My last two articles (part 1 and part 2) gave you some advanced tools to analyze deductive reasoning. Now it’s time to dive into the wonderful world of inductive reasoning, which appears much more often, especially in the following GMAT question types:

• Assumption
• Strengthen
• Weaken
• Evaluate
• Fill in the blank
• Identify the role
• Identify the overall reasoning
• Identify the conclusion
• Mimic the reasoning (sometimes)

According to Wikipedia:

“Inductive reasoning (as opposed to deductive reasoning) is reasoning in which the premises seek to supply strong evidence for (not absolute proof of) the truth of the conclusion. While the conclusion of a deductive argument is supposed to be certain, the truth of an inductive argument is supposed to be probable, based upon the evidence given.”

Therefore, in inductive arguments, conclusions are a matter of opinion, some more strongly supported than others.

Beyond the basics: P.O.S.E.

First, from class and your own study, you should be able to DECONSTRUCT arguments–in other words, identify the background, conclusion, premises, counterpoint, and counter premises of all inductive arguments. Our books cover that skill thoroughly if you need more work.

Next, you should learn to categorize each conclusion by type.

Fortunately, the GMAT uses only a few basic argument patterns, with similar assumptions and a limited number of ways to strengthen or weaken those assumptions. If you can spot and name those patterns, you’re well on your way to drastically improving your CR score.
Read more

My last article discussed the difference between inductive and deductive arguments. Today’s article will focus mostly on the rules of deductive arguments. I promise to nerd out on inductive reasoning in later articles.

Here’s a quick quiz on the difference between inductive and deductive logic: //www.thatquiz.org/tq/previewtest?F/Z/J/V/O3UL1355243858

To review: In a deductively “valid” argument, if all the premises are true, the conclusion must also be true, with 100% certainty. Luckily, on the GMAT, we should usually act as if the premises of an argument are true, especially when the question specifies, “the statements above are true.”

Deductive reasoning shows up most often on inference (aka “draw a conclusion”) questions and “mimic the reasoning” questions, but it often appears on other types of questions, and even on reading comprehension!

On inference questions, the correct answer will usually be deductively valid (or very very strong, inductively). An incorrect answer will be deductively invalid, with some significant probability that it could be false.

What follows are most of the formal rules of deductive reasoning (from a stack of logic textbooks I have on my shelf), with examples from the GMAT. For shorthand, I’ll label the arguments with a “P” for premise and a “C” for conclusion:

P) premise
P) premise
C) conclusion

Remember: these are not the same kind of conclusions (opinions) you’ll see on strengthen and weaken questions. Deductive conclusions are deductively “valid” facts that you can derive with 100% certainty from given premises.

EASY STUFF: Simplification/conjunction (“and” statements)

This is kind of a “duh” conclusion, but here goes: If two things are linked with an “and,” then you know each of them exist. Conversely, if two things exist, you can link them with an “and.”

Simplification:

P) A and B
C) Therefore, A

Conjunction:

P) A
P) B
C) Therefore, A and B

P) Bill is tall and was born in Texas.
P) Bill rides a motorcycle.
C) Therefore, Bill was born in Texas (simplification).
C) Therefore, at least one tall person named Bill was born in Texas and rides a motorcycle (conjunction).

CAUTION: Fallacies ahead!!

Don’t confuse “and” with “or.” (More about this later.) More importantly, don’t confuse “and” with causality, condition, or representativeness. Bill’s tallness probably has nothing to do with Texas, so keep an eye out for wrong answers that say, “Bill is tall because he was born in Texas” or “Most people from Texas ride motorcycles.”

MEDIUM STUFF: Disjunctive syllogism (“or” statements)

With “or” statements, if one thing is missing, the other must be true.

Valid conclusions:

P) A or B
P) not B (shorthand: ~B)
C) Therefore, A

P) We will go to the truck rally or to a Shakespeare play
P) We won’t go to the Shakespeare play.
C) Therefore, we will go to the truck rally.

CAUTION: Fallacies ahead!!

Unlike in the real world, “or” statements do not always imply mutual exclusivity, unless the argument explicitly says so. For example, in the above arguments, A and B might both be true; we might go to a play and go to the movies. Yes, really. A wrong answer might say “We went to a play, so we won’t go to the movies.” This error is called “affirming the disjunct.”

Invalid:

P) A or B
P) B
C) Not A

GMAT example:

To see this in action, check out your The Official Guide for GMAT Review 13th Edition, by GMAC®*, question 41. This argument opens with an implied “or” statement:

“Installing scrubbers in smokestacks and switching to cleaner-burning fuel are the two methods available to Northern Power…”

The author here incorrectly assumes that by using one method, Northern Power can’t use both methods at the same time. Question 51 does the same thing; discuss it in the comments below?

TOUGH STUFF: Fun with conditional statements

This is important! Keep a sharp eye out for statements that can be expressed conditionally and practice diagramming them. Look for key words such as “if,” “when,” “only,” and “require.”

I use the symbol “–>” to express an if/then relationship, and a “~” to express the word “not.” Use single letters or abbreviations to stand in for your elements.
Read more

Consistently and overwhelmingly, the evidence showed that experts are always made, not born. (“The Making of an Expert” by K. Anders Ericsson, Michael J. Prietula, and Edward T. Cokely, Harvard Business Review, July-August 2007)

Standardized test-taking is a skill–like winning a chess game, swinging a golf club, or playing a Bach concerto. And to master a skill, you need high-quality practice. Of course, the more content you know the better, but no matter how much you study for the GMAT, you won’t improve without practice. (I tried reading a book about snowboarding before my first time on the slopes, with predictably laughable results.) According to the scientific research, the most efficient and most effective kind of practice-the way Tiger Woods become the golfer he is today–is called “Deliberate Practice.”

If you spend time reading motivational blogs such as LifeHacker you’ll see many articles about “Deliberate Practice.” You may have even heard of whole books–Talent is Overrated by Geoffrey Colvin or Outliers by Malcolm Gladwell–about exceptional individuals such as Bobby Fischer and Tiger Woods. All those blogs, as well as Colvin and Gladwell, base their ideas on the research of K. Anders Ericsson, a Professor of Psychology at Florida State University and probably the world’s number-one expert on expertise. His good-news thesis can be summed up as follows:

New research shows that outstanding performance is the product of years of deliberate practice and coaching, not of any innate talent or skill. (Ericsson et al., “The Making of an Expert”)

First of all, relax. You may have heard about Ericsson’s 10,000 hour rule. Apparently, it takes about 10 years and 10,000 hours of “deliberate practice” to achieve true mastery. Yes, Tiger Woods, Bobby Fischer, Mozart, and other one-in-a-million people needed 10,000 hours to get to where they are. Luckily, the GMAT is much less difficult to master than golf, chess, or composition. Also, you’re not looking to be one in a million–at best 1 in 100 (a score of 760-800)–so you don’t need 10,000 hours. Maybe a few hundred hours, depending on how much you want to improve.

But what is “Deliberate Practice?”  And how do you apply it to the GMAT? At the end of this article, I’ve given you a few links, but to save you time, I’ve pulled my favorite Ericsson quotes and applied them to the GMAT:

1) Get motivated.

The most cited condition concerns the subjects’ motivation to attend to the task and exert effort to improve their performance. (“The Role of Deliberate Practice in the Acquisition of Expert Performance” by K. Anders Ericsson, Ralf Th. Krampe, and Clemens Tesch-Romer. Psychological Review. 1993, Vol. 100. No. 3)

Moving outside your traditional comfort zone of achievement requires substantial motivation and sacrifice, but it’s a necessary discipline. (Ericsson et al., “The Making of an Expert”)

If you’re reading this, you want a higher GMAT score. You’re already motivated. If you need more motivation, research schools. Take a diagnostic test and see how far you are from your dream school’s median. After that, the best way to get motivated is to sign up for the real GMAT a few months from now. (How many people don’t lose weight until they schedule the wedding or high school reunion?) Read more

On the GMAT, you may see a 3 to 5 ratio expressed in a variety of ways:

3:5
3 to 5
x/y = 3/5
5x = 3y (Yes, that’s the same as the other 3. Think about it.)

In the real world, we encounter ratios in drink recipes more often than anywhere else (3 parts vodka, 5 parts cranberry), perhaps explaining why–after drinks that strong–we forget how to handle them.

Keep in mind: ratios express a “part to part” relationship, whereas fractions and percentages express a “part to whole” relationship. So the fraction of the above drink is 3/8 vodka (or 37.5% of the whole). Either way, hold off on mixing that drink until after this post.

I like to set up ratios using a “ratio box.” The box is a variant on the “Unknown Multiplier” technique from page 65 of our FDPs book, but it’s a nice way to visually manage ratios without resorting to algebra.

Let’s take the beginning of a typical ratio question:

“The ratio of men to women in a class is 3:2…”

Instead of doing anything fancy with variables, I just set up a tracking chart:

From this point alone, I have sufficient information to answer a bunch of questions.

-What fraction of the students are men? (3/5)

-What percent of the students are women? (40%)

-What is the probability of choosing a man? (3/5)

-etc.

However, I have nowhere near enough information to answer anything about the REAL numbers of students in this class. Suppose the GMAT were to add a little more information:

“The ratio of men to women in a class is 3:2. If there are 35 students in the class…”

Now we can calculate almost everything about the real numbers of people. First, make a bigger box with 3 lines. The unfilled box looks like this:

Read more

You don’t have to pore over a Strategy Guide in order to prepare for the GMAT. Here are some things you can do in “normal” life to improve your overall test-taking skills.

1. Work out your brain. Learn to do Sudoku, simple crossword puzzles, or other brain-teasers (iPod applications, even). Do some brain exercise every day, especially in the morning. Choose word puzzles and logic games over action.
2. Work out–period. Study after study has shown that regular exercise, especially aerobic, has a profound effect on your cognitive performance. See Brain Rules by John Medina for more about this.
3. Beef up your analytical and logical skills. Read a good book about logical thinking (Being Logical by D.Q. McIreny).
4. Buy a book. Read it!

More about this: Other than intensive study and practice of test-specific strategies, the best way to improve your overall score on standardized tests is to read more for fun. If you don’t read every day, start with something light and entertaining”Harry Potter, romance novels, science fiction, Tom Clancy, or anything interesting to you. Keep the book with you and read whenever you have a spare 5 minutes. Eventually, move on to good contemporary non-fiction, which is closer to what you’ll see on the test itself.

Read more