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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91
An Easy Way to Solve Theoretical Math Problems on the SAT  [#permalink]

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07 May 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

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91
How to Quickly Solve Standard Deviation Questions on the GMA  [#permalink]

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08 May 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

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91
GMAT Tip of the Week: Mother Knows Best on Sentence Correcti  [#permalink]

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09 May 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

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91
A Remainders Shortcut for the GMAT  [#permalink]

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12 May 2014, 09:00
 FROM Veritas Prep Admissions Blog: A Remainders Shortcut for the GMAT We firmly believe that teaching someone is a most productive learning for oneself and every now and then, something happens that strengthens this belief of ours. It’s the questions people ask – knowingly or unknowingly – that connect strings in our mind such that we feel we have gained more from the discussion than even our students!The other day, we came across this common GMAT question on remainders and many people had solved it the way we would expect them to solve. One person, perhaps erroneously, used a shortcut which upon reflection made perfect sense. Let me give you that question and the shortcut and the problem with the shortcut. We would like you to reflect on why the shortcut actually does make sense and is worth noting down in your log book.Question: Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?(A) 3(B) 12(C) 18(D) 22(E) 28Solution: We are assuming you know how people do the question usually:The logic it uses is discussed here and the solution is given below as Method I.Method I:Positive integer n leaves a remainder of 4 after division by 6. So n = 6a + 4n can take various values depending on the values of a (which can be any non negative integer).Some values n can take are: 4, 10, 16, 22, 28, …Positive integer n leaves a remainder of 3 after division by 5. So n = 5b + 3n can take various values depending on the values of a (which can be any non negative integer).Some values n can take are: 3, 8, 13, 18, 23, 28, …The first common value is 28. So n = 30k + 28Hence remainder when positive integer n is divided by 30 is 28.Answer: E.Perfect! But one fine gentleman came up with the following solution wondering whether he had made a mistake since it seemed to be “super simple Math”.Method II:Given in question: “n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5.”Divide the options by 6 and 5. The one that gives a remainder of 4 and 3 respectively will be correct.(A) 3 / 6 gives Remainder = 3 -> INCORRECT(B) 12 / 6 gives Remainder = 0 -> INCORRECT(C) 18 / 6 gives Remainder = 0 -> INCORRECT(D) 22 / 6 gives Remainder = 4 but 22 / 5 gives  Remainder = 2 -> INCORRECT(E) 28 / 6 gives Remainder = 4 and 28 / 5 gives Remainder = 3 ->  CORRECTNow let us point out that the options are not the values of n; they are the values of remainder that is leftover after you divide n by 30. The question says that n must give a remainder of 4 upon division by 6 and a remainder of 3 upon division by 5. This solution divided the options (which are not the values of n) by 6 and 5 and got the remainder as 4 and 3 respectively. So the premise that when you divide the correct option by 6 and 5, you should get a remainder of 4 and 3 respectively is faulty, right?This is where we want you to take a moment and think: Is this premise actually faulty?The fun part is that method II is perfectly correct too. Method I seems a little complicated when compared with Method II, doesn’t it? Let us give you the logic of why method II is correct:Recall that division is nothing but grouping. When you divide n by 30, you make complete groups of 30 each. The number of groups you get is called the quotient (not relevant here) and the leftover is called the remainder. If this is not clear, check this post first.When n is divided by 30, groups of 30 are made. Whatever is leftover is given in the options. 30 is completely divisible by 6 and by 5 hence the groups of 30 can be evenly divided into groups of 6 as well as groups of 5. Now, whatever is leftover (given in the options) after division by 30, we need to split that into further groups of 6 and 5. When we split it into groups of 6 (i.e. divide the option by 6), we must have remainder 4 since n leaves remainder 4. When we split it into groups of 5 (i.e. divide the option by 5), we must have remainder 3 since n leaves remainder 3. And, that is the reason we can divide the options by 6 and 5, check their remainders and get the answer!Now, isn’t that neat!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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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91
SAT Tip of the Week: Should You Retake the Test?  [#permalink]

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13 May 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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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91

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14 May 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

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91
How to Keep a Proactive Approach when Solving Critical Reaso  [#permalink]

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15 May 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

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91

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16 May 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

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91
Medians, Altitudes and Angle Bisectors in Special Triangles   [#permalink]

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19 May 2014, 11:00
 FROM Veritas Prep Admissions Blog: Medians, Altitudes and Angle Bisectors in Special Triangles on the GMAT We are assuming you know the terms median, angle bisector and altitude but still, just to be sure, we will start our discussion today by defining them:Median – A line segment joining a vertex of a triangle with the mid-point of the opposite side.Angle Bisector – A line segment joining a vertex of a triangle with the opposite side such that the angle at the vertex is split into two equal parts.Altitude – A line segment joining a vertex of a triangle with the opposite side such that the segment is perpendicular to the opposite side.Usually, medians, angle bisectors and altitudes drawn from the same vertex of a triangle are different line segments. But in special triangles such as isosceles and equilateral, they can overlap. We will now give you some properties which can be very useful.I.In an isosceles triangle (where base is the side which is not equal to any other side):- the altitude drawn to the base is the median and the angle bisector;- the median drawn to the base is the altitude and the angle bisector;- the bisector of the angle opposite to the base is the altitude and the median.II.The reverse is also true. Consider a triangle ABC:- If angle bisector of vertex A is also the median, the triangle is isosceles such that AB = AC and BC is the base. Hence this angle bisector is also the altitude.- If altitude drawn from vertex A is also the median, the triangle is isosceles such that AB = AC and BC is the base. Hence this altitude is also the angle bisector.- If median drawn from vertex A is also the angle bisector, the triangle is isosceles such that AB = AC and BC is the base. Hence this median is also the altitude.and so on…III.In an equilateral triangle, each altitude, median and angle bisector drawn from the same vertex, overlap.Try to prove all these properties on your own. That way, you will not forget them.A few things this implies:-          Should an angle bisector in a triangle which is also a median be perpendicular to the opposite side? Yes.-          Can we have an angle bisector which is also a median which is not perpendicular? No. Angle bisector which is also a median implies isosceles triangle which implies it is also the altitude.-          Can we have a median from vertex A which is perpendicular to BC but does not bisect the angle A? No. A median which is an altitude implies the triangle is isosceles which implies it is also the angle bisector.and so on…Let’s take a quick question on these concepts:Question: What is ∠A in triangle ABC?Statement 1: The bisector of ∠A is a median in triangle ABC.Statement 2: The altitude of B to AC is a median in triangle ABC.Solution: We are given a triangle ABC but we don’t know what kind of a triangle it is.Jump on to the statements directly.Statement 1: The bisector of ∠A is a median in triangle ABC.The angle bisector is also a median. This means triangle ABC must be an isosceles triangle such that AB = AC. But we have no idea about the measure of angle A. This statement alone is not sufficient.Statement 2: The altitude of ∠B to AC is a median in triangle ABC.The altitude is also a median. This means triangle ABC must be an isosceles triangle such that AB = BC (Note that the altitude is drawn from vertex B here). But we have no idea about the measure of angle A. This statement alone is not sufficient.Using both statements together, we see that AB = AC = BC. So the triangle is equilateral! So angle A must be 60 degrees. Sufficient!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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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91

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20 May 2014, 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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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91

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20 May 2014, 12:01
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

_________________
Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91
SAT Tip of the Week: Can You Answer These 3 Comma Questions?  [#permalink]

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21 May 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

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91

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21 May 2014, 14:00
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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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91
Use This Process When Solving Sentence Correction Questions   [#permalink]

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22 May 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

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91

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22 May 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

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91

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23 May 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

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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91
GMAT Tip of the Week: The Most Important Word on the GMAT  [#permalink]

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23 May 2014, 14:00
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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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91
When Permutations & Combinations and Data Sufficiency Come T  [#permalink]

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27 May 2014, 09:00
 FROM Veritas Prep Admissions Blog: When Permutations & Combinations and Data Sufficiency Come Together on the GMAT! While discussing Permutations and Combinations many months back, we worked through several examples of arranging people in seats. Today we bring you an interesting question based on those concepts. It brings to the fore the tricky nature of both Data Sufficiency and Combinatorics – so much so that when the two get together, it is unlimited fun!In some circumstances, we suggest you to travel the whole nine yards – i.e. solve for the answer in Data Sufficiency questions too even if you feel that sufficiency has already been established. This is especially true for quadratic equations which we assume will give us two values of x but might actually give just a single unique value (such that both roots are the same). In Combinatorics too, sometimes what may look like two distinct cases could actually give the same answer. Let’s jump on to the question.Question 1: There are x children and y chairs in a room where x and y are prime numbers. In how many ways can the x children be seated in the y chairs (assuming that each chair can seat exactly one child)?Statement 1: x + y = 12Statement 2: There are more chairs than children.Solution:There are x children and y chairs.x and y are prime numbers.Statement 1: x + y = 12Since x and y are prime numbers, a quick run on 2, 3, 5 shows that there are two possible cases:Case 1: x=5 and y=7There are 5 children and 7 chairs.Case 2: x=7 and y=5There are 7 children and 5 chairsAt first glance, they might look like two different cases and you might feel that statement 1 is not sufficient  alone. But note that the question doesn’t ask you for number of children or number of chairs. It asks you about the number of arrangements.Case 1: x=5 and y=7If there are 5 children and 7 chairs, we select 5 chairs out of the 7 in 7C5 ways. We can now arrange 5 children in 5 seats in 5! ways.Total number of arrangements would be 7C5 * 5!Case 2: x = 7 and y = 5If there are 7 children and 5 chairs, we select 5 children out of the 7 in 7C5 ways. We can now arrange 5 children in 5 seats in 5! ways.Total number of arrangements would be 7C5 * 5!Note that in both cases the number of arrangements is 7C5*5!. Combinatorics does not distinguish between people and things. 7 children on 5 seats is the same as 5 children on 7 seats because in each case you have to select 5 out of 7 (either seats or children) and then arrange 5 children in 5! ways.So actually this statement alone is sufficient! Most people would not have seen that coming!Statement 2: There are more chairs than people.We don’t know how many children or chairs there are. This statement alone is not sufficient.Answer: AWe were tempted to answer the question as (C) but it was way too easy. Statement 1 gave 2 cases and statement 2 narrowed it down to 1. Be aware that if it looks too easy, you are probably missing something!Now, what if we alter the question slightly and make it:Question 2: There are x children and y chairs arranged in a circle in a room where x and y are prime numbers. In how many ways can the x children be seated in the y chairs (assuming that each chair can seat exactly one child)?Statement 1: x + y = 12Statement 2: There are more chairs than children.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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Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91

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27 May 2014, 13:00
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

_________________
Veritas Prep Representative
Joined: 21 Jan 2010
Posts: 91

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28 May 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

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