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Permutations and Combinations Part II: Formulas

Friday, March 19th, 2010

Once you’ve figured out whether to use permutation or combination, there is actually very little work to be done if you know the formulas for permutation and combination or if you know where the function is hidden on your calculator.

As I mentioned before, permutation is used when the order matters and combination when you just want to choose, but not order, the items. Let’s dive straight into the formulas then go through a few examples.

The number of ways of permuting r objects out of n objects is given by

n P r = n!/(n-r)! where n! = n * (n-1) * (n-2) * … * (2) * (1)

The number of ways of combining r objects out of n objects is given by

n C r = n!/r!(n-r)!

Note that 0! is defined as 1.

Example 1

How many ways are there of arranging 4 letters out of the following F R I E N D?

FRIEND has 6 different letters, and since the order of letters matter, I know I have to use the permutation formula. Applying the formula directly, the answer is given by

6 P 4 = 6!/(6-4)! -= 6!/2! =360

You can double-check this by using the fundamental counting principle that we covered in Part I. Drawing a tree diagram will also work, but it might get a little messy as the tree gets bigger and bigger.

Example 2

If there are 3 entrees and 5 desserts, how many ways are there of choosing 1 entrée and 2 desserts? Note, that the question does not say anything about the order in which the entrees and desserts are eaten, so we know to use the combination principle. Because we are choosing entrees and desserts separately, we have to apply the combination formula twice.

First, to choose 1 entrée out of 3, we apply the formula 3 C 1 = 3!/1!(3-1)! = 3!/1!2! = 3

Next, to choose 2 desserts out of 5, we apply the formula 5 C 2 = 5!/2!(5-2)! = 5!/2!3! = 10

Then because for each entrée, there are 10 possible 2-dessert combinations and there are 3 ways of choosing 1 entrée, to get the total number of possibilities, we take 3*10 = 30.

Example 3

What if the question throws you a curveball and asks you to permute something that has a repeated item. For example, how many ways are there of arranging the letters A G H A S T?

The ‘A’ is repeated twice so first we pretend that the letters are distinct and find the number of possibilities. Then divide that value by 2! because ‘A’ is repeated twice.

AGHAST has 6 letters, and if we permute all the letters, we get 6!

Because A is repeated, we divide 6! by 2! to get the answer 360

Supposing I asked you to permute only 4 out of 6 of the letters from AGHAST, then you would do 6 P 4 as per normal, and divide that answer by 2! since A is repeated. The answer should be 180.

Check out Grockit for more GMAT permutations and combinations practice!

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GMAT Solving Linear Equations with 1 Unknown

Wednesday, March 17th, 2010

A linear equation is any equation where the highest power of the unknown, which I shall call x, is 1. To illustrate more clearly with a few examples:

x+1 = 4; 10x = 3; x = 18 – 4x are three examples of linear equations

x² + 2 = 2x and x³ = 8 are not linear equations because there are x’s that are raised to a higher power than 1.

A linear equation with 1 variable is the simplest type to solve. There is 1 equation and 1 unknown, which means that the unknown can always be determined. To solve such an equation, you need to rearrange the equation to have like terms on either side of the equal sign. Put another way, you are trying to isolate x (or whatever the variable is called) on one side of the equation.

For example, if 2x = 234, to isolate x, we have to divide the entire equation by 2. Doing this, we get x = 117.

If there are x’s and numbers on either side of the equal sign, we add and subtract values to isolate x on one side. Suppose 2x – 17 = 18 – 3x

The first thing we could do is to add 17 to both sides to get: 2x – 17 + 17 = 18 – 3x + 17

This reduces to 2x = 35 – 3x

Now, we need to have all the x’s on one side so we add 3x to both sides to get: 2x + 3x = 35 – 3x + 3x

This reduces to 5x = 35

Dividing by 5 on both sides, we get x = 7

What I just went through was a fairly simple algebraic equation. The questions on the GMAT will look more complicated but you are essentially doing the same thing: manipulating both sides of the equation in the same way to isolate x. Let’s try a practice problem from Grockit.

To tackle this question, we multiply both sides by 2+3/x to get 3 = 2+3/x. . (This is also known as cross multiplying where in general if a/b-c/d,

then ad = bc

To simplify 3 = 2+3/x,

we multiply the entire equation by x to get 3x = 2x + 3. This leaves you with a much simpler equation that you already know how to solve.

What’s a little trickier than manipulating algebraic equations is translating a word problem into an algebraic equation. Here’s another practice problem:

Jack and his brother are sharing a monster piece of licorice that is 28 inches long. Since Jack is older, his share is 8 inches longer than his brother’s. How long, in inches, is Jack’s brother’s piece?

The way to solve this problem is to let something be x. Here’s what happens if we let Jack’s piece be x inches.

Jack’s piece = x inches

Jack’s brother’s piece = x – 8 inches

Total length of licorice = Jack’s piece + Jack’s brother’s piece = 28 = x + (x-8)

This means that x = 18 inches. But remember that the question wants the length of Jack’s brother’s piece, which we have defined as x – 8. So the correct answer is 10 inches.

Here’s what happens if we let Jack’s brother’s piece be x inches.

Jack’s brother’s piece = x inches

Jack’s piece = x + 8 inches

Total length of licorice = 28 = x + (x+8) and we determine that x = 10. In this case, since we have already defined Jack’s brother’s piece to be x, there is no further step we need to take.

In general, here are a few things to keep in mind.

if there is only one unknown, you only need one equation to determine the value of the unknown
in dealing with algebraic equations, remember that anything you do to one side (be it adding, subtracting, multiplying or dividing) you need to do to this other side too.
in dealing with word problems, define something to be x and see if you can define other things in terms of x only. (For example, in the question about licorice, you would not want to let Jack’s piece be x inches and his brother’s be y inches) Don’t introduce unnecessary variables if it can be expressed in terms of an existing variable.

Posted in Data Sufficiency, GMAT, Quantitative, Series | No Comments »

Permutations and Combinations Part I: Counting

Friday, March 12th, 2010

When dealing with permutations and combinations, you are essentially trying to find the number of different outcomes given a set of items and a number of restrictions. The difference between permutation and combination merely depends on whether the order matters. Let me illustrate with an example. Suppose you have three food items, apples, bananas and carrots. If you were asked to only pick two of them, how many possibilities are there? If you got 3, that’s the right answer. You have apples & bananas, apples & carrots and bananas and carrots. This is combination. If I told you however, that the order in which you eat the food matters, then you have more possibilities, because instead of just apples & bananas, you have to consider bananas & apples too. The latter is permutation.

Listing

What I did earlier, when I listed out the 3 choices is called, not surprisingly, listing. But there is a method to listing to ensure that you don’t leave any possibilities out. Everyone tends to have his or her own method, let me share mine. If I have four items – a, b, c and d – and I’m supposed to choose 2:

Step 1: I take the first item a and combine it with b. Then I go down the list and combine it with c and d to get a total of three possibilities: ab, ac, ad.

Step 2: I take the second item b and combine it with the rest of the list. I don’t combine it with a because I already did that in step 1. So I get: bc, bd

Step 3: Keep doing the same thing for the next thing on the list, which is c. For c, there’s only one thing behind it on the list – d. So there’s only 1 possibility here: cd

Step 4: Keep going until you get to the second last item. In this case, we already reached it in step 3. Tally up your choices: ab, ac, ad, bc, bd, cd

Tree Diagram

If you noticed, listing is a good method for figuring out combinations. The Tree Diagram is a graphical method that helps you with permutation. Using the previous example of 4 items, here’s the tree diagram that illustrates the number of ways of permuting items.

If you look at the last line of the tree diagram and count the number of boxes, you will see that there are 12 possible ways to permute 2 items out of 4. Each item can be combined with 3 other things. Another way of seeing this is that you have two spaces you need to fill ___ and ___. Looking at the first space, you have 4 possible items you could place there. Looking at the second space, you have 3 possible items you could place there, since you have already put 1 item in the first space. So there are 4 x 3 = 12 ordered possibilities.

Fundamental Counting Principle

The spaces-and-number-of-options-to-fill-that-space method of thinking is essentially the fundamental counting principle. The principle states that

if task A can be done in m ways and after Task A is complete, Task B can be done in n ways, then there are m*n ways of completing Task A then Task B.

Let’s see if you understand the principle with a quick example. How many different ways are there are arranging these letters: T A N G O

Did you get 120?

Imagine five spaces ___ ___ ___ ___ ___

You have 5 possible letters to put in the first space, and when that’s done, you have 4 possible letters to put in the second space, 3 letters for the third space and so on. So the answer is 5*4*3*2*1 or 5!

If you’re comfortable using these methods to solve permutation and combination problems, stay tuned for the second installment that uses direct formulas to calculate the number of possibilities. In the meantime, check out Grockit for GMAT quantitative practice.

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Interest and Compound Interest Problems

Wednesday, March 10th, 2010

Interest and Compound Interest

There are two types of interest problems on the GMAT, and they include simple interest and compound interest. Simple interest is the most basic and is a function of P, the principle amount of money invested, the interest rate earned on the principle, i, and the amount of time the money is invested, t (this is usually stated in periods, such as years or months). The resulting equation is: I = iPt

In basic terms, the above equation tells us the amount of interest that would be earned on a principle amount invested (P), for a given time (t) at a given interest rate (i).

Example:

If you invested $1,000 (P = your principle) for one year (t = one year) at 6% simple interest (i = given interest rate), you would get $60 in interest at the end of the year and would have a total of $1,060.

For compound interest, you would earn slightly more.

Let’s look at similar type problem, though this one involves compound interest.

Mr. Riley deposits $500 into an account that pays 10% interest, compounded semiannually. How much money will be in Mr. Riley’s account at the end of one year?

For compound interest, first you need to divide the interest rate by how many compound periods there are. So for in the above question, because we are compounding semiannually, we need to divide 10% by 2 (because of 2 compounding periods), and if we were compounding quarterly, we would need to divide 10% by 4.

In the above question, Mr. Riley deposited $500 into his account at a rate of 10% compounded semiannually and the bank will divide his interest into two equal parts. They will pay 5% interest (10%/2) at the end of six months, and then will pay another 5% at the end of the year. Compound interest can essentially be translated into “interest paid on interest”, meaning that after one period, you are paid interest on the interest that was paid in prior periods, hence the phrase “compounding”.

So at the end of the six months, Mr. Riley has $525 because the bank paid $25 in interest ($500*5%) into his account. For the second half of the year, Mr. Riley is then paid 5% on the $525 balance that was in his account at the end of the first six months. This interest is equal to $525*5% = $26.25. Therefore, at the end of the year, Mr. Riley has $551.25, which is equal to his balance of $500, plus the $25 interest paid at the end of 6 months, plus $26.25 paid at the end of the year. Mr. Riley earns $1.25 more with this compound interest than he would have been paid if he were paid only 10% simple interest (would have been only $550). The lesson? Compound interest always pays more!

Let’s look at another similar type of problem that involves interest.

Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $2500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?

A. $3,750

B. $5,600

C. $8,100

D. $15,000

E. $22,500

At first glance, this one seems pretty tricky because you are given x% as the interest rate and it asks you about compounding and it might seem difficult where to find a starting point for this. For this one, it might be a bit easier to think about this without the use of compound interest, which might unnecessarily confuse you. Here, we are given x% as 8%, so all we need to do is take 112/8 = 14. Thus, we know that the money triples in value every 14 years. Further, we know that the money will triple exactly twice in 28 years, once in 14 years and one more time at the 28^th year. So first we need to multiply the original $2500 invested by 3 to get the balance at the end of year 14 (because it triples), to get $7,500 (or $2,500*3). Now, we know that this balance of $7,500 will triple again, so the final balance at the end of the next 14 year period will be $22,500 (or $7,500*3). The correct answer choice is E.

Overall, the three types of interest problems you will most likely encounter come test day will be simple interest, compound interest, and word problems involving the mention of interest, but that can be solved without the application of interest or compound interest methods. The key to deciphering between compound interest and simple interest is to see how many periods the interest is paid….interest paid in one period is simple interest and interest “paid on interest” in multiple periods is compound interest. Finally, remember that some questions can be solved intuitively.

Check out Grockit for more GMAT quantitative practice!

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Grockit Live Online Courses Are Here

Tuesday, March 9th, 2010

GMAT quant lesson 1 We’re excited to announce that Grockit now offers personalized courses to students preparing for the SAT, ACT, GRE, and GMAT. Grockit courses offer a set schedule of live lessons with the best instructors in the country. Students pick the instructor and schedule that works best for them. Students and instructors are connected online and also through audio conferencing.

Each course lesson is a combination of slide based lecture and group practice questions. The curriculum adapts to each students’ strengths and weaknesses as they progress through the course material. Students also get 24/7 access to Grockit Group Study where they can work with or compete against students all over the world who preparing for the same exam. We’re so confident about the effectiveness of our courses that we’re offering a money back guarantee on score improvement.

Please select an exam to see how that Grockit courses compare to others in the industry:

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How is the GMAT Scored?

Thursday, March 4th, 2010

An official GMAT score report consists of four parts: a Verbal Scaled Score (on a scale from 0 to 60), a Quantitative Scaled Score (on a scale from 0 to 60), a Total Scaled Score (on a scale from 200 to 800) and an Analytical Writing Assessment Score (on a scale from 0 to 6). For each of these four scores, you will receive a percentile rank. Each rank shows the percentage of test-takers who scored below you based on the scores for the most recent three-year period. The percentile rankings change from year to year but your scaled score is fixed. To see how the score report looks, you can download a sample score report at www.mba.org.

The GMAT scores the multiple choice and the writing sections differently. There are a total of 78 multiple choice questions: 41 in the verbal section and 37 in the quantitative section. To compute the scaled score for each section, the GMAT uses an algorithm that takes into account the total number of questions answered, the number of questions answered correctly, and the level of difficulty of the questions answered.

The AWA score is an average of the scores given to both essays. Each essay is given two independent ratings. According to the official GMAT website, one of which may be determined by an automated essay-scoring engine. If the two ratings differ by more than one point, another evaluation is required to determine the final score. Once both essays have been scored, the four scores are averaged to provide the overall score. If for any reason you believe your AWA score is inaccurate, you may request that your essays be rescored using the Essay Rescore Request Form.

When you schedule your GMAT appointment you will be asked to indicate if you wish to access your Official Score Report online or in the mail. Unofficial scores for the multiple-choice section are available immediately after the test. You will receive your official scores within 20 days of testing. It is usually faster to receive them online and if you opt to do so keep your authorization number from your unofficial score report. You will need this number to access your online score report.

As for the multiple-choice sections, at the beginning of each section the computer will present a question in the middle range of difficulty. If the question is answered correctly, the next question will be harder and the score will adjust upwards. If the question is answered incorrectly, the next question will be easier and the score will adjust downwards. The computer is constantly recalculating the scaled score as the student progresses through the section to determine the precise ability of the test-taker.

This is why questions at the beginning of a section count much more than questions at the end of a section. While the total scaled score ranges from 200 to 800, approximately two-thirds of test takers score between 400 and 600. The most recent percentiles can be found in the chart to the left.

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Rectangular Solids and Cylinders

Monday, March 1st, 2010

Questions involving rectangular solids, particularly data sufficiency questions, test whether you understand the concept of volume and surface area. You essentially need to remember that you need three different values to find volume and surface area (the length, the width and the height). If the prompt and statements 1 and 2 are lacking some these values or some way to find them, neither of the statements will be sufficient.

A rectangular solid is formed by 3 pairs of similar rectangular faces. In other words, 6 rectangular faces in total.

The formulas you need to remember for a rectangular solid are

Volume = Length (l) x Width (w) x Height (h)

Surface Area = (2 x Length x Width) + (2 x Length x Height) + (2 x Width x Height)

If length = width = height, that means that the rectangular solid is, in fact, a cube.

Other vocabulary that might be important is the terms vertex and edge. A vertex is a mathematical way of referring to the corner of any figure. The rectangular solid above has 8 vertices (plural of vertex), can you identify them? The edge is simply the lines you see in the diagram above: the line where two surfaces meet.

Questions involving cylinders are similar and perhaps easier because there are only two values you need to know to solve cylinder-problems – the radius (r) and the height (h).

If you don’t know the radius, anything that enables you to determine the radius, such as the diameter (radius = diameter / 2) or the circumference (radius = circumference / 2pi) will suffice.

Regarding cylinders, the formulas you need to know are

Volume = area of the base circle x height = pi x (radius)² x height

Surface Area = (2 x pi x (radius)² )+ (pi x (diameter) x height)

Let’s try a problem: A cylindrical water tank has a stripe painted around its circumference, as shown in the figure provided. What is the surface area of this stripe?
(1) y = 0.7
(2) The height of the tank is 2 meters.

To find the surface area of the stripe, you need to know the circumference of the cylinder, but there is not data in the question that gives you the radius or diameter to let you find the circumference. Hence the answer should be that neither statement together is sufficient.

Posted in Data Sufficiency, GMAT, Quantitative | No Comments »

Weighted Averages On The GMAT

Friday, February 26th, 2010

This post will introduce weighted average questions you’ll see on the GMAT. There is one main formula you need to solve simple GMAT Average questions:

Average = SUM / # of observations

Note that this can be rearranged to read:

SUM = Average x (# of obs)
# obs = SUM / Average

So, if you are given ANY 2 of the 3 values, you should be able to find the 3rd. For example:

John drinks an average of 1.5 cups of water/day. After how many days has he drank 3 gallons of water? (1 gallon = 16 cups.)

In this case, we are looking for the number of days (or observations) such that we total 48 cups (3 gallons) of water.

# = SUM / Average

# days = 48 cups / 1.5 cups/day
# days = 32 days

NEVER AVERAGE AVERAGES!

Class A has 15 students and an average height of 60”. Class B has 20 students. What is class B’s average height if the average height of both classes is 65”.

One might say: (A + B) / 2 = 65”; A = 60”; so B must be 70”. However, keep in mind:

TOTAL AVERAGE = TOTAL SUM / TOTAL OBS

CLASS A + CLASS B = BOTH

15 students + 20 students = 35 students
60” average + 68.75” average = 65” average
900” total in A + 1375” total in B = 2275” total in Both

The given information is in black. The necessary intermediate steps are in blue, and the red is your answer. Note that the average of the averages ≠ total average. We must calculate each average separately, and to do this we need the SUM and # of observations for each category. This brings us to the idea of WEIGHTED AVERAGES.

A WEIGHTED AVERAGE is needed when you are taking average of a large group in which there are subgroups with a different number of observations in each. Take a look at this generalized formula, assuming there are 3 groups A, B and C.

(Average of A x Obs in A) + (Average of B x Obs in B) + (Average of C x Obs in C)

(Obs in A) + (Obs in B) + (Obs in C)

Think of weighted averages like a tug of war between numbers. The “stronger” one side (dog) is, the more that weighted average (tennis ball) will be “pulled” in that direction.

In the previous question, we had:

CLASS A + CLASS B = BOTH

15 students + 20 students = 35 students
60” average + 68.75” average = 65” weighted average

Note that the weighted average is CLOSER to B’s average than it is to A’s. This is because there are 20 students in Class B compared to only 15 students in Class A.

Two More Examples

At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2

B. 5

C. 9

D. 15

E. 30

WITHOUT using the formula, we can see that today the restaurant served 30 customers above the average. The total amount ABOVE the average must equal total amount BELOW the average. This additional 30 customers must offset the “deficit” below the average of 90 created on the x days the restaurant served only 75 customers per day.

30/15 = 2 days. Choice (A).

WITH the formula, we can set up the following:

90 = (75x + 120)/(x + 1)
90x + 90 = 75x + 120
15x = 30

x = 2 Answer Choice (A)

Use whichever makes more sense to you!

Anita spent a total of $780 on 52 bottles of wine for her wedding. She then decided to buy 8 bottles of sparkling wine for the toasts, as well. Was the average (arithmetic mean) price per bottle of wine less than $20?

(1) Each bottle of sparkling wine cost more than $15.

(2) Each bottle of sparkling wine cost less than $40.

Take another look at what exactly the question is calling for: the TOTAL average price of all the wine at the wedding. We should look at the suggested average ($20) and use that as our threshold amount.

60 bottles * $20/bottle = $1200 total
$1200 total – $780 (given) = $420 (left for sparkling wine)
$420 / 8 bottles = $52.50/bottle of sparkling wine (for the total average to equal $20)

Which of the answer choices are conclusively above or below $52.50/bottle of sparkling wine? Only (2). With (1), we can be below OR above the threshold, so (1) is not sufficient.

Answer Choice (B)

Now, you’re score will be above average! Please visit the Grockit forum or leave a comment here if you have more questions on weighted averages.

Good luck!

Posted in GMAT, Problem Solving, Quantitative | No Comments »

Test Day Prep

Wednesday, February 24th, 2010

Test day needs to be given the weight it deserves. While you can retake the test over and over until you do what you think is the best you can do, if you master it the first time you will save yourself a lot of time and at US$250 a pop, a lot of money.

Time is of the essence.

Once you have decided that you are properly prepared to attempt the test, you need to schedule it. That very decision can help or hurt your score. You need to pick a time and date that works very well for you. Every person has a time of the day where they are at their peak. For some it is the early morning, most likely with the aid of their coffee, but for others it is right after lunch. Think about what this time is for you and make that time your GMAT test time.

Location, Location, Location.

Pick a location that you are familiar with or become familiar with the location that is offered. If need be take a drive to the facility and figure out how to get there and where you will be parking, because you do not want to have the stress of finding parking tax your brain on that day.

It’s a date?

You need to pick a date that will not be surrounded by chaos. This might seem obvious, but don’t pick a date when your parents are coming to visit or you have a vacation starting the next day. You will be distracted and that can hurt you.

Treat the day as a vacation day itself. If possible tell your boss that you need to take the entire day off, or if you are taking it in the morning, maybe a half day the day before and a half day for the test.

If you have time in the morning do something mildly athletic, take a jog or go for a walk to get the blood going. Do not roll out of bed, slam a cup of coffee and wing this thing (although I am sure some of you believe that is when you are at your best). Eat something, but don’t stuff yourself, you don’t need the blood digesting when it needs to be working on Data Sufficiency.

What are you wearing?

Depending on the time of year and given the fact that you do not know what the facility will be like, I would dress with some layers. Walking into a test center with so much A/C blasting that it makes Siberia feel like the tropics without a sweater or sweatshirt would be really bothersome.

Finally, have a good attitude about it. You can take it over, but set your goal high and aim at it. If you aim at 500 then 450 becomes a real possibility, if you aim at 800 then 750 becomes more real. Don’t sell yourself short, it’s a game and if you prepared you have a shot at doing very well on it.

Good luck.

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GMAT Verbal Study Plan for Non-Native Speakers (and Others Who Want the Practice)

Monday, February 8th, 2010

By far, the easiest and fastest way to learn English is to be a tiny baby growing up in an English-speaking environment. If you are reading this article, though, you are no longer in a position to take advantage of that opportunity, and will have to improve your English the hard way: practice. Not all practice is equally good, however! English, like all living languages, is complex and constantly-changing; what is acceptable in spoken English is not always accepted in Standard (written) English. The key to improving your English reading, processing, and writing skills for the GMAT is consistent high-quality practice. It’s true that native speakers have a big advantage — they have typically been listening to correct English for at least two decades. Non-native speakers, however, have a small advantage — they (unlike native speakers) have not been listening to incorrect English for two decades. Build your study around quality writing and daily practice — and start as early as you can.

Quality writing:
New Yorker
The Economist
Harper’s Magazine
The Atlantic

A note about The Economist in particular: you may be tempted to choose that above all the others, as it is the most business- and world news-focused. I believe doing so would be a mistake! The Economist is known for its very precise and concise use of language; you all should be reading it for this reason. On the other hand, The Economist assumes a very high level of familiarity and comfort with not only standard language usage, but also the rarer, more complex, and more concise usage of English found more commonly in the humanities (it also occasionally chooses British English usage over American English usage). The other three periodicals mentioned above have a smaller portion of their content devoted to finance and business and a greater portion devoted to the humanities — often without The Economist’s trademark concision. You will get more practice tracking longer English sentences, which can also shed more light on English usage: sometimes things are easier to understand when more words are used to explain! In addition, the greater variety present in the other periodicals prepares you better for the variety of topics you’ll get in GMAT Reading Comprehension passages. In short: use The Economist, but not only The Economist.

One Year Away From Test Day

One half hour per day reading (or even listening to) quality English writing. Podcasts/audio books are an acceptable occasional substitute; reading words on the page is better, but only one of the two is legal or smart while you’re driving to work
Look up words you don’t know, every time.

Six Months From Test Day

The above, plus:

Take a full-length practice test to assess your weaknesses; take two more in the next two months
Take inventory of the places you are likely to be caught due to language differences
Start writing down idioms that give you trouble; take note of movie/book/song titles, or other key phrases in English that can help you remember the idioms
Begin a weekly commitment to GMAT study, starting with the Official Guide. Move to other sources when you have exhausted the Official Guide material

Three Months From the Week of Your Test

Begin taking at least two full-length practice tests every three weeks; you are taking full-length tests because the Quantitative section is also written in English. The goal is to improve your comfort level with the overall timing of the test, and to help you adjust to the range of English that appears on the full test
One half hour per day of Grockit GMAT Verbal Study minimum; do not save it all for one weekend afternoon
For harder CR and RC passages, you can also use LSAT prep materials
Keep reading!

One Month From the Week of Your Test

Take one full-length practice test per week
Study every day, even if it’s just 15 minutes. You gain much more from repetition than you do from cramming
Keep reading!

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GMAT

Archive for the ‘GMAT’ Category

Permutations and Combinations Part II: Formulas

GMAT Solving Linear Equations with 1 Unknown

Permutations and Combinations Part I: Counting