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# Veritas Prep Blog

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

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03 Feb 2014, 10:00
 FROM Veritas Prep Blog: How Well Do You Know Your Factors? In the last three weeks, we discussed a couple of strategies we can use to solve max-min questions: ‘Establishing Base Case’ and ‘Focus on Extremes’. Now try to use those to solve this question:Question: A carpenter has to build 71 wooden boxes in one week. He can build as many per day as he wants but he has decided that the number of boxes he builds on any one day should be within 4 off the number he builds on any other day.(A) What is the least number of boxes that he could have build on Saturday?(B) What is the greatest number of boxes that he could have build on Saturday?Meanwhile, let’s move on to something else today. What we will discuss today is a very simple concept but it seems odd to us when we first confront it even if we are very comfortable with factors and divisibility. If we tell you the concept right away, you will probably not believe us when we say that many people are unable to come up with it on their own. Hence, we will first give you a question which you need to answer in 30 seconds. If you are unable to do so, then we will discuss the concept with you!Question: A, B, C and D are positive integers such that A/B = C/D. Is C divisible by 5?Statement 1: A is divisible by 210Statement 2: B = 7^x, where x is a positive integerSolution: Let’s discuss the solution till the point I assume you will be quite comfortable.We need to find whether C is divisible by 5. So let’s separate the C out of the variables.C = AD/BSince C is an integer, AD will be divisible by B but what we don’t know is that after the division, is the quotient divisible by 5?Statement 1: A is divisible by 210We still have no idea what B is so this statement alone is not sufficient. Let’s take an example of how the value of B could change our answer. Assume A is 210.If B is 3, AD/B will be divisible by 5.If B is 10, AD/B may not be divisible by 5 (depending on the value of D).Statement 2: B = 7^x, where x is a positive integerWe have no idea what A and D are hence this statement alone is not sufficient.Using both together: Now, this is where the trick comes in. Using both statements together, we see that C = (210*a*D)/(7^x)Now we can say for sure that C will be divisible by 5. If you are not sure why, read on.The Concept:As you know, factors (also called divisors) of a number N are those positive integers which completely divide number N i.e. they do not leave a remainder on dividing N. If F is a factor of N, N/F leaves no remainder. This also means that N can be written as F*m where m is an integer. Sure you feel this is elementary but this concept is not as internalized in your conscience as you believe. To prove it, let me give you a question.Example 1: Is 3^5 * 5^9 * 7 divisible by 18?Did you take more than 2 seconds to say ‘No’ confidently?For N to be divisible by F, you should be able to write N as F*m i.e. N must have F as a factor. F here is 18 (= 2*3^2) but we have no 2 in N (which is 3^5 * 5^9 * 7) though we do have a couple of 3s. Hence this huge product is not divisible by 18.This helps us deduce that odd numbers are never divisible by even numbers.Example 2: Is 3^5*7^6*11^3 divisible by 13?The answer is simply ‘No’.For the numerator to be divisible by the denominator, the denominator MUST BE a factor of the numerator. In the entire numerator, there is no 13 so the numerator is not divisible by 13.Example 3: On the other hand, is 3^5*7^6*11^3*13 divisible by 13?Yes, it is. 13 gets cancelled and the quotient will be 3^5*7^6*11^3.Example 4: Is 2^X divisible by 3?No. No matter what X is, you will only have X number of 2s in the numerator and will never have a 3. So this will not be divisible by 3.Let’s come back to the original question now:Given that C = (210*a*D)/(7^x)Whatever x is, 7^x will get cancelled out by the numerator and we will be left with something. That something will include 5 (obtained from 210) since only 7s will be cancelled out from the numerator. Hence C is divisible by 5.Answer (C)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!
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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Marisa

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Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

### Show Tags

04 Feb 2014, 11:00
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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

### Show Tags

04 Feb 2014, 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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

### Show Tags

05 Feb 2014, 11:00
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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

### Show Tags

05 Feb 2014, 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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

### Show Tags

06 Feb 2014, 11:00
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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

### Show Tags

07 Feb 2014, 11:00
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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

### Show Tags

07 Feb 2014, 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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

### Show Tags

10 Feb 2014, 11:00
 FROM Veritas Prep Blog: Properties of Absolute Values on the GMAT We have talked about quite a few concepts involving absolute value of x in our previous posts. But some absolute value questions involve two variables. Then do we need to consider the positive and negative values of both x and y? Certainly! But there are some properties of absolute value that could come in handy in such questions. Let’s take a look at them:(I)    For all real x and y, |x + y| <= |x| + |y|(II)   For all real x and y, |x – y| >= |x| – |y|We don’t need to learn them of course and there is no need to look at how to prove them either. All we need to do is understand them – why do they hold, when is the equality sign applicable and when can they be useful. Let’s look at both the properties one by one.(I)     For all real x and y, |x + y| <= |x| + |y|The result of both the left hand side and the right hand side will be positive or zero. On the right hand side, the absolute values of x and y will always get added irrespective of the signs of x and y. On the left hand side, the absolute values of x and y might get added or subtracted depending on whether they have the same sign or different signs. Hence the result of the left hand side might be smaller than or equal to that of the right hand side.For which values of x and y will the equality hold and for which values will the inequality hold? Let’s think logically about it.The absolute values of x and y get added on the right hand side. We want the absolute values of x and y to get added on the left hand side too for the equality to hold. This will happen when x and y have the same sign. So the equality should hold when they have the same signs.For example, x = 4, y = 8:|4 + 8| = |4| + |8| = 12OR x = -3, y = -4:|-3 -4| = |-3| + |-4| = 7Also, when at least one of x and y is 0, the equality will hold.For example, x = 0, y = 8:|0 + 8| = |0| + |8| = 8OR x = -3, y = 0:|-3 + 0| = |-3| + |0| = 3What happens when x and y have opposite signs? On the left hand side, the absolute values of x and y get subtracted hence the left hand side will be smaller than the right hand side (where they still get added). That is when the inequality holds i.e. |x + y| < |x| + |y|For example, x = -4, y = 8:|-4 + 8| < |-4| + |8|4 < 12OR x = 3, y = -4:|3 -4| < |3| + |-4|1 < 7Let’s look at our second property now:(II) For all real x and y, |x – y| >= |x| – |y|Thinking on similar lines as above, we see that the right hand side of the inequality will always lead to subtraction of the absolute values of x and y whereas the left hand side could lead to addition or subtraction depending on the signs of x and y. The left hand side will always be positive whereas the right hand side could be negative too. So in any case, the left hand side will be either greater than or equal to the right hand side.When will the equality hold?When x and y have the same sign and x has greater (or equal) absolute value than y, both sides will yield a positive result which will be the difference between their absolute valuesFor example, x = 9, y = 2;|9 – 2| = |9| – |2| = 7OR x = -7, y = -3|-7 – (-3)| = |-7| – |-3| = 4Also when y is 0, the equality will hold.For example, x = 8, y = 0:|8 – 0| = |8| – |0| = 8OR x = -3, y = 0:|-3 – 0| = |-3| – |0| = 3What happens when x and y have the same sign but absolute value of y is greater than that of x?It is easy to see that in that case both sides have the same absolute value but the right hand side becomes negative.For example, x = -4, y = -9|x – y| = |-4 – (-9)| = 5|x| – |y| = |-4| – |-9| = -5So even though the absolute values will be the same since we will get the difference of the absolute values of x and y on both sides, the right hand side will be negative. If we were to take further absolute value of the right hand side, the two will become equal i.e. the right hand side will become |(|x| – |y|)| = |-5| = 5 in our example above. In that case, the equality will hold again.Similarly, what happens when only x = 0? The right hand side becomes negative again so taking further absolute value will make both sides equal.For example, x = 0, y = -5|x – y| = |0 – (-5)| = 5|x| – |y| = |0| – |5| = -5Taking further absolute value, |(|x| – |y|)| = |-5| = 5So when we take further absolute value of the right hand side, this property becomes similar to property 1 above: |x – y| = |(|x| – |y|)| when x and y have the same sign or at least one of x and y is 0.Now let’s look at the inequality part of property 2.Whenever x and y have opposite signs, |x – y| > |x| – |y|On the left hand side, the absolute values will get added while on the right hand side, the absolute values will get subtracted. So the absolute value of the left hand side will always be greater than the absolute value of the right hand side. The left hand side will always be positive while the right hand side could be negative too. Hence even if we take the further absolute value of the right hand side, the inequality will hold: |x – y| > |(|x| – |y|)| when x and y have opposite signsFor example, x = -4, y = 8:|-4 – 8| > |-4| – |8|12 > -4Taking further absolute value of the right hand side, we get |(|x| – |y|)| = |-4| = 4Still, 12 > 4 i.e. |x – y| > |(|x| – |y|)|OR x = 3, y = -4:|3 –(-4)| > |3| – |-4|7 > -1Taking further absolute value of the right hand side, we get |(|x| – |y|)| = |-1| = 1Still, 7 > 1 i.e. |x – y| > |(|x| – |y|)|Note that the inequality of the original property 2 also holds when x and y have the same sign but absolute value of y is greater than the absolute value of x since the right hand side becomes negative. It also holds when x is 0 but y is not.To sum it all neatly,(I) For all real x and y, |x + y| <= |x| + |y||x + y| = |x| + |y| when (1) x and y have the same sign (2) at least one of x and y is 0.|x + y| < |x| + |y| when (1) x and y have opposite signs(II) For all real x and y, |x – y| >= |x| – |y||x – y| = |x| – |y|when (1) x and y have the same sign and x has greater (or equal) absolute value than y (2) y is 0|x – y| > |x| – |y| in all other cases(III) For all real x and y, |x – y| >= |(|x| – |y|)||x – y| = |(|x| – |y|)| when (1) x and y have the same sign (2) at least one of x and y is 0.|x – y| > |(|x| – |y|)| when (1) x and y have opposite signsNote that property (III) matches property (I).There is another property we would like to discuss but let’s take it up next week along with some GMAT questions where we put these properties to use.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!
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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

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10 Feb 2014, 17:00
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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

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11 Feb 2014, 12:00
 FROM Veritas Prep Blog: School Profile: Work Hard and Play Hard at the California Institute of Technology If you have an impassioned desire to probe the far reaches of deep space, get chills at the thought of programming DNA for molecular robots, or long to one day win a Nobel Prize, then Caltech may be the school for you. California Institute of Technology, located in Pasadena, California, is a premier private research university whose mission it is to “expand human knowledge and benefit society through research integrated with education.”When you go to the homepage of most colleges, the information you find there is about the logistics of the college. When you go to the California Institute of Technology website, the homepage presents beautiful color photos linked to news stories about all the things the school and those associated with it are accomplishing and discovering. There is a lot going on here! Caltech is also home to NASA’s Jet Propulsion Laboratory, which in itself is astounding. This school has a long history of accomplishments; they don’t just give lip service to their mission, they put 100% action behind it. Caltech alumni and faculty have amassed 32 Nobel Prizes among 31 recipients. Even Einstein dropped by campus for a visit in 1931. Their ongoing dedication to excellence in science and technology is unsurpassed.Student housing at Caltech is one of the more unusual arrangements among elite colleges. The school has a house system where most of their 900+ undergraduate students live in on-campus houses. There are seven houses on campus divided into two groups. On the north end of campus are four 1920s Spanish-style houses named Blacker, Dabney, Fleming, and Ricketts. Students who live in those houses are referred to as Moles, Darbs, Flems, and Scurves. On the south end of the campus are three 1950s modern-style houses named Lloyd, Page, and Ruddock; their inhabitants are called Lloydies, Pageboys, and Rudds. All students are required to be associated with one of the seven houses. Incoming freshmen participate in “Rotation” the first week of school and visit each of the seven houses. They choose their top four; houses hold a kind of NFL draft situation to choose who will be in each house.If your main goal in going to college is to play college sports, then this may not be the school for you. The Division III school has losing records in nearly every sport year after year. Aside from 1944 when the football team went undefeated during a season cut short by war with a team stacked with Stanford players, they have arguably one of the worst college football teams. One sports website joked Caltech students’ average IQ of 140 approached their weight – a great statistic for one of the best colleges in the nation, not so great for sports. Caltech, however, plays to their strength, which is brilliance. In 1961, they pulled off perhaps the greatest college prank ever at the Pasadena Rose Bowl when they tricked Washington Huskies fans into turning over flip-cards at halftime that spelled out CALTECH in front of 33 million TV viewers.If you are lacking a sense of humor, Caltech is definitely not the place for you. It’s impossible to put this much brainpower in a single location and expect them not to use it for a little fun from time to time. Although the 1961 Rose Bowl prank was their most famous (so far), they have a long tradition of pranks, so much so that it has become part of their identity. In 1984, they manipulated the scoreboard to read Caltech and MIT as the opponents during the Rose Bowl game. In 1987, they changed the Hollywood sign to read Caltech on Hollywood’s 100th birthday. In 2005, they even flew across the country to longtime rival MIT and pranked incoming freshmen. In fact, you can read all about their long list of pranks in Legends of Caltech, Volumes I, II, and III. If you don’t have the time to read all three volumes, you can just watch the 1985 movie Real Genius, where Pacific Tech is loosely based on the school.Brilliance, excellence, dedication, hard work, and a sense of humor are all you need to attend Caltech. Join others in changing the world for the better, while still remembering to have a little fun.You’ll certainly need a high SAT score to get into Caltech too. We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter! Also, take a look at our profiles for The University of Chicago, Pomona College, and Amherst College to see if those schools are a good fit for you.By Colleen Hill
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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

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11 Feb 2014, 15:00
 FROM Veritas Prep Blog: Take the 2014 MBA Applicant Survey and Win \$500! It’s that time of year again! The Association of International Graduate Admissions Consultants (AIGAC) has launched the 2014 edition of its business school applicant survey. If you are applying to business school now, or have recently been admitted and plan on starting an MBA program in 2014, you could win \$500 just for spending 5 minutes completing!Why does AIGAC run this survey every year? AIGAC is an industry group representing admissions consultants all over the world, and the organization gathers this data every year to help its member consultants better serve their clients. Also, the data that AIGAC gathers is — 100% anonymously — shared with business school admissions officers, who are always eager to gain more insights into how business school applicants research and choose MBA programs. (You can see last year’s survey results here.)One lucky survey participant will be randomly selected to win \$500. But you only can win if you complete the survey, so do it now! You can access the survey here.Thanks in advance for helping us serve our clients better, and good luck!By Scott Shrum.
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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

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12 Feb 2014, 10:00
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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

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12 Feb 2014, 16:00
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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

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13 Feb 2014, 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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

### Show Tags

13 Feb 2014, 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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

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14 Feb 2014, 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

_________________

Marisa

Veritas Prep | Veritas Prep Representative

Save \$100 on live Veritas Prep GMAT Courses

Veritas Prep Reviews

Kudos [?]: 167 [0], given: 2

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Joined: 21 Jan 2010
Posts: 1285

Kudos [?]: 167 [0], given: 2

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17 Feb 2014, 21:00
 FROM Veritas Prep Blog: Properties of Absolute Values on the GMAT - Part II We pick up this post from where we left the post of last week in which we looked at a few properties of absolute values in two variables. There is one more property that we would like to talk about today. Thereafter, we will look at a question based on some of these properties.(III)     |x – y| = 0 implies x = yx and y could be positive/negative integer/fraction; if the absolute value of their difference is 0, it means x = y. They cannot have opposite signs while having the same absolute value. They must be equal. This also means that if and only if x = y, the absolute value of their difference will be 0.Mind you, this is different from ‘difference of their absolute values’|x| – |y| = 0 implies that the absolute value of x is equal to the absolute value of y. So x and y could be equal or they could have opposite signs while having the same absolute value.Let’s now take up the question we were talking about.Question: Is |x + y| < |x| + |y|?Statement 1: | x | ≠ | y |Statement 2: | x – y | > | x + y |Solution: One of the properties we discussed last week was“For all real x and y, |x + y| <= |x| + |y||x + y| = |x| + |y| when (1) x and y have the same sign (2) at least one of x and y is 0.|x + y| < |x| + |y| when (1) x and y have opposite signs”We discussed in detail the reason absolute values behave this way.So our question “Is |x + y| < |x| + |y|?” now becomes:Question: Do x and y have opposite signs?We do not care which one is greater – the one with the positive sign or the one with the negative sign. All we want to know is whether they have opposite signs (opposite sign also implies that neither one of x and y can be 0)? If we can answer this question definitively with a ‘Yes’ or a ‘No’, the statement will be sufficient to answer the question. Let’s go on to the statements now.Statement 1: | x | ≠ | y |This statement tells us that absolute value of x is not equal to absolute value of y. It doesn’t tell us anything about the signs of x and y and whether they are same or opposite. So this statement alone is not sufficient.Statement 2:| x – y | > | x + y |Let’s think along the same lines as last week – when will | x – y | be greater than | x + y |? When will the absolute value of subtraction of two numbers be greater than the absolute value of their addition? This will happen only when x and y have opposite signs. In that case, while subtracting, we would actually be adding the absolute values of the two and while adding, we would actually be subtracting the absolute values of the two. That is when the absolute value of the subtraction will be more than the absolute value of the addition.For Example: x = 3, y = -2| x – y | = |3 – (-2)| = 5| x + y | = |3 – 2| = 1orx = -3, y = 2| x – y | = |-3 – 2| = 5| x + y | = |-3 + 2| = 1If instead, x and y have the same sign, | x + y | will be greater than| x – y |.If at least one of x and y is 0, | x + y | will be equal to| x – y |.Since this statement tells us that | x – y | > | x + y |, it implies that x and y have opposite signs. So this statement alone is sufficient to answer the question with a ‘Yes’.Answer (B)Takeaway from this question:If x and y have the same signs, | x + y | >| x – y |.If x and y have opposite signs, | x + y | <| x – y |.If at least one of x and y is 0, | x + y | =| x – y |.You don’t need to ‘learn this up’. Understand the logic here. You can easily recreate it in the exam if need be.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!
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18 Feb 2014, 11:00
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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18 Feb 2014, 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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Re: Veritas Prep Blog   [#permalink] 18 Feb 2014, 15:00

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