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.
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We’ve been on a CR kick lately! In the first two parts of this series, we talked about how to tackle Fill in the Blank and Complete the Passage questions. This time, I’ve got something different for you: a question that looks very familiar at first glance but turns a bit… well, weird.

Let’s try it before I say anything more. This GMATPrep© problem is from the two free exams that come with the GMATPrep software. Give yourself about 2 minutes (though it’s okay to stretch to 2.5 minutes on a CR as long as you are making progress.)

“On of the limiting factors in human physical performance is the amount of oxygen that is absorbed by muscles from the bloodstream. Accordingly, entrepreneurs have begun selling at gymnasiums and health clubs bottles of drinking water, labeled “SuperOXY,” that has extra oxygen dissolved in the water. Such water would be useless in improving physical performance, however, since the amount of oxygen in the blood of someone who is exercising is already more than the muscle cells can absorb.

Which of the following, if true, would serve the same function in the argument as the statement in boldface?

“(A) world-class athletes turn in record performances without such water
“(B) frequent physical exercise increases the body’s ability to take in and use oxygen
“(C) the only way to get oxygen into the bloodstream so that it can be absorbed by the muscles is through the lungs
“(D) lack of oxygen is not the only factor limiting human physical performance
“(E) the water lost in exercising can be replaced with ordinary tap water”

Step 1: Identify the Question

The boldface font is immediately obvious, of course. Boldface denotes a Describe the Role question.

The question stem does have one little idiosyncrasy, though: it asks what answer would serve the same function. Normally, Role questions ask what function the boldface statement plays in the argument. The question stem also contains “if true” wording, which we normally see on Strengthen, Weaken, or Discrepancy (paradox) questions.

Glance at the answers. Notice anything? This is not what Role answers typically look like! Usually they say something such as “The statement provides evidence supporting the author’s claim” or similar.

What’s going on here? Read the argument.

Step 2: Deconstruct the Argument

Here’s what I thought and wrote while I did the problem. Your own thought process won’t be exactly the same as mine and, of course, your notes will probably look quite different, since we all have our own ways of abbreviating things. (Note: R = role; note that I put a question mark next to it because I wasn’t 100% sure what was actually going on).

So back to that weird question stem. If this were just a straight Role question, then what would the answer be? The boldface statement is support for the conclusion; it’s a premise.

But what’s the goal for this question?

Step 3: State the Goal

The answers don’t describe the existing boldface statement. Rather, they contain new facts that we’re supposed to accept as true. Further, the question asked us to find an answer that “would serve the same function” as the original statement.

What function did the original statement serve? Aha! The original statement served as a premise to support the conclusion. So we need to find another statement that serves that same purpose.

Will it support the conclusion in exactly the same way? I’m really not sure. (Seriously! When I first saw this question, I didn’t know!) So I’m going to keep an open mind and look for anything that could support the conclusion in general.

Work from Wrong to Right

The correct answer is (C).

Interesting. We just learned something new. Most Describe the Role (or Boldface) questions ask us to describe the role of the given statement. We might be asked, though, to demonstrate our knowledge of the role by finding a different, completely new statement that serves the same role as the original statement in the argument.

What do we have to do? We have to “decode” the original statement (in the above case, we had a premise supporting the conclusion) and then we have to find another statement that could also serve as a premise.

That new premise might be really different from the original premise. In this problem, the original premise focused on the oxygen already in our blood. The new premise, answer (C), provided a different piece of the puzzle: we have to take oxygen in through our lungs in order to get that oxygen into the bloodstream. Either piece of information serves to support the idea that OXY is useless, but each does so in different ways.

Take-aways for “Same Function As” Role Questions:

(1) The standard task on role questions is to describe the role of the statement given in the argument.

(2) You might see a variation on this standard task: you may be asked to find a new statement that plays the same role as the original.

(3) This new statement may discuss a different aspect of the argument. That’s perfectly all right as long as the statement overall plays the same role as the original boldface statement.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

Some interesting —and alarming—articles have been making the rounds lately, following on the heels of an academic study published by professors at the University of Akron and Cleveland State University. The more reputable articles report such sweeping conclusions that I actually wondered whether the journalists got it wrong, so I went to the source (I can link only to the abstract here, but I did read the full study).

When I read the study’s methodology, I knew I had my next article topic. We’re going to test our Critical Reasoning (CR) skills on an actual academic study! You might have to do something similar in business school (admittedly with a business case, not an academic study), so let’s test your b-school readiness now!

(Note: I refer to the “more reputable articles” because some blogs have picked this up and publishing under headlines such as “Is the GMAT the root of all evil?” As much as you may hate studying for this test, I think we can agree that this characterization is a bit over the top. : ) )

Correlation vs. Causation

We need to define a couple of terms first. You may already have learned about correlation and causation in your CR studies; here’s a refresher.

Correlation: two phenomena tend to occur or appear at the same time or in conjunction with one another

Causation: one phenomenon causes another phenomenon

Correlation does not imply causation. One of two correlated phenomena could cause the other but those two things could also have absolutely no causation between them. Alternatively, the two things could both be caused by a third thing. The two things could even cause each other! (Predator-prey dynamics are an example of this kind of two-way dependency.)

For example, have you ever noticed how, when the ground is wet, people often seem to be carrying around umbrellas? Those two phenomena are correlated. Which one causes the other? Read more

Going for 90^th+ percentile on verbal? Chances are you’ve spent most of your Critical Reasoning study time focused on the major question types, and that is a good place to start. If you’re going for a very high verbal score, though, then you’ll also need to tackle the minor question types.

That’s what we’re going to do today; below is a GMATPrep CR problem. Give yourself about 2 minutes to do this problem.

In Asia, where palm trees are non-native, the trees’ flowers have traditionally been pollinated by hand, which has kept palm fruit productivity unnaturally low. When weevils known to be efficient pollinators of palm flowers were introduced into Asia in 1980, palm fruit productivity increased”by up to 50 percent in some areas”but then decreased sharply in 1984.

Which of the following statements, if true, would best explain the 1984 decrease in productivity?

(A) Prices for palm fruit fell between 1980 and 1984 following the rise in production and a concurrent fall in demand.

(B) Imported trees are often more productive than native trees because the imported ones have left behind their pests and diseases in their native lands.

(C) Rapid increases in productivity tend to deplete trees of nutrients needed for the development of the fruit-producing female flowers.

(D) The weevil population in Asia remained at approximately the same level between 1980 and 1984.

(E) Prior to 1980 another species of insect pollinated the Asian palm trees, but not as efficiently as the species of weevil that was introduced in 1980.

(Note: if you aren’t yet familiar with the 4-step process for answering CR questions, take a look at this article.)

Step 1: Identify the Question

This question stem contains the classic clues for an Explain a Discrepancy question. These questions, like Strengthen and Weaken questions, typically include the words if true (or the equivalent). Further, the question literally asks what would explain something.

Step 2: Deconstruct the Argument

All right, this is a Discrepancy question. The argument won’t contain a conclusion. It’ll contain some facts, at least one of which is surprising in some way. It won’t fit with the rest of the information.

Here’s what I thought and wrote while I did the problem. Your own thought process won’t be exactly the same as mine and, of course, your notes will probably look quite different, since we all have our own ways of abbreviating things. (Note: ED = Explain Discrepancy)

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Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.

Which Critical Reasoning question type drives you crazy? Boldface? Find the Assumption? Inference?

I’ve put together what I’m calling the Master Resource List for Critical Reasoning. A couple of disclaimers. First, this list includes only free resources, no paid ones. There are a lot of good resources out there that cost some money—they’re just not on this list!

Second, this list for Critical Reasoning is limited to my own articles. I’m not trying to claim that only my articles are good enough to make such a list—far from it. I’m most familiar with my own articles, so that’s what I’m using. (And, okay, I will admit that I think the Manhattan Prep Critical Reasoning process is the best one out there. But I’m biased. ?) Read more

Many a true word is said in jest.—I don’t know, but I heard it from my mother.

I think that Critical Reasoning is my favorite part of the exam because it is the purest of the pure.  I’ve written before that the GMAT is an aptitude test rather than a knowledge test.  On the simplest level, in both the quant and the verbal, the exam tests a logic system: be specific, don’t assume, and don’t rationalize.  Nowhere is this more true than in Critical Reasoning—there is no mathematical foundation work nor are there grammar rules.  As Gertrude Stein used to say, There is no there, there.  Of course, she was talking about Oakland. . .fill in your own joke.  When I’m being* mean to students, I say, If you know what all the words mean, you should get them all right.

But students don’t get them all right.  Even those who know what all the words mean.  Why is that?  Because people think.  They assume, they rationalize, and they inject opinions.  Why is this bad?  Because it’s a game.  Critical Reasoning doesn’t take place in reality.  Here’s an analogy I thought up all by myself, so it isn’t in the Strategy Guide: Critical Reasoning bears the same relationship to reality that Monopoly does.  When you play Monopoly, you don’t think about how reasonable free parking or building hotels is, you exploit the rules.  It’s the same thing.  A lot of OG arguments involve medical issues, but you hardly ever care whether people live or die because that’s usually not the conclusion.   Play the game.

As a by the way, if students struggle with the CR, it’s often half of their trouble in the quant.  Folks are not specific; they read the question or the given incorrectly.  And they don’t recognize the types and patterns.  In other words, they don’t play that game.  However, folks fail to notice these mistakes because they are too consumed with worry about their math foundations.  Conversely, engineers with strong foundations also suffer here, especially in the DS because they try to use brute mathematical force instead of playing the game.  It is a behavioral problem.  People don’t do; they think.  Don’t think—much like in life, it only gets you into trouble.
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Recently, I published an article challenging those going for a 750+ to answer a certain Quant question in 30 seconds. I received a lot of positive feedback about that article—and requests for more of the same.

I’m happy to oblige: here’s a GMATPrep CR problem. The normal timeframe is about 2 minutes—but if you’re going for a 750+, you’d need to be able to answer something like this much more quickly. Read more

Find the Assumption questions are very common Critical Reasoning question types. If you don’t yet know the general process for tackling Critical Reasoning problems, learn how before you keep reading this article.

Ready to try a question? Set your timer for 2 minutes and try this GMATPrep problem:

In a study conducted in Canada, servers in various restaurants wrote Thank you on randomly selected bills before presenting the bills to their customers. Tips on these bills were an average of three percentage points higher than tips on bills without the message. Therefore, if servers in Canada regularly wrote Thank you on restaurant bills, their average income from tips would be significantly higher than it otherwise would have been.

Which of the following is an assumption on which the argument relies?

(A) The Thank you messages would have the same impact on regular patrons of a restaurant as they would on occasional patrons of the same restaurant.

(B) Regularly seeing Thank you written on their bills would not lead restaurant patrons to revert to their earlier tipping habits.

(C) The written Thank you reminds restaurant patrons that tips constitute a significant part of the income of many food servers.

(D) The rate at which people tip food servers in Canada does not vary with how expensive a restaurant is.

(E) Virtually all patrons of the Canadian restaurants in the study who were given a bill with Thank you written on it left a larger tip than they otherwise would have.

Got your answer? Let’s start going through this one!

Step 1: Identify the Question

The question stem contains the word assumption, which is a pretty good clue that this is a Find the Assumption (FA) question. This question type always contains a conclusion and I know it’s important to find that conclusion. Also, if I can, I’m going to brainstorm any assumptions I can think of without taking too much time.
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A colleague here at Manhattan GMAT forwarded me this infographic about the value (or lack thereof) of an MBA. Though the author doesn’t explicitly say so, the statistics she chose to display indicate that she believes an MBA is by and large overvalued.

The great irony here, of course, is that the training you get as an MBA is exactly the training that sharpens your ability to think critically about arguments like this one. In fact, that’s what the GMAT actually tests with its Critical Reasoning section. Just to demonstrate, I’d like to break down this infographic from top to bottom, using the same strategy I teach my students: pointing out the (flawed) assumptions necessary to conclude that an MBA is overvalued.

Premise: The cost of an MBA program including expenses is $120,000.

Assumption #1: Students actually pay all of that $120,000.

Attack: I’d estimate that around half of my MBA classmates had some scholarship or corporate support that significantly defrayed their cost. This, by the way, is probably the most underrated reason to ace your GMAT “ a high GMAT score can open the door to many merit-based scholarships.

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We’ve talked about various types of Assumption Family questions in the past (find the assumption, strengthen, weaken, and evaluate the conclusion), but we haven’t yet tackled a Flaw question. This is the least frequently tested of the 5 Assumption Family question types, so you can ignore this type if you aren’t looking for an extra-high score. If you do want an 85^th+ percentile verbal score, though, then you have to make sure you know how to tackle Flaw questions.

If you haven’t yet, read this article before we try our GMATPrep problem. Then set your timer for 2 minutes and go!

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