<?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>Two Minutes of GMAT Quant – GMAT</title> <atom:link href="https://www.manhattanprep.com/gmat/blog/tag/two-minutes-of-gmat-quant/feed/" rel="self" type="application/rss+xml" /> <link>https://www.manhattanprep.com/gmat</link> <description>GMAT Prep Course, Best GMAT Class & Study Books | Manhattan Prep GMAT</description> <lastBuildDate>Thu, 05 Sep 2019 15:59:58 +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>Two Minutes of GMAT Quant: A Breakdown (Part 3)</title> <link>https://www.manhattanprep.com/gmat/blog/two-minutes-of-gmat-quant-a-breakdown-part-3/</link> <dc:creator><![CDATA[Emily Madan]]></dc:creator> <pubDate>Wed, 27 Apr 2016 21:07:15 +0000</pubDate> <category><![CDATA[Algebra]]></category> <category><![CDATA[Fractions, Decimals, Percents]]></category> <category><![CDATA[GMAT Prep]]></category> <category><![CDATA[How to Study]]></category> <category><![CDATA[Quant]]></category> <category><![CDATA[Word Problems]]></category> <category><![CDATA[and Percents]]></category> <category><![CDATA[Decimals]]></category> <category><![CDATA[fractions]]></category> <category><![CDATA[Ratio Problems]]></category> <category><![CDATA[Two Minutes of GMAT Quant]]></category> <guid isPermaLink="false">http://www.manhattanprep.com/gmat/?p=11378</guid> <description><![CDATA[<p>Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here. Ready for the long awaited conclusion of how to tackle a quant problem in two minutes? We’ll finally get to the point where you can […]</p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/two-minutes-of-gmat-quant-a-breakdown-part-3/">Two Minutes of GMAT Quant: A Breakdown (Part 3)</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p> ]]></description> <content:encoded><![CDATA[<p><strong><em><img decoding="async" fetchpriority="high" class="alignleft size-full wp-image-11390" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/4-27-2016-blog-2.png" alt="Manhattan Prep GMAT Blog - Two Minutes of GMAT Quant a Breakdown Part 3" width="676" height="264" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/4-27-2016-blog-2.png 676w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/4-27-2016-blog-2-300x117.png 300w" sizes="(max-width: 676px) 100vw, 676px" />Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! <a href="https://www.manhattanprep.com/gmat/classes/?utm_source=manhattanprep.com%2Fgmat%2Fblog&utm_medium=blog&utm_content=GMAT%20Complete%20Courses%20Plug&utm_campaign=GMAT%20Blog">Check out our upcoming courses here</a>.</em></strong></p> <hr /> <p>Ready for the long awaited conclusion of how to tackle a quant problem in two minutes? We’ll finally get to the point where you can submit an answer! If you haven’t been keeping up, catch up <a href="//www.manhattanprep.com/gmat/blog/2016/02/10/two-minutes-of-gmat-quant-a-breakdown-part-1-of-3/?utm_source=manhattanprep.com%2Fgmat%2Fblog&utm_medium=blog&utm_content=EM%209%20-%20Two%20Minutes%20of%20GMAT%20Quant%3A%20A%20Breakdown%20Part%203%20Linkback%20to%20EM%205&utm_campaign=GMAT%20Blog">here</a>.<span id="more-11378"></span></p> <h3>From 0:30 To 2:00: Work</h3> <p>After thirty seconds, you know what the problem is asking, you’ve inserted some common sense, and you may have even eliminated some answer choices. Now it’s time to work efficiently.</p> <p>If, in the first thirty seconds, you were able to see some equations fairly easily, meaning expressing the real world relationships as math doesn’t seem unreasonable, then it’s time to move into direct solving. Practice the first 30 seconds of analysis and then create whatever equations you can for this problem:</p> <p style="padding-left: 30px;">For every three boys, there are four girls in the group. If five boys join the group, and four girls leave the group, there will be an equal number of boys and girls in the group. How many boys are there initially?</p> <ul> <li>14</li> <li>21</li> <li>27</li> <li>32</li> <li>36</li> </ul> <p>Did you catch the answer choices that you could eliminate? Look again if you didn’t – there are two that are proven wrong with very little math.</p> <p>We know that initially we have more girls than boys. Beyond that, we know the total number of boys, at least initially, is some multiple of three. (The initial number of girls is some multiple of four, but that’s less helpful since the answers are referring to the boys.) The right answer, therefore, must be a multiple of three. Experiment with different possible values of boys and girls keeping the ratio of three to four if you don’t quite see why. Once you’ve convinced yourself, eliminate answers (A) and (D), because they are not divisible by three.</p> <p>From here, some of you out there will be able to read this problem, write the correct equations, and quickly solve. Excellent work. However, the many people have some trouble converting this situation into algebra. We’ll go through how in just a moment (and if you want an in-depth analysis of how to solve ratio problems like this one, check out our <a href="//www.manhattanprep.com/gmat/store/strategy-guides/fractions-decimals-and-percents/?utm_source=manhattanprep.com%2Fgmat%2Fblog&utm_medium=blog&utm_content=Fractions%2C%20Decimals%2C%20%26%20Percents%20Strategy%20Guide%2C%206th%20Edition%20Plug&utm_campaign=GMAT%20Blog">Fractions, Decimals, and Percents Strategy Guide</a>), but let’s first play with the idea that the equations are either challenging or potentially incorrect.</p> <p>As soon as you think direct algebra may be a waste of time, either because it will take too long or you’re not confident that you could do it correctly, consider alternative strategies. In this case, working backwards is a great choice. Céilidh, one of our instructors, has recently published <a href="https://www.manhattanprep.com/gmat/blog/2016/04/21/think-like-an-expert-how-when-to-work-backwards-on-gmat-problem-solving/?utm_source=manhattanprep.com%2Fgmat%2Fblog&utm_medium=blog&utm_content=EM%209%20-%20Two%20Minutes%20of%20GMAT%20Quant%3A%20A%20Breakdown%20Part%203%20Linkback%20to%20CE%206&utm_campaign=GMAT%20Blog">a phenomenal post</a> on how to determine when to work backwards, so feel free to check it out if you want more insight into this process.</p> <p>Arguably the most important aspect of working backwards is organization, so consider creating a table to help yourself out. Let’s start with answer (B).</p> <p><img decoding="async" class="wp-image-11381 aligncenter" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-1.png" alt="2_Minutes_of_GMAT_Quant_a_Breakdown_Part_3_Table_1" width="902" height="75" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-1.png 841w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-1-300x25.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-1-768x64.png 768w" sizes="(max-width: 902px) 100vw, 902px" /></p> <p>At this point, I often ask myself “What is the easiest thing to solve for next?” The beauty of working backwards is you select a series of simple steps, which eventually push you to either confirm or deny this answer choice as the correct answer. In this case, I think finding the number of boys after five more boys join is pretty easy. Let’s add that column to our table:</p> <p><img decoding="async" class="wp-image-11382 aligncenter" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-2.png" alt="2_Minutes_of_GMAT_Quant_a_Breakdown_Part_3_Table_2" width="894" height="70" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-2.png 842w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-2-300x24.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-2-768x60.png 768w" sizes="(max-width: 894px) 100vw, 894px" /></p> <p>Again, what’s the easiest thing to solve for next? My vote is for the current number of girls because it’s the same as the current number of boys.</p> <p><img decoding="async" loading="lazy" class="wp-image-11383 aligncenter" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-3.png" alt="2_Minutes_of_GMAT_Quant_a_Breakdown_Part_3_Table_3" width="892" height="73" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-3.png 843w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-3-300x25.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-3-768x63.png 768w" sizes="(max-width: 892px) 100vw, 892px" /></p> <p>The only thing left to solve for is the initial number of girls, which we can get easily enough by adding 4 from the current number of girls.</p> <p><img decoding="async" loading="lazy" class=" wp-image-11384 aligncenter" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-4.png" alt="2_Minutes_of_GMAT_Quant_a_Breakdown_Part_4" width="895" height="65" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-4.png 840w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-4-300x22.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-4-768x56.png 768w" sizes="(max-width: 895px) 100vw, 895px" /></p> <p>The final step of working backwards is to compare the numbers we’ve calculated to what’s given to find whether this is correct or not. The only thing we haven’t used yet is the initial ratio of three boys to four girls in the group. For answer (B), the initial ratio is 21 to 30, which we can reduce to 7 to 10, but is not the same as 3 to 4. So let’s try another. How about C?</p> <p><img decoding="async" loading="lazy" class=" wp-image-11387 aligncenter" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-5.png" alt="2_Minutes_of_GMAT_Quant_a_Breakdown_Part_3_Table_5" width="895" height="97" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-5.png 840w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-5-300x33.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-5-768x83.png 768w" sizes="(max-width: 895px) 100vw, 895px" /></p> <p>Try to fill in the rest of the chart and verify whether (C) is correct or not before reading on.</p> <p><img decoding="async" loading="lazy" class="wp-image-11388 aligncenter" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-6.png" alt="2_Minutes_of_GMAT_Quant_a_Breakdown_Part_3_Table_6" width="895" height="91" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-6.png 846w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-6-300x30.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/04/2-minutes-of-gmat-quant-a-breakdown-part-3-table-6-768x78.png 768w" sizes="(max-width: 895px) 100vw, 895px" /></p> <p>Our ratio is 27 to 36, which reduces to 9 to 12 aka 3 to 4. This is a perfect fit and C is the right answer.</p> <p>Just as an aside, working backwards was much easier because we’d knocked out two answer choices from the start. We had a maximum of three choices to test.</p> <p>Now, as promised, let’s work through algebraically. Here’s the question again:</p> <p style="padding-left: 30px;">For every three boys, there are four girls in the group. If five boys join the group, and four girls leave the group, there will be an equal number of boys and girls in the group. How many boys are there initially?</p> <ul> <li><span style="text-decoration: line-through;">14</span></li> <li>21</li> <li>27</li> <li><span style="text-decoration: line-through;">32</span></li> <li>36</li> </ul> <p>To start, you need to assign variables. Let’s make <em>b</em> and <em>g</em> the initial number of boys and girls in the group. We can express the ratio of three to four as b/g = 3/4. Now the tricky part. Five boys join the group, so we should create other variables for the new number of boys and girls. Try this:</p> <p>b<sub>n </sub>= b + 5 and g<sub>n</sub> = g – 4. We now have four variables, which is way too many. We can break it down by using the last bit of information; the new number of boys equals the new number of girls, or, mathematically, b<sub>n </sub>= g<sub>n</sub>. This is very helpful, because it allows us to substitute our expressions for b<sub>n</sub> and g<sub>n</sub>, giving us two equations with two unknowns: b + 5 = g – 4 and b/g = 3/4. You can solve using substitution like so:</p> <p>b/g = 3/4 so 4b = 3g and 4b/3 = g</p> <p>b + 5 = g – 4 so substitute to get b + 5 = 4b/3 – 4 and solve for b to get 27.</p> <p>Most problems can be solved multiple ways, like this one. As you start to work, be sure you are using the most efficient process, not just the most obvious ones. ?</p> <hr /> <p><em><strong>Of course, the most in-depth way to learn the ins-and-outs of the GMAT is to <a href="https://www.manhattanprep.com/gmat/classes/?utm_source=manhattanprep.com%2Fgmat%2Fblog&utm_medium=blog&utm_content=GMAT%20Complete%20Courses%20Plug&utm_campaign=GMAT%20Blog">take a complete course</a> with one of our master instructors. You can try out any first session for free! No strings attached. We promise.</strong></em></p> <hr /> <p><a href="https://www.manhattanprep.com/instructors/emily-madan/?utm_source=manhattanprep.com%2Fgmat%2Fblog&utm_medium=blog&utm_content=GMAT%20Blog%20Emily%20Madan%20Instructor%20Bio&utm_campaign=GMAT%20Blog" target="_blank"><img decoding="async" loading="lazy" class="alignleft wp-image-10901 size-thumbnail" title="Emily Madan Manhattan Prep GMAT Instructor" src="//d27gmszdzgfpo3.cloudfront.net/gmat/wp-content/uploads/sites/18/2016/01/emily-madan-150x150.png" alt="Emily Madan Manhattan Prep GMAT Instructor" width="150" height="150" /></a><em><strong><a href="https://www.manhattanprep.com/instructors/emily-madan/?utm_source=manhattanprep.com%2Fgmat%2Fblog&utm_medium=blog&utm_content=GMAT%20Blog%20Emily%20Madan%20Instructor%20Bio&utm_campaign=GMAT%20Blog" target="_blank">Emily Madan</a> is a Manhattan Prep instructor based in Philadelphia. </strong>Having scored in the 99th percentile of the GMAT (770) and LSAT (177), Emily is committed to helping others achieve their full potential. In the classroom, she loves bringing concepts to life and her greatest thrill is that moment when a complex topic suddenly becomes clear to her students. <a href="https://www.manhattanprep.com/gmat/classes/?utm_source=manhattanprep.com%2Fgmat%2Fblog&utm_medium=blog&utm_content=GMAT%20Blog%20Emily%20Madan%20Upcoming%20Courses&utm_campaign=GMAT%20Blog#instructor/344">Check out Emily’s upcoming GMAT courses here</a>. Your first class is always free!</em></p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/two-minutes-of-gmat-quant-a-breakdown-part-3/">Two Minutes of GMAT Quant: A Breakdown (Part 3)</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p> ]]></content:encoded> </item> </channel> </rss>