Archives For Critical Reasoning

gmat-Advanced-Critical-ReasoningMy 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.
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gmat-advanced-critical-reasoning-2
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: http://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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critical-reasoningWe’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).

Screen Shot 2013-11-25 at 5.03.55 PM

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

Screen Shot 2013-11-25 at 5.10.38 PM

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.

critical-reasoningLast time, we talked about Fill in the Blank CR questions: what are they and how do we tackle them efficiently? If you haven’t already read that article, go ahead and do so.

Then, come back here and test your new-found skills on this GMATPrep© problem (it’s from the two free exams). 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.)

“Which of the following best completes the argument?

“A new machine for harvesting corn will allow rows to be planted only fifteen inches apart, instead of the usual thirty inches. Corn planted this closely will produce lower yields per plant. Nevertheless, the new machine will allow corn growers to double their profits per acre because ________________

“(A) with the closer spacing of the rows, the growing corn plants will quickly form a dense canopy of leaves, which will, by shading the ground, minimize the need for costly weed control and irrigation
“(B) with the closer spacing of the rows, corn plants will be forced to grow taller because of increased competition for sunlight from neighboring corn plants
“(C) with the larger number of plants growing per acre, more fertilizer will be required
“(D) with the spacing between rows cut by half, the number of plants grown per acre will almost double
“(E) with the closer spacing of the rows, the acreage on which corn is planted will be utilized much more intensively than it was before, requiring more frequent fallow years in which corn fields are left unplanted”

Step 1: Identify the Question

The blank line tell us that we have an argument in the “complete the passage” format.
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critical-reasoningI was talking to a student today about Complete the Passage CR arguments (people also call these the Fill in the Blank questions). The student was struggling with these and talking about them as though they were their own category. The problem: they’re not actually a separate category at all!

Try this GMATPrep© problem out (it’s from the free set that comes with the software) and then we’ll talk about it. 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.)

“Which of the following best completes the passage below?

“People buy prestige when they buy a premium product. They want to be associated with something special. Mass-marketing techniques and price reduction strategies should not be used because ________________

“(A) affluent purchasers currently represent a shrinking portion of the population of all purchasers
“(B) continued sales depend directly on the maintenance of an aura of exclusivity
“(C) purchasers of premium products are concerned with the quality as well as with the price of the products
“(D) expansion of the market niche to include a broader spectrum of consumers will increase profits
“(E) manufacturing a premium brand is not necessarily more costly than manufacturing a standard brand of the same product”

Step 1: Identify the Question

The blank line immediately leaps to eye of course: as soon as you see that, you know you have an argument in the “complete the passage” format.

What kind of question type is it? Actually these fall into one of the regular types that you already know: Strengthen, Weaken, Find the Assumption, Inference, and so on. The trick is that it’s a bit harder to tell which type.

The majority of Complete the Passage questions are Strengthen. The second most common category is Find the Assumption. Typically, if you see the word because or since right before the underline (as in this problem), then you probably have a Strengthen question. The word because (or since) indicates that the correct answer will add a piece of evidence to support some statement. You’ll need to read the argument to be sure, but you can have a pretty strong hunch.

Step 2: Deconstruct the Argument

This is likely a strengthen question, so it should contain a conclusion.

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: S = strengthen; at first I put a question mark next to it because I wasn’t 100% sure until I finished the argument.)

Screen Shot 2013-11-25 at 2.19.52 PM

If the conclusion is NOT to use mass-marketing techniques and price reduction strategies because of some reason, then that reason must support that conclusion. This is, indeed, a Strengthen question.

Step 3: State the Goal

The goal on Strengthen questions is to find a new piece of information that makes the conclusion at least a little more likely to be valid. I’m trying to validate the idea that you should NOT use certain strategies. (Note: in Complete the Passage format, sometimes the correct answer won’t really be new; it will mostly just restate something that the argument already said. This is acceptable as long as it strengthens!)

Why not? The first two sentences said that premium products are all about prestige and “something special.” If you’re trying to sell premium products, then, mass-market techniques probably aren’t going to make people feel “special.” Likewise, a reduction in price doesn’t scream “premium product!” We expect premium products to cost more and we don’t expect everyone in the world to have them.

I’m going to keep that in mind while I examine the answers!

Work from Wrong to Right

Screen Shot 2013-11-25 at 2.57.16 PM

The correct answer is (B).

Note that answers (A) and (D) both seem to go along with the idea that we might want to use mass-marketing techniques or price-reduction strategies. Both are trap answers designed to catch someone who didn’t notice or forgot that the conclusion says these strategies should NOT be used.

Looking for more help on Critical Reasoning? Check out the Master Resource List for Critical Reasoning.

Take-aways for Complete the Passage formats:

(1) These are not a separate question type. A “complete the passage” question falls into one of the same categories as all other questions; you have to figure out which it is.

(2) Most often, these questions are Strengthen (as in the above case) or Find the Assumption. If you see the word because or since right before the underline, you probably have a Strengthen question. If you see something else, then you may have an Assumption question instead.

(3) As with any CR question, the key is to identify the type of question and follow the standard process from there!

 

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

Is that a comparison?

One way to classify conclusions on GMAT Critical Reasoning conclusions is comparative versus absolute.  Why should you care about this classification?  Because this distinction can be very helpful in eliminating wrong answers and finding right answer.

A comparative conclusion will make a comparison between two or more groups.

Car A is better family car than Car B.

An absolute conclusion will just express an opinion about one specific topic or situation.

Therefore, A monorail should not be installed in Town C’s central district.

As a start, let’s get used to classifying conclusions as absolute or comparative.  If the conclusion is comparative, identify the two groups being compared.

1) Therefore, children in the United States who spend at least two hours a day outdoors are less likely to be obese than other children.

2) Thus, Springfield’s recycling program is likely to achieve its aim.

3) For these reasons, isolationism should not be considered a viable trade strategy.

4) The service sector will become more important to Caloda’s economy in the future.

5) Brand D is the best brand of vacuum cleaner available.

(See bottom of this post for answers)

Now that you are comfortable identifying different types of conclusions, we will consider how this classification will help you find the right answer. In many critical reason question types, your job in finding the answer is to influence the conclusion (strengthen the conclusion, weaken the conclusion, find the assumption).  Let’s consider answer choices that are most likely to influence these different types of conclusions. Continue Reading…

gmat breaking bad test

In honor of the final season of Breaking Bad, we decided to put together our ultimate Breaking Bad GMAT quiz. Those of you who fall in the overlapping section of the “Breaking Bad Fan” “GMAT student” Venn diagram should test your skills below… yo!

1. Data Sufficiency

Does x+4 = Walter White?

(1) x+4 is the danger
(2) x+4 is the one who knocks

A. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient
B. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D. EACH statement ALONE is sufficient
E. Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed

2. Discrete Quant

walter white's roof pizza
The front portion of Walter White’s Roof is a 7 ‘ by 15’ rectangle. If the diameter of a pizza is 22”, what is the approximate area of the shaded region of this diagram?

A. 13,600 inches sq.
B. 14,740 inches sq.
C. 15,120 inches sq.
D. 15,500 inches sq.
E. 16,640 inches sq.

3. Critical Reasoning

Today, Walter White will cook 100 pounds of methamphetamine.

This argument is flawed primarily because:

A. Cooking methamphetamine presents a moral dilemma for Walter White.
B. Walter White has to prioritize the needs of his wife and children and be a better father.
C. Walter has already paid for his cancer treatment and no longer needs to cook methamphetamine.
D. There is a fly in the laboratory.
E. He was told not to cook that day and is obeying his instructions.

4. Critical Reasoning

Hank’s collection of rocks includes over 400 different items. Hank’s rock collection is clearly the most impressive in New Mexico.

This argument is flawed primarily because:

A. Rock collections are not judged by the total number of rocks but by the rarity of each item included.
B. Rock collections are not impressive to anyone.
C. Hank’s rock collection is a metaphor and therefore cannot be judged against other rock collections.
D. Hank’s wife stole most of the rocks and it is therefore ineligible for any superlatives.
E. They aren’t rocks, they are minerals.

5. Discrete Quant

Walter Junior eats 3 eggs for breakfast every morning. Given that Walter Junior never misses breakfast, how many eggs does Walter Junior consume in March?

A. 60
B. 74
C. 82
D. 93
E. 107

 

Answers are after the jump…

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gmat critical reasoning boldfaceRecently, we published the Master Resource List for Critical Reasoning, but I had to link to an older version of a Boldface explanation because I hadn’t yet written an article using the new process. I’m remedying that gap now. (Note: technically, these are called Describe the Role questions.)

Try this problem out! Give yourself about 2 minutes (though it’s okay to stretch to 2.5 minutes on a long one like this as long as you are making progress.)

Consumer advocate: It is generally true, at least in this state, that lawyers who advertise a specific service charge less for that service than lawyers who do not advertise. It is also true that each time restrictions on the advertising of legal services have been eliminated, the number of lawyers advertising their services has increased and legal costs to consumers have declined in consequence. However, eliminating the state requirement that legal advertisements must specify fees for specific services would almost certainly increase rather than further reduce consumers’ legal costs. Lawyers would no longer have an incentive to lower their fees when they begin advertising and if no longer required to specify fee arrangements, many lawyers who now advertise would increase their fees.

In the consumer advocate’s argument, the two portions in boldface play which of the following roles?

(A) The first is a generalization that the consumer advocate accepts as true; the second is presented as a consequence that follows from the truth of that generalization.

(B) The first is a pattern of cause and effect that the consumer advocate argues will be repeated in the case at issue; the second acknowledges a circumstance in which that pattern would not hold.

(C) The first is a pattern of cause and effect that the consumer advocate predicts will not hold in the case at issue; the second offers a consideration in support of that prediction.

(D) The first is evidence that the consumer advocate offers in support of a certain prediction; the second is that prediction.

(E) The first acknowledges a consideration that weighs against the main position that the consumer advocate defends; the second is that position.

Step 1: Identify the Question

The argument itself contains the most common clue for a Describe the Role question: boldface font in the text. This clue doesn’t always exist but it is usually there. The question stem also signals the type by asking for the role played by the two portions in boldface.

Step 2: Deconstruct the Argument

All right, this is a Role question. The argument will contain a conclusion, and the boldface portions will relate to the conclusion in one of three broad ways:

  1. The boldface text could be the conclusion.
  2. The boldface text could support the conclusion.
  3. The boldface text could be anything else (including neutral background), though most commonly it will be either  counter-premise or a counter-conclusion.

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