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How to Rock Sequences on the GRE

On the GRE, there are two types of sequences to watch out for: arithmetic, and geometric. An arithmetic sequence occurs when there is a constant difference between terms. For example, in a sequence of 3, 5, 7, 9…, then the difference is +2. In a geometric sequence, there is a constant ratio and not a constant difference.

The common ratio is found by dividing the 1st term into the 2nd term. For example, in a sequence of 2, 4, 8, 16…, the ratio is 2, since each term is multiplied by 2 to get the next term.

The concept of sequences is fairly simple, but what to do when a question asks for an impossibly high term, such as the 149th term? There isn’t enough time to write the sequence out that far, so we’d use one of the following formulas:

For Arithmetic: an = a1 + (n – 1)d

For Geometric: an = a1 * r(n-1)

In these equations, an = nth term, a1 = first term in the sequence, d = difference, r = ratio, and n = the number of the term you want to find. For example, if we were asked to find the 33rd term in the geometric sequence above, we would plug in as follows:

an = 2 * 2(33 – 1)
an = 233

Let’s look at a practice question:

1. In the sequence of numbers, a1, a2, a3, a4, a5, each number after the first is 5 times the preceding number. If a4 – a1 is 93, what is the value of a1?
For this question, it is best to choose simple numbers to see the pattern. If a1 is 1, then we know that a2 = 5, a3 = 25 and a4 = 125, so we know that a4 will be 5*5*5 or 125 times the value a1,. No matter what we choose as a1, a4 will always be 125 times greater than a1. We need to find a value such that 125x – x = 93

124x = 93
x = 3/4

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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!

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: Free Passages to Practice GMAT Reading

If you’ve used up the Reading passages in the GMAT Official Guide and don’t have the money for more books or a prep course, here’s where to find reliable GMAT RC practice material online!

In this video, BeatTheGMAT.com expert Dana walks through an example of how you can break down one of the toughest question types on the GMAT–the Science RC passage. Since Science RC passages are relatively uncommon, it’s great to see one here! Use this video as a warm-up before diving into the remaining resources.

If you haven’t downloaded this free GMATPrep™® software from GMAC, it’s a MUST. It’s free, contains 90 questions and 2 full-length adaptive practice tests, and its RC passages are the closest you’ll find to the actual questions on the official GMAT.

Once you’ve taken the two GMATPrep CATs and thoroughly reviewed them, be sure to download this comprehensive collection of ALL the Reading Comp passages and questions from GMATPrep. You may have seen many of them on your practice CATs, but there’s definitely going to be some new ones!

This is a great way to exhaust more official material with forking over the cash for the GMAT Packs sold on MBA.com.

Here’s the answer key to the 126 GMAT Prep Reading Comp questions found in the previous document. Though explanations aren’t provided, most of these questions have been discussed on various forums and explanations are easily found by typing the question-step into Google. Enjoy!

Check out more free GMAT practice reading passages on Learnist!

Learnist: Best Reading Strategies for the SAT

The Critical Reading section of the SAT consists of approx 70% passage-based questions. Remember the SAT test booklet is your scratch paper – don’t be afraid to use it to take notes on the passages as you read!

To focus your brain, it is especially important to take notes as you read and practice what is known as “active reading.” This video from Kaplan describes a system of notes you might find helpful called a “Passage Map.” A Passage Map helps you track:

  • Main Ideas
  • Beliefs and Opinions
  • Details

Even if you don’t want to write a full Passage Map, make sure you at least underline the main idea of the paragraph and circle any relevant details. It will be much easier to get the questions correct later on if you thoroughly understood the passage the 1st time through. Never skim!