 400;">What if I removed three groups of 10? Then I must have started with 3 x 10 + 2, or 32. </span></p> <p><span style="font-weight: 400;">That’s how you list all of the numbers with a certain remainder! Start with the number you would have had if you removed </span><i><span style="font-weight: 400;">one</span></i><span style="font-weight: 400;"> group. That will be the sum of the remainder and the number you’re dividing by. Here, that was 12. Then, find the next largest value. Here, since we’re removing groups of size 10, we’ll have to count up by 10s. The possible values for </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> were 12, 22, 32, 42, 52… on up to infinity.</span></p> <p><span style="font-weight: 400;">Let’s try one final GRE remainder problem to wrap things up:</span></p> <p style="padding-left: 30px;"><i><span style="font-weight: 400;">The integer x is between 50 and 60, inclusive</span></i><span style="font-weight: 400;">. </span><i><span style="font-weight: 400;">The remainder when x is divided by 7 is 3. What is the sum of all possible values of x?</span></i></p> <p><span style="font-weight: 400;">The remainder when </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is divided by 7 is 3. That means that when we removed groups of 7 brownies, we ended up with 3 brownies left over. The smallest possible number that works would be 10 brownies. That’s too small, though, since it isn’t between 50 and 60! Count up by 7s to find other numbers that could work: 10, 17, 24, 31, 38, 45, 52, 59, 66. The only two values in the range are 52 and 59. The problem asks for their sum, so plug those numbers into your calculator (</span><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/2017/08/02/mental-math-magic/" target="_blank" rel="noopener"><span style="font-weight: 400;">or use some of the mental math magic you learned from Neil</span></a><span style="font-weight: 400;">): the answer is 111. ?</span></p> <hr /> <p><b><i>See that “SUBSCRIBE” button in the top right corner? Click on it to receive all our GRE blog updates straight to your inbox!</i></b></p> <hr /> <p><b><i><em><strong><a id="bloglink" href="https://www.manhattanprep.com/instructors/chelsey-cooley/" target="_blank" rel="noopener noreferrer">Chelsey Cooley</a><a href="https://www.manhattanprep.com/instructors/chelsey-cooley/?utm_source=manhattanprep.com%2Fgre%2Fblog&utm_medium=blog&utm_content=CooleyBioGREBlog&utm_campaign=GRE%20Blog" target="_blank" rel="noopener noreferrer"><img decoding="async" loading="lazy" class="alignleft" title="Chelsey Cooley Manhattan Prep GRE Instructor" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2015/11/chelsey-cooley-150x150.jpg" alt="Chelsey Cooley Manhattan Prep GRE Instructor" width="150" height="150" data-pin-nopin="true" /></a> is a Manhattan Prep instructor based in Seattle, Washington.</strong> </em></i></b><i><em>Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. </em></i><i><em><a id="bloglink" href="https://www.manhattanprep.com/gre/classes/#instructor/48" target="_blank" rel="noopener noreferrer">Check out Chelsey’s upcoming GRE prep offerings here</a>.</em></i></p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-remainder-problems/">GRE Math for People Who Hate Math: Remainder Problems</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gre">GRE</a>.</p> ]]></content:encoded> </item> </channel> </rss>