Circular Permutations Questions

We’ve all seen those tricky Permutation/Combination questions involving people around a circular table. How do we solve them? Well, they’re actually pretty ridiculously easy!

Let’s examine one:

There are 7 people and a round table with 5 seats. How many arrangements are possible?

This question might seem complex at first because there are more people than there are seats. It’s kind of a Permutation AND a Combination in one!

So first we’re wondering, how many ways to choose 5 from 7? This is a simple Comb:

7C5 = 7! / 5!2! = 7 x 6 / 2 = 42/2 = 21 ways

So now for each of those ways, we’re wondering, how many ways can we order 5 people around a table?

For any table with “x” seats, the number of possible arrangements is (x-1)!, so here 4! = 4 x 3 x 2 = 24.

21 x 24 = 504

The correct answer is 504.

The key takeaway here is that “choosing” X from Y always allows for the Combination formula (x! / (x-y)! y!), and the number of arrangements around a circular table with “X” seats is always (X-1)! There’s actually not that much to memorize!

Advertisements

4 Easy Steps to Rock GMAT Reading Comprehension Passages

Step 1. Find the answers as you read. You already know the types of RC questions you’ll see on Test Day: main idea, detail, logical structure, inference, etc. So why not look for those things the first time you go through the passage? Don’t take notes summarizing. Instead, find the topic, scope, function of each paragraph, author’s point of view, tone, and purpose on your own. Make the inferences ahead of time and read for the implications behind the words. Don’t focus on the details and the subject matter itself.

Step 2. Put the question stem in your own words. Especially for long-winded inference questions, restate the question stem in simpler terms, as if you were asking the question of a small child. For “NOT” and “EXCEPT” questions this is especially important since 4/5 answer choices will actually be correct, and you’ll be required to find the 1 incorrect choice (the opposite of what is usually expected).

Step 3. Write down a prediction. Even for open-ended inference questions, there’s a limited number of logical inferences that can be drawn based on the implications in the passage. Use your notes on the passage to help you eliminate. Process of elimination is a much more effective means of getting the correct answer. You can’t “unread” the answer choices once you’ve looked at them, so if you don’t write down your prediction you will likely adjust it in your head to “fit” answer choices that may be incorrect.

Step 4. Eliminate out of scope choices. Just what does “out of scope” mean? “Scope” is the focus of the passage, how it narrows down the topic. What does the author spend the majority of his time discussing? Think of it like a circular fence. Everything that relates to the passage fits inside the fence. There may be answer choices that relate to the topic, but would not really go “inside the fence.” This would be considered out of scope.

Step 5. Be wary of extreme language. Answer choices that use words like “no”, “none”, “never”, “always” are typically incorrect. It’s possible a choice containing extreme language is the correct answer, but you should only select it once you’ve confidently eliminated the other choices, and confirmed that the tone of the passage does in fact warrant the use of such a strong statement.

Learnist: How to Interpret your GMAT Score

Your GMAT score is calculated using a complex algorithm — here’s what you need to know about the scores you’ll receive before and after the exam.

This video above from GMAT PrepNow gives you a basic idea how the GMAT scoring works. Notice the point it makes about CATs: an adaptive test changes based on your response. 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 GMAT is constantly recalculating the scaled score as the student progresses through the section to determine the precise ability of the test-taker.

It’s not the number of correct questions that matters most, but how hard the questions you answer correctly are! This is why you must challenge yourself with harder questions in your practice!

An official GMAT score report consists of four sections. There is 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).

Keep in mind: 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 standard error for the GMAT is +/- 30 points, meaning you have a significant advantage if you score 30 points higher than the average score of your dream school.

In this Kaplan video, you’ll see how the average GMAT score of all the top programs listed here is around 718. In order to be above par, a 750 score is required. This guarantees you a helpful push in your application (though GPA matters significantly as well).

That’s how you can evaluate your competitiveness for each school: look up the average GMAT score of accepted students, then add 30 points to it.

Get more tips for interpreting your GMAT score on Learnist!

Learnist: 8 Ways to Beef Up your GMAT Vocabulary

A strong vocabulary will help your Analytical Writing, Verbal, Integrated Reasoning, and even Quantitative accuracy! Here’s how to build yours from the ground up, and use it to break down the toughest GMAT questions.

You can ignore most of the challenging vocabulary on sentence corrections as long as you identify what part of speech each word is, and how it functions within the sentence.

To do this, you’ll need to spend some time with a solid English grammar review book. I recommend pairing a heavy-duty review book, like the Oxford Guide or those published by McGraw-Hill or Longman, with a “fun” book like Writer’s Express or English Grammar for Dummies. If you don’t have time to go through an entire book, this “English Grammar for Dummies Cheat Sheet” is a great overview!

It is much, MUCH easier to memorize synonyms for words than their full definitions. Start grouping words together mentally (and on paper) according to their meaning. For example, words like “pusillanimous,” “poltroonish,” and “timorous” might go on the “shy” list.

According to this “Word Group” blog from Kaplan, an easy way to learn these word groups is the “reverse flash card” method:

  1. Read the word group
  2. Write the heading on one side of the card
  3. Write only the words you recognize from the list on the back.

Learn more ways to beef Up your GMAT vocabulary on this Learnboard!

Learnist: How to Beat GMAT Critical Reasoning (even if you can’t tell Correlation from Causation)

LearnistThere are 41 questions on the GMAT Verbal section, and about a dozen of them will be Critical Reasoning problems: paragraphs that require you to dissect arguments and understand logic. Here’s how to conquer them with minimal fuss!

Step 1 – Cover the Basic by Going to the Source

The best place to start getting familiar with what “Critical Reasoning” looks like is on the official testmaker’s website: http://www.mba.com.

According to GMAC, the CR questions measure your ability to reason effectively in three areas:

  • Argument construction:  Questions of this type may ask you to recognize the basic structure of an argument, properly drawn conclusions, underlying assumptions, well-supported explanatory hypotheses, or parallels between structurally similar arguments.
  • Argument evaluation:  Questions of this type may ask you to analyze a given argument, recognize factors that would strengthen or weaken an argument, reasoning errors committed in making an argument, or aspects of the methods by which an argument proceeds.
  • Formulating and evaluating a plan of action:  Questions of this type may ask you to recognize the relative appropriateness, effectiveness, or efficiency of different plans of action; factors that would strengthen or weaken a proposed plan of action; or assumptions underlying a proposed plan of action.

Next, purchase the Official Guide on Amazon!

Step 2 – Learn what an “Argument” is (according to the GMAT, that is!)

Arguments have a tendency to follow predictable patterns of organization and are always comprised of a conclusion, premise (or evidence), and assumptions.

The conclusion and the evidence will be explicitly stated in the passage, while the assumptions will require you to sit and consider the author’s point of view. What needs to be true in order for the conclusion to be correct based on the given evidence?

Check out Steps 3-7 on this Learnboard to learn more about How to Beat GMAT Critical Reasoning!