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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 97
Quarter Wit, Quarter Wisdom: When Can You Divide by a Variable?  [#permalink]

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06 Mar 2017, 20:01
 FROM Veritas Prep Admissions Blog: Quarter Wit, Quarter Wisdom: When Can You Divide by a Variable? We have often come across test takers confused about division by a variable. When is it allowed, when is it not allowed? Why is it allowed in some cases and not in others? What are the constraints we need to look out for?For example:Is division by x allowed here: x^2 = 10x?Is division by x allowed here: y = 4x?Is division by x allowed here: x^2 < 4x?Let’s take a detailed look at all these questions today.The basic guidelines:Division by 0 is not allowed, hence you cannot divide by a variable until and unless we know that it cannot be 0.In the case of an inequality, when you divide by a negative number, the sign of the inequality flips. So we cannot divide by a variable until and unless we know that it cannot be 0 AND whether it is positive or negative.Let’s look at the three questions given above and try to solve them using these guidelines:Is division by x allowed here: x^2 = 10x?The first thing to find out here is whether or not x can equal 0.Case 1: If no other information has been given, then x can be 0 and we cannot divide by it. This is how we proceed in that case:x^2 – 10x = 0x(x – 10) = 0x = 0 or 10Case 2: If the question stem tells us that x is not 0, then we can divide by x.x^2/x = 10x/xx = 10Obviously, we don’t get the second solution (x = 0) in this case, as we already know that x cannot be 0. Now let’s look at the second problem:Is division by x allowed here: y = 4x?Again, this is an equation and we need to know whether or not x can equal 0.Case 1: If x can be 0, you cannot divide by it. In this case, x = 0 and y = 0 is one of the infinite possible solutions.Case 2: If the question stem states that x cannot be 0, then we can do the following:y/x = 4Now let’s look at the final question:Is division by x allowed here: x^2 > -4x?Here, we have an inequality. Before deciding whether we can divide by x or not, we need to know not only whether x can be equal to 0, but also whether x is positive or negative.Case 1: If we know nothing about the possible values that x can take, then this is how we proceed:x^2 + 4x > 0x(x + 4) > 0Now we can use the method discussed in the first problem to arrive at the range of x.x > 0 or x < -4Case 2: If we know that x is positive, then we can proceed like this:x^2/x > -4x/xx > -4Since we are given that x is positive, we know that that x > 0 (looking at the two options above).Case 3: If we know that x is negative, then this is how we will proceed:x^2/x < -4x/x (we flip the sign of the inequality because we divide by x, which is negative)x < -4The results obtained are logical, right? When x can be anywhere on the number line, we get the range as x > 0 or x < -4.If x has to be positive, the range is x > 0.If x has to be negative, the range is x < -4.Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!The post Quarter Wit, Quarter Wisdom: When Can You Divide by a Variable? appeared first on Veritas Prep Blog.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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The Best Ways to Study and Practice Vocabulary for the GRE Exam  [#permalink]

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07 Mar 2017, 16:01
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Posts: 97
SAT Subject Tests: Which Exams You Should Take and When to Take Them  [#permalink]

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08 Mar 2017, 20:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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09 Mar 2017, 19:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Posts: 97
The GRE Exam for Law School?  [#permalink]

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10 Mar 2017, 19:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Joined: 21 Jan 2010
Posts: 97
Beware of Assuming in GMAT Critical Reasoning Options  [#permalink]

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13 Mar 2017, 18:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Posts: 97
Beware of Assumption in GMAT Critical Reasoning Options  [#permalink]

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14 Mar 2017, 09:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Posts: 97
3.14 Reasons to Love Pi  [#permalink]

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14 Mar 2017, 12:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Deciding Between the SAT and ACT: Which Test is Right for You?  [#permalink]

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15 Mar 2017, 18:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Surprising Insights from the 2018 U.S. News Ranking of Top Business Sc  [#permalink]

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16 Mar 2017, 15:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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GMAT Tip of the Week: The Song Remains the Same  [#permalink]

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17 Mar 2017, 18:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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GMAT Tip of the Week: Make J. Cole One of Your Critical Reasoning Role  [#permalink]

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31 Mar 2017, 09:01
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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GMAT Tip of the Week Is Not A Player, It Just Crushes A Lot  [#permalink]

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31 Mar 2017, 18:01
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Quarter Wit, Quarter Wisdom: Dealing with Complex Word Problems  [#permalink]

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19 Apr 2017, 14:01
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Tackling GMAT Critical Reasoning Boldface Questions  [#permalink]

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19 Apr 2017, 14:01
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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How to Leverage Scholarship Money  [#permalink]

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28 Apr 2017, 16:01
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Which is Worse to Encounter on a GMAT Question: Median or Mean?  [#permalink]

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01 May 2017, 19:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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SAT Quotes to Keep You Focused and Driven as You Approach Test Day  [#permalink]

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02 May 2017, 17:01
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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03 May 2017, 17:01
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Joined: 21 Jan 2010
Posts: 97

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04 May 2017, 16:01
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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