Tuesday, August 31, 2010

Venn Diagram


Venn diagrams or set diagrams are diagrams that show all hypothetically possible logical relations between a finite collection of sets. A Venn diagram is constructed with a collection of simple closed curves drawn in the plane. John Venn, an English mathematician introduced a diagrammatic way of representing sets. The diagrams representing sets are called Venn Diagrams template.


Venn diagrams normally comprise overlapping circles. The interior of the circle symb olically represents the elements of the set, while the exterior represents elements which are not members of the set.

venn diagram maker article is the best online feature to learn about the sets and Venn diagram. Venn diagram is nothing but a pictorial representation of a set. Sets and the! ir representations is very much simple through venn diagram maker.


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Work Problem 5 Solution

This is the solution to the work problem # 5 which read: Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?



Ok Tony takes 1 and 1/2 hours which is 90 minutes, and then we got jim at 30 minutes and Sue at 45 minutes. Convert everything to find out how much each can do in 1 minute. Tony does 1/90 th of his job in 1 minute Jim 1/30 th and Sue 1/45 th. So lets take just one individual persons job say Sue for example. If someone says Sue takes how long to finish her job if you know that she can do 1/45 of her job in a minute what would u say? 45 minutes. Or you can look at it as x/45 = 1 which means how many over 45 would = 1? The answer of course would be 45 again. So we set this problem up just like that only were ADDING the other peoples jobs together and setting it equal to 1.

So we got x/45 + x/90 + x/30 = 1 *Multiply both sides by 90 and get

2x + x + 3x = 90

6x = 90

x= 90/6 = 15

So it would take 15 minutes if all 3 worked together to finish the job.


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LSAT Prep Book Recommendations

Here's the moment you've all been waiting for: my LSAT prep book recommendations.

Happy holidays to everyone. There WILL be more tips next week too, don't worry - not everyone is on vacation. :D Recommendations below. Stay warm!


PrepTests 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, and 56
by LSAC

Each are only sold individually, as LSAC has not yet published a book of ten exams containing them. Because the exam has changed in recent years, you'll need several of these to study effectively.

When to use: after you've completed the other PrepTests.

The Next 10 Actual, Official LSAT PrepTests
by LSAC (older edition)

Contains PrepTests 29-38 and is the newest book of ten. It's essential that you get your hands on these in order to study effectively.

When to use: during exam prep.

10 More Actual, Official LSAT PrepTests
by LSAC (older edition)

Contains PrepTests 19-28.

When to use: during exam prep.

10 Actual Official LSAT PrepTests
< br />by LSAC (older edition)

Contains most PrepTests from 7-18. Only worth doing if you're studying far enough in advance that you'll have enough time to do the most recent exams as well.

Note: These exams are really old - from 12/92 - 9/95. Don't be concerned if some of the games are a bit difficult. You'll rarely see these types on recent exams.

When to use (if at all): in early stages of preparation to familiarize yourself with the exam.

The Official LSAT SuperPrep
by LSAC (older edition)

Contains a few exams you can't find anywhere else: 2/96, 2/99, and 2/00. The explanations within are the biggest selling point, but most people find them to be confusing and technical.

When to use (if at all): in early stages of preparation.


June 2007 LSAT exam (PDF)
by LSAC

Free sample exam. Treat it as if it were PrepTest 52.5 when making your study schedule.

LSAT Logic Games Bible (2003)
by Powerscore (2008)

This book contains the best Logic Games diagramming techniques I've seen, and I've reviewed all the LSAT prep books out there. The drills are useful, the organization is clear, and the book demonstrates its techniques on real LSAT PrepTests.

Skip the section on "Pattern Games" and "The Forgotten Few" unless you've already mastered other game types. Also, don't worry too much about the book's complicated subclassifications. You'll be fine if you can distinguish between the main game-types: linear/sequencing, grouping, and combination.

Unless you have a lot of time, I recommend the 2003 edition. Why? Because the 2008 edition is nearly twice the size. It appears the author beefed it up to justify the $65 retail price tag. Also, the 2008 edition exposes you to recent games you'll want to save for later practice tests.

When to use: Before you attempt logic games from the books of PrepTests.

Logic Made Easy: How to Know When Language Deceives You
by Deborah Bennett (older edition)

Although not explicitly written for test-prep purposes, this book contains several logical reasoning-type questions and reviews several common fallacies. The author is clearly familiar with the LSAT, and this makes the book more relevant for our purposes. I highly recommend reading this because it is clear, full of simple examples, and concise. You can skip the parts on the history of logic.

American Scientist's review.
When to read: Before you begin LSAT prep or when you need! a break from practice exams.

Informal Logic: A Pragmatic Approach

by Douglas N. Walton (older edition)

Clearly explains and demonstrate multiple examples of valid and invalid arguments. Walton is obsessed with logical fallacies and covers many of the common ones appearing on the LSAT.

When to read: Before you begin studying or when you need! a break.

Elementary Logic: Revised Edition
by William V. Quine

At 144 pages, it's short and sweet. It's also the first-ever logic textbook (originally published 1941, revised 1980). It discusses many basic issues (necessary/sufficient, etc.) relevant to LSAT logic. If you have the time/inclination, feel free to look it up, but it's by no means necessary.

When to read: Before you begin studying or when you need a break.

How to Solve It: A New Aspect of Mathematical Method
by George Polya (Older editions)

Simple advice on problem solving and logical thinking. It's useful because it gives you a framework to identify and analyze the relationship between evidence and conclusion. Wikipedia, this summary, and the following will probably be enough for you.

The book gives you some questions to ask yourself about any Logic Game or Logical Reasoning Stimulus:

1. What information is unknown/provided? Does the evidence/premise satisfy the conclusion?
2. How is this game/stimulus similar to others you've done? Questions do tend to come back in future exams (with different topics, of course).
3. ! Does a restatement (the contrapositive) of the argument help?
4. What inferences can you make?
5. How can you use these inferences?

Another nice summary.

When to read it: Before you begin studying or when you need a break.

The Little Luxe Book of Sudoku: 335 Easy to Hard Puzzles and The Little Black Book of Sudoku: 400 Puzzles
by Will Shortz

Number puzzles exercise your brain and get it ready for the logic games.

When to use: Before you begin studying or when you need a break.

T! hat's it - see you next year!

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! Next wee k: How to study for a retake (or what to do when you've already used too many PrepTests)...
Continue Reading...»


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Trigonometric Identities

Table of Trigonometric Identities:

Trig identity solver

Reciprocal Identities: sin

cosec u inverse function will be sin u

sec u inverse function will be cos u

Cot u inverse function will be Tan u

u inverse function will be co sec u

Cos u inverse function will be sec u

Cot u is the inverse function of Tan u

more details on

Factor rules

Trinomial calculator



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Printable TAKS Tests Math Reading, Science, Social Studies All Grades

All years, all grades, both English and Spanish, with answer keys.

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Korean Automaker Made a Big Investment in the South

A few days ago, New York Times has article on Korean car maker’s investment in U.S. (see http://www.nytimes.com/2009/04/22/us/22kia.html?ref=global-home). A few things really catch my attentions. First, Korean auto manufacturers, like Japanese auto manufacturers, mostly set up their plants in the southern states of U.S (in this case, a small town of 3000 people). &n bsp;As late entrants, why did East Asian car markets choose southern states in U.S.? How did they pick those locations? Apparently union is one of the important reasons. But there are other reasons to choose southern states over other states. I will write a more detailed analysis next time. The second point is that the article mentioned that “In the case of Kia, which is based in South Korea, state and local officials doled out some $400 million in tax breaks and other incentives.”

Actually, almos! t every state has some investment tax incentives to attract business investment. Since the investment opportunity is so precious now that state and local governments also are willing to dole out additional public subsidies.

Recently, I collect some investment tax incentives from several Midwest states. I choose Midwest because this is a region that is traditionally specialized in manufacturing.
Five states that have Investment Tax Credit programs are analyzed here. While each program is unique there are some similarities (see Table 1).






Table 1








All five states have som! e Enterprise Zone or special zone programs, which are aimed to! direct investment to specific communities and locations. The other similarity is that most states award tax credits based on the additional economic activity induced by the investors. The usual measurements for the additional economic activity include the minimum investment criteria, the number of new jobs, and the average wage of new jobs. The Enterprise Zone Program in Iowa provides a basket of public incentives, such as a property tax exemption, a supplemental New Jobs Credit (260E), a sales and use tax refund to the construction period, an Investment Tax Credit, and a supplemental Research Activities Tax Credit. Illinois’s enterprise zone program offers an Investment Tax Credit equal to one half of one percent of the value of qualified property, a sales tax exemption, and an enterprise zone tax credit for new jobs created (Illinois Department of Commerce and Economic Opportunity). Indiana’s enterprise zone program only offers credits for increased wages of local emp! loyees in private companies in the enterprise zone. Nebraska has programs specially aimed to promote investments in rural areas. For Wisconsin, both investment and the new jobs are awarded with the tax credits.


Final point is that the list in the table does not include all incentive programs that promote business investment in those states. More often, the terms and conditions of public incentives are subject to negotiation. For those big name investors with deep pockets, asking the governments to tailor a new tax incentive for them is a quite normal practice.


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