800Score GMAT Guide
Critical Reasoning
Section 1:  Introduction
Section 2:  Argument Structure
Section 3:  Reasoning Skills
Section 4:  Question Types
Section 5:  Advanced Question Types

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Section 1: Introduction

In this chapter, you'll learn how to think critically and use the rules of logic to find errors in reasoning, such as circular argumentation and faulty analogy. You will learn how to quickly identify logical flaws in an argument, evaluate an argument’s strength and determine its validity.

This chapter will help you with the 12-14 Critical Reasoning questions in the Verbal section; many of these strategies will also be useful for the Analysis of Argument essay.

Critical Reasoning questions consist of a passage, a stem, and the answer choices.

Let's look at an example:

 The postal service of Fairfield is badly mismanaged. Thirty years ago first-class letter delivery cost only three cents. The price has increased sevenfold since then, but the reliability and speed have declined. This is the passage, what you read to start the question. All of the following would tend to weaken the argument above EXCEPT: This is the stem, which sets up the question. Be on the lookout for words like "EXCEPT." The volume of mail handled by the postal service has increased dramatically during the last thirty years. Unprecedented increases in the cost of fuel for trucks and planes have put severe upward pressures on postal delivery costs. Private delivery services usually charge more than the postal service does for comparable delivery services. The average delivery time for a first-class letter three decades ago was slightly longer than it is today. The average level of consumer prices overall has increased fourfold during the last thirty years These are the answer choices. Most of these should be easy to eliminate.

800score's Critical Reasoning Techniques are easy-to-use and intuitive. Use this six-step method to attack critical reasoning questions:

Step 1: Identify the argument
Read the passage and try to identify the premise and conclusion of the argument. Is it an argument? What is going on? Do any assumptions pop out? Put it into your own words. Read critical reading questions actively and examine the implications of every sentence.

Step 2: Read the stem
Find out specifically what the question is asking for and apply it to the question. Watch out for words like “EXCEPT.”

Step 3: Develop a basic idea of the right answer
If necessary, re-read the passage to examine it more carefully. Put a general idea of the right answer into your own words. Make sure it corresponds to what the stem wants.

Don't overdo this step. Remember that one of the five choices must be right, so they will provide hints about the right answer. If you hit a wall, the answer choices can sometimes provide clues; just don't jump prematurely to the answers, which can make you susceptible to trap choices.

Step 4: Move on to the answer choices.
If you have an idea of what the answer could be, start running through the answer choices and you'll probably find something similar.

Step 5: Process of Elimination (POE)
Eliminate choices and then pick the best answer. Choice A may be a good answer, but choice (E) may be better. This means that you should read all the choices before making a decision. Usually, you can narrow it down to one or two options. As a rule, your first strong hunch is usually the right answer.

Step 6: Double-Check
Unless you are running short on time, take a moment to double-check your answer.

 The "Stem First" Controversy If you noticed above, we tell you to read the passage first and then the stem second in a natural order. Many test prep companies tell you to read the stem first, then the passage. This does make some sense: if you read the stem first you can then read the passage with an eye toward what the question wants. However, there are several problems with this "stem first" technique: Advanced students can read the passage and have a rough idea what the question wants before even getting to the stem. If you have taken hundreds of practice questions, you can see the patterns. It is distracting to have to bounce from the stem back up to the passage. You are putting the stem into short-term memory. This process can be awkward and distracting because you are asking your brain to hold this bit of data while trying to process a complex argument. Obviously, you are the test taker and the decision is yours to make. Try both approaches and see which works best for you.

Section 2: Argument Structure

Is the text an argument? In this case, an argument doesn't mean a dispute or controversy. It is an attempt to prove one thing by citing something else. It is an attempt to show that something is true, or probably true, by presenting some reason or evidence that supports it.

You see arguments everyday in advertisements, in which companies are making arguments to persuade you to buy their product. For example:

A GMAT course will teach you how to attack the common GMAT question types so that you can beat the GMAT. You should therefore buy a GMAT course.

In many of the Critical Reasoning questions, there will be a gap between the premise and the conclusion – the assumptions.

Premise(s) + Assumptions = Conclusions (inferences)

 Target: Assumptions On many critical reasoning questions, the question will turn on assumptions. Premises (evidence) on the GMAT will never be false. So you don't have to worry about that. The conclusion is often stated, so the whole game usually revolves around evaluating the assumptions.

Let's look at this argument to buy a GMAT course.

A GMAT course will teach you how to attack the common GMAT question types so that you can beat the GMAT. You should therefore buy a GMAT course.

Premise: A GMAT course can teach you how to attack the common GMAT question types in order to improve your score.
Conclusion: You should therefore buy a GMAT course.

There are some "assumptions" or "gaps" in this statement:

1. A GMAT course can teach you common question types, but not all question types. A GMAT course can try to prepare you, but obviously a course can't prepare you for every question that appears on the GMAT.
2. The GMAT comes up with new questions all the time, so it is possible that you can come across a question that no one has seen before.
3. A GMAT course may have the content, but will you have the willpower to use it?

 Valid vs. True The GMAT is looking for valid arguments, not necessarily true ones. A valid argument follows from its premises. An ostrich is a bird. All birds fly. Conclusion: an ostrich can fly. The above argument is valid, but not true. Try not to argue or bring in external knowledge to the GMAT. You are just looking for valid arguments based on the information that they have given you. Why are flying ostriches so important to skilled critical thinking? In this chapter we regularly discuss absurd things. This isn't entirely for humorous effect. Skilled critical thinkers often employ the argument ad absurdum, which means taking a logical argument and stretching it to its breaking point to determine its validity. In this case, we use flying ostriches to show that arguments may be true but not valid.

Section 2-1: Argument Structure – The Assumption Hunt

When you assume, you make an ass out of u and me
- Felix Unger, The Odd Couple

Unstated assumptions are a breeding ground for faulty logic. The best, most effective arguments will state their assumptions and not leave them out. Searching for unstated assumptions is a key aspect of testing arguments for flaws in reasoning.

We call this process the "Assumption Hunt." Many GMAT questions contain hidden assumptions, and it's your job to find them. You will need to use this "Assumption Hunt" on the critical reasoning and AWA Analysis of Argument essay.

Since assumptions lie between the premises and conclusions, we first need to find the premises and the conclusion. The GMAT is usually nice enough to use set "red flag" phrases to help you identify these parts of an argument.

 How do you identify premises and conclusions? Reliable clues are provided by certain key words, which are often used to identify premises and conclusions. Here are some of the most common: Premise indicators: The reason is that premises are indicated by keywords. Because premises are indicated by keywords. Since premises are indicated by keywords. As premises are indicated by keywords. On the basis of premises indicated by keywords. It follows from premises indicated by keywords. In view of premises indicated by keywords. We may infer from premises indicated by keywords. Conclusion indicators: Accordingly, conclusions are easy to find. Clearly, conclusions are easy to find. Consequently, conclusions are easy to find. This indicates that conclusions are easy to find. Hence, conclusions are easy to find. It follows that conclusions are easy to find. So, conclusions are easy to find. Therefore, conclusions are easy to find. This indicates that conclusions are easy to find. This shows that conclusions are easy to find. Thus, conclusions are easy to find. We may infer that conclusions are easy to find.

Section 2-2: Argument Structure – Rewording and Evaluating

Now that you know how to break down arguments into premises, assumptions, and conclusions, you are able to translate a passage into your own words. Usually the passage describes something very simple in a complicated manner. Putting it in your own words helps you understand what the passage means.

Let’s look at the following argument:

Apartment building owners argue that rent control should be abolished. Although they acknowledge that, in the short term, rents would increase, they argue that the long-term effect would be a reduction in rents. This is because rent increases would lead to greater profitability. Higher profits would lead to increased apartment construction. Increased apartment construction would then lead to a greater supply of residences, and lower prices would result because potential apartment residents would have a better selection. Thus, abolishing rent control would ultimately reduce prices.

To make that complicated argument easy to understand, try breaking it down into your own words:

 Premise #1 Abolishing rent control will increase the supply of housing. Premise #2 Greater supply leads to lower prices. Conclusion Abolishing rent control leads to lower rents. Analysis This is a supply/demand argument. Assumptions The marketplace for housing is flexible. New construction will more than keep pace with any increases in demand for apartments. New construction won't result in a gentrification of neighborhoods, leading to a rise in average rent levels.

More than simply "putting it in your own words," you need to evaluate an argument's persuasiveness. The more unstated assumptions or logical flaws there are, the weaker the argument will be.

 GMAT arguments usually aren't sweeping On the GMAT, arguments are short and have assumptions, so sweeping statements aren't likely to be correct. All sweeping statements should be noticed. Always notice sweeping statements. Never ignore sweeping keywords. None of these keywords should be ignored. Only ignore sweeping statements at your peril. The problem with these sweeping statements is that it takes only a single exception to disprove the argument. All business school students just want a higher salary! Sounds like someone got a lousy score on the GMAT? But, if we use a qualifier, that sweeping generalization suddenly becomes plausible: Some business school students just want a higher salary. Qualifiers: Some Usually Sometimes Probably Most Often These words soften an argument and make it harder to refute because it can withstand some exceptions.

Section 2-3: Argument Structure – Finding the Right Answer

When you finish reading the passage and the stem and you have analyzed everything using the preceding techniques, you usually can come up with a pre-phrase of the right answer, before even getting to the answer choices. With practice, you'll have a reliable notion of what the question wants before considering the answer choices.

Test takers should not be discouraged, however, if they cannot come up with a pre-phrase. Some questions are difficult, and an immediate answer will not always jump out at you. Often, reading the answer choices will give you hints about what the argument is about – after all, one of those five choices must be right. But be careful not to fall for trap answer choices.

Eliminate wrong answers and then select the right one.

Coming up with the right pre-phrase of the answer is only half the battle. You have to then pick the answer choice that most closely resembles your pre-phrased answer. As we discussed in the Reading Comprehension section, there is rarely "one true" answer on the hard GMAT questions. Instead, there are usually several answer choices that are "good," with a small nuance distinguishing the best from the rest.

f you jump at the first answer choice that looks "good," you might get the question wrong because there could be a better choice. The best strategy is to narrow down answer choices using the process of elimination until you get the best choice.

Beware of trick answer types!

Test writing is an extremely time-consuming task. One of the most difficult parts of test writing is generating the "junk" wrong answer choices. Here is an overview of how choices for a question might be constructed:

(A) If you misread the passage, this looks right.
(B) Maybe right – close call with some subtle difference most students miss.
(C) Correct answer!
(D) The opposite of the correct answer.
(E) Something completely off topic, but it sounds impressive.

Test writers have an easy way out. On nearly every question you will see wrong answers that they pull out of a bin of typical junk answers. These wrong answers do not do much to test ability; they are simply there to fool inexperienced and unskilled test takers. Test writers like to use them because they take only a few seconds to write and catch students who aren't "on the ball."

If you have gone far enough to be able to identify and assess an argument, don't fall into a trap when picking an answer.

On the positive side, a skilled test taker can identify trap answer types quickly and then use process of elimination to increase the chances of getting the right answer.

Trick Answer Type #1: The Sentimental Favorite

The GMAT has trap answer choices that appeal to your higher ideals.

The level of diabetes in the United States among those over 50 has been attributed to high levels of sugar usage. In Zaire, however, diabetes rates among those over 50 are nearly as high as those in the US and individual sugar consumption levels are much lower.

What is the most reasonable conclusion from the above passage?

(A) If most people used sugar-replacement sweeteners instead of sugar, the rate of diabetes worldwide would drop rapidly.
(B) There are other factors besides sugar usage that determine diabetes levels.

Choice (A) sounds good, but answer choices that espouse high ideals or provide convenient explanations or easy solutions may not be correct.

Choice (B) is the correct answer because it gets to the flawed causal argument: sugar usage may not be the sole factor behind diabetes rates.

Trick Answer Type #2: Scope Trap

If you've found the main point, you must also identify what is in the range of the argument. Scope is related to more than just the general topic being discussed: it is the narrowing of the topic. Is the article about graduate-school admissions, MBA admissions, or helping international students get into the business school program of their choice? Each step represents a narrowing of the scope.

Let’s look at this critical reasoning question to examine scope.

Apartment building owners argue that rent control should be abolished. Although they acknowledge that, in the short term, rents would increase, they argue that the long-term effect would be a reduction in rents. This is because rent increases would lead to greater profitability. Higher profits would lead to increased apartment construction. Increased apartment construction would then lead to a greater supply of residences, and lower prices would result because potential apartment residents would have a better selection. Thus, abolishing rent control would ultimately reduce prices.

Name an assumption made by the owners:
(hint: this is a difficult question, but you can eliminate four of the five answers as outside the scope of the argument).

(A) Current residents of rent-controlled apartments would be able to find new apartments once their rents increased.
(B) The fundamental value of any society is to house its citizens.
(C) Only current apartment owners would profit significantly from market deregulation.
(D) New apartment construction will generate a great number of jobs.
(E) The increase in the number of apartments available would exceed the number of new potential apartment residents.

Which possible answers are outside of the scope? The scope is the argument that deregulation will increase supply and lower prices. "Name an assumption" means find a direct assumption of the supply/demand argument.

(A) Current residents of rent-controlled apartments would be able to find new apartments once their rent increased.
Is this outside of the scope?
This sentence expresses a nice sentiment for the welfare of renters, but it has nothing to do with our argument, which is about a supply/demand dynamic.

(B) The fundamental value of any society is to house its citizens.
Is this outside of the scope?
Again, nice sentiment, but this has no bearing on the argument. This is a "Sentimental Favorite" trick answer choice.

(C) Only current apartment owners would profit significantly from market deregulation.
Is this outside of the scope?
The issue at hand is not profits made by owners but the prices of apartments. And there is a secondary problem with this choice: "Only current owners." Why wouldn't future owners profit? As previously mentioned, be suspicious of answer choices that use words such as only; they are usually more restrictive than the passage intends.

(D) New apartment construction will generate a great number of jobs.

This is clearly outside of the scope.

(E) The increase in the number of apartments available would exceed the number of new potential apartment residents.
Aha! This is an argument about supply and demand and we are looking for an answer about supply and demand. This is clearly within the scope of the argument, and it is the correct answer. If demand rises as new apartments are constructed, prices would not decline – they might even rise – invalidating the owners' argument.

Trick Answer Type #3: Trick Opposites

This trap involves contradicting the question stem. This trap is very common on Strengthen/Weaken questions where the answer choice does the opposite of what the stem wants:

Here are examples of these deliberate tricks intended to catch students who rush through questions:

1. All of the following may be inferred from the passage EXCEPT:
Then the GMAT gives one answer that absolutely may be inferred from the passage (which test-takers tend to pick automatically if they forget the "EXCEPT").

2. The stem asks for an assumption in an argument, and one of the answer choices is a summary of the argument (but not an underlying assumption).

3. Which of the following weakens the argument above?
Then the GMAT gives an answer choice that obviously strengthens the argument.

 On test day, expect to run into a stem that looks like this: All of the following are true, EXCEPT: The translation of "EXCEPT" is that, of the five choices, all of them fit the condition EXCEPT one of them. All of the following are reasons to go to business school EXCEPT: (A) networking with future powerful executives (B) eager to learn accounting (C) increase your income (D) impress your friends (E) hone your poetry skills

Section 3: Reasoning Skills

Walking into the GMAT without learning formal reasoning is like walking into a used car lot without knowing anything about cars. You need to know the common flaws or you won't be able to spot them.

Note that some of these logical error types won't appear on the GMAT, but learning how to think logically and pull out assumptions will help you get a higher score and will also help you on the AWA Analysis of Argument section.

You don't have to memorize every logical fallacy with its formal Latin name, but you do need to get a general idea about what fallacies are and how to spot them.

Section 3-1: Reasoning Skills – Logical Fallacies

The following are eight logical fallacies you might encounter on the GMAT.

1. Ad hominem

One of the most often employed fallacies, ad hominem means "to the man" and indicates an attack that is made upon a person rather than upon the statements that the person has made.

Your medical advice isn't worthy of consideration because you aren't a doctor.

Don't vote for him to be president; he is an incorrigible womanizer.

The converse of ad hominem is called an appeal to authority. In this case, an argument is valid based simply on the person's title or reputation:

Take my advice because I am a doctor.

Let me handle the operation; I am a surgeon.

Strengthen:
You can bolster an ad hominem argument by showing that a personal characteristic is in fact relevant.

Don't vote for him to be president; he is an incorrigible womanizer.

Could be strengthened by: 1) numerous affairs could be a distraction from governance; or 2) numerous affairs may open a president to blackmail.

Weaken:
Show that personal traits aren't important at all.

Don't hire him as your landscaper, he is an incorrigible womanizer.

It is difficult to see how a landscaper's personal life could have any impact on his ability to create an attractive garden.

2. Straw Man

Here the speaker attributes to an opponent an argument that does not represent the opponent's true position. For instance, a political candidate might charge that his opponent "wants to let all prisoners go free," when in fact his opponent simply favors a highly limited furlough system. The opponent is portrayed as someone he is not.

The congressman wants to cut funding for the attack submarine program. I disagree entirely. I do not understand how he can be so irresponsible and leave us defenseless like that.

Perhaps the congressman does not believe that the attack submarine would have any defensive benefit. This is similar to an ad hominem attack because it attacks the person by creating a caricature of the person's beliefs.

Weaken: Show that this person really isn't the exaggerated caricature that the argument suggests.

The assault on the congressman's character is far off-base. The congressman knows that the defense budget is finite and prefers spending scarce dollars on more effective defense systems unlike the already obsolete attack submarines.

Strengthen: Show that the person really is the straw man that he is portrayed to be.

The congressman has stated numerous times that the Department of Defense should be shut down and that true peace can only be achieved by an open dialogue with rival powers.

3. The Fallacy of Faulty Analogy
(very common on the GMAT)

Reasoning by analogy functions by comparing two similar things. Faulty analogy arguments draw similarities between the things compared that are not relevant to the characteristic inferred in the conclusion.

The logic behind analogies is this: All X does Y. This does Y. Therefore, this must also be an X. Here's an example of a faulty analogy fallacy:

Ted and Jim excel at both football and basketball. Since Ted is also a track star, it is likely that Jim also excels at track.

In this example, numerous certain similarities between Ted and Jim are taken as the basis for the inference that they share additional traits. You can't "compare apples and oranges."

Strengthen: The assumption is that two things are parallel, so you can strengthen a faulty analogy argument by strengthening similarities.

Ted and Jim excel at both football and basketball. Since Ted is also a track star, it is likely that Jim also excels at track.

Football and basketball emphasize speed, so it is likely that Jim would excel at track.

Weaken: Emphasize the differences between the points being discussed in the analogy.

Ted plays point guard in basketball and wide receiver in football, two positions that emphasize speed. Jim plays center in basketball and nose tackle in football, two positions that emphasize size. Therefore, it is fallacious to suggest that Jim might excel in track just because Ted does.

Analogy Sample Questions:

1. Long-distance runners sometimes get shin splints from over-training. Shin splints are also common among freestyle skiers. Freestyle skiers are also guilty of over-training.

Which of the following, if true, most weakens the conclusion drawn above?

(A) Sprinters are also prone to getting shin splints.
(B) Freestyle skiers often exhibit other signs of over-training such as dehydration.
(C) Long-distance runners are less prone to long-term stress injuries.
(D) Freestyle skiers get shin splints from landing jumps incorrectly.
(E) Freestyle skiers, on average, train fewer hours than do long distance runners.

The passage tells us two facts: one about long-distance runners (they sometimes get shin splints from over-training), and one about freestyle skiers (they also get shin splints). The conclusion, that freestyle skiers must also over-train, depends on the faulty assumption that because runners’ shin splints are caused by over-training, skiers’ must be as well. Choice (A) is irrelevant. Choice (B) strengthens the conclusion. Choice (C) is irrelevant.

Choice (D) attacks an assumption on which the conclusion depends. If skiers’ shin splints are not caused by over-training, then it is not necessarily true that freestyle skiers are guilty of over-training. This weakens the conclusion considerably. Choice (E) seems also to weaken the conclusion, but in reality all it does is encourage the false assumption that over-training is a matter of hours spent training, and that the passage tells us how many hours are too many. In truth, (E) is irrelevant, and (D) is the best answer.

2. The mayor of Town T decided to lower sales tax in order to boost sales volume. He believes that lowering the tax will increase the sales tax generated since there will be much more total sales volume. The mayor wants to follow the example of Town J, where such an experiment helped increase the budget twice in a three-year term.

Which of the following statements is the best proof the opponents of the mayor's proposal can use in order to persuade the population of town T not to support this decision?

(A) Town J is located very close to the borders of three other states. The sales taxes in those other states are higher than in Town J's state. This causes residents of the other states to shop in town J, to save money. Town T is located far from any state border.
(B) Town T receives only a small portion of its tax receipts from sales taxes. Most taxes come from property taxes, and this policy would have no impact on property-tax revenue.
(C) Town J has many more industrial plants that purchase raw materials from the town's mines.
(D) This kind of experiment did not work in any other of the six towns that lowered sales tax.
(E) The mayor is in the sway of several special-interest groups in town T. These groups are anxious to see the town's sales tax rate lowered because this would make them much richer.

This is an example of faulty comparison.
(A) provides a reasonable explanation of why the experiment worked in town J and why it would not work in town T. This is the correct answer. This answer works by emphasizing the differences between the two towns.
(B) Although the tax benefit may be small, this does not invalidate the mayor's claim that his plan would increase tax revenues.
(C) is out of scope because the number of industrial plants is irrelevant.
(D) does not provide sufficient information about those six other towns to enable us to evaluate whether the mayor is right or wrong to base his plan on the experience of Town J.
(E) is out of scope. The motivation of the special-interest groups has no bearing on whether the plan will generate more tax revenue for the town.

4. The "After This, Therefore, Because of This" Fallacy (Post hoc ergo propter hoc)

This is a causal fallacy in which something is associated with something else because of mere proximity of time. This error is very common on the GMAT and is often a component of chronological questions (look for phrases such as "over the years," "last week," "yesterday," etc). It relies on the assumption that, because one thing happened after another, the first must have caused the second. For example:

I touched a toad last week; now I have a wart. The toad caused the wart.

The quarterback forgot to shave one morning and had the best game of his career. Since then he has stopped shaving to boost his performance.

This isn't to say that you can never claim something is caused by something else that preceded it. The trick is to look for evidence of a causal link that is more than just "this occurred after that."

The last thing I remember was a bus coming at me full speed. I am now in a hospital in a full body cast. The bus must have caused my injuries.

Ten minutes after walking into the auditorium, I began to feel sick to my stomach. There must have been something in the air in that building that caused my nausea.

You could strengthen the sickness argument by adding "the auditorium was later closed due to a gas leak," which shores up the assumption that something was in the air.

You could weaken the argument by targeting the assumption: "Before going to the auditorium, I ate lunch at a restaurant that has recently reported a high incidence of food poisoning."

The stock market declined shortly after the election of the president, thus indicating the lack of confidence the business community has in the new administration.

This example highlights a fallacy all too common in modern news reporting. The only evidence offered to support the claim that the decline in the stock market was caused by the election of the president is the fact that the election preceded the decline. The real cause of the stock market decline might have been a factor entirely unrelated to the election, such as the collapse of a bank in Asia. The view that B follows A, therefore A caused B wrongly jumps to the assumption that there are no other factors at work that might be the true cause of B.

Sample Question

Over the past three years, the crime rate in the city has declined steadily. Four years ago, a new mayor took office on a third party ticket whose platform included a tougher stance on crime and improved funding for after-school and other youth programs. Without this mayor’s leadership, it is certain that this positive change in the crime rate would not have occurred.

Which of the following statements, if true, would most weaken the argument above?

(A) In the first year the mayor was in office, the crime rate rose by 1.5%.
(B) Due to budget cuts, the mayor’s proposed funding for after-school and other youth programs was never implemented.
(C) Three years ago, a local TV station began sponsoring a neighborhood watch scheme.
(D) The crime rate in neighboring cities has been on the rise for the past three years.
(E) The after-school programs had an even higher rate of attendance than was expected.

This question asks you to weaken the argument. The author writes that without the new mayor’s leadership, the recent decline in the crime rate would not have occurred. However, the only evidence we’re given is that the mayor’s platform, including anti-crime programs, preceded the drop in crime. There are dozens of possible reasons for a decline in crime, therefore this After This, Therefore, Because of This argument isn't very persuasive. To weaken the argument, look for an answer choice that suggests the decline in the crime rate may have been due to something unconnected to the mayor’s leadership.

Choice (C) suggests that the decline in the crime rate could have been caused at least in part by the neighborhood watch scheme promoted by the TV station. Choice (A) is irrelevant; we’re only concerned with the past three years. Choice (B) fails to weaken the conclusion because it’s possible that, while the youth programs were never implemented, other of the mayor's anti-crime programs were. Choice (D) is irrelevant. Choice E strengthens the argument.  Choice (C) weakens the argument, and is the best answer.

5. The "All Things are Equal" Fallacy (very common on the GMAT)

Plus ça change, plus c'est la même chose
(The more things change, the more they remain the same.)
- Jean-Baptiste Alphonse Karr

This fallacy occurs when it is assumed, without justification, that background conditions have remained the same at different times or locations. In most instances, this is an unwarranted assumption for the simple reason that things rarely remain the same over extended periods of time, or rarely are the same from place to place.

Questions giving rise to this fallacy can be spotted easily because they refer to a time in the past ("last year," etc.) or to one place, and try to create an analogy with a different time (the present or the future, for instance) or place. But there are all sorts of dynamic factors inherent in the circumstances of one time or location that are subject to change, making it dangerous to draw conclusions that about different times or places.

Ten years ago I got a 750 on the GMAT, so I expect to get the same score again.

The last winner of the New Hampshire Democratic primary won the general election. Therefore this year's winner of the New Hampshire Democratic primary will win the general election.

The assumption operating in these arguments is that nothing changes over time. But the passages offer no evidence or justification for such an assumption.

6. Either / Or Thinking

This is the so-called "black or white" assumption. Essentially, it says "Either you believe what I'm saying, or you must believe exactly the opposite." Here is an example of the black or white assumption:

Either you are with me or you are against me.

The argument above assumes that there are only two possible alternatives open to us. There is no room for a middle ground.

You can strengthen these arguments by showing that there generally isn't a middle ground. The problem is that most arguments do have a middle ground, meaning that this argument doesn't work and the underlying assumption is very often a fallacy.

7. Argument ad populum

Argumentum ad populum is the belief that truth can be determined by, essentially, putting it to a vote.

A group of kindergartners is studying a frog, trying to determine its sex.

"I wonder if it's a boy frog or a girl frog," says one student.

"I know how we can tell!" pipes up another.

"All right, how?" asks the teacher, resigned to the worst.

The child replies, "We can vote!"

Democracy is a very nice thing, but it doesn't determine truth. Polls are good for telling you what people think, not necessarily what is true.

8. Slippery Slope

This argument assumes that just because things go badly, they will automatically get much, much worse. If one were to create a graph to support a "slippery slope" argument, it would look like a hockey stick.

Crime has risen sharply three years in a row. At this rate, in ten years the gangsters will run our society. We must take drastic action and throw criminals in jail for lifetime sentences and re-institute the death penalty.

The sharp increases may not continue for 10 years at the same rate. This may just be a statistical blip. The argument does not provide the justification for draconian action.

Section 3-2: Reasoning Skills – Statistical Reasoning Skills

There are lies, damn lies - and statistics.
Mark Twain

To help you prepare for the many statistical reasoning questions that you likely will encounter on test day, we provide a primer on statistical reasoning similar to what you would get in a college-level introductory statistics class.

1. The Biased Sample Fallacy

The Fallacy of the Biased Sample is committed whenever the data for a statistical inference is drawn from a sample that is not representative of the population under consideration. The data drawn and used to make a generalization are drawn from a group that does not represent the whole. Here is an argument that commits the fallacy of the biased sample:

A soda manufacturer conducted a taste-testing of its Supa Cola brand. At shopping malls around the country, it asked customers who were about to buy a cola to compare Supa Cola to five competitors' colas. In Oregon, over 60% of those questioned – by far the highest percentage anywhere in the country – considered Supa Cola to be the best-tasting of the six colas offered. As a result, the manufacturer allocated a greater proportion of its advertising budget than before to Oregon, and diverted almost all of it to Supa Cola away from its other flavors of soda.

This manufacturer focused its advertising budget on Oregon and Supa Cola on the basis of unreliable data (biased sample). Oregonians who happened to be buying cola at a given moment aren't necessarily representative of Oregonians generally; and even they may not prefer cola to other kinds of soda.

Here is another example:

In a recent survey conducted by Wall Street Weekly of its readers, 80% of the respondents indicated their strong disapproval of increased capital gains taxes. This survey clearly shows that increased capital gains taxes will meet with strong opposition from the electorate.

The data for the inference in this argument is drawn from a sample that is not representative of the entire electorate. The survey was conducted of just readers of a very specialized magazine, and not random members of the electorate. People who read about investing are likely to have a different opinion on the topic of taxes on investment different than that of the population at large.

2. The Insufficient Sample Fallacy
(Hasty Generalization/Sweeping Generalization)

The Fallacy of the Insufficient Sample is committed whenever an inadequate sample is used to justify the conclusion drawn. In a Biased Sample, people are pulled from a non-representative group. In an Insufficient Sample, not enough people are polled to make a statistically significant result.

I have worked with three people from New York City and found them to be obnoxious, pushy and rude. It is obvious that people from New York City have a bad attitude.

Observations of three people are not sufficient to support a conclusion about 10 million. Bad luck could account for meeting three bad people. Contrast with this:

After living and working in New York City for 12 years, I have met thousands of people and with very rare exception, I have found them to be obnoxious, pushy and rude. It is obvious that people from New York City have a bad attitude.

This latter argument is something to take more seriously given the larger pool from which the observation is drawn. Of course, the disgruntled New Yorker may work in an industry or company with an aggressive culture (producing a biased sample).

3. Correlation does not prove causality

A correlation is a statistical linking between two items that seem to be related. One of the GMAT's Greatest Hits, that you see time and time again, is a linking of two distinct pieces of information which seem to correlate statistically in a way that attempts to establish one as the "cause" of the other.

The relation between an association and a cause is difficult.

Heavier people tend to be taller.

Therefore: Weight is correlated with height.

Therefore: Gaining weight will make you taller.

This assumes a relationship between correlated data such that, when one element is changed, so automatically is the other.

Another obvious one:

1. The more serious the fire, the more fire trucks tend to be at the scene.
2. We can reduce the severity of fires by reducing the number of fire trucks that attend them.

Here is a more challenging example:

1. Studies suggest that young people who watch a lot of TV violence are more likely to engage in violence.
2. The recent increase in TV violence is associated with an increase in violence society-wide.
3. If children watched less TV, society would be less violent.

This one seems intuitive enough and it is the "sentimental favorite," but the reality is that 3 doesn't necessarily follow from 1 and/or 2. You can't assume that just because things correlate you can change one factor and it will automatically change the other. Children who watch large amounts of TV may have inattentive parents, and this may be the underlying hidden causal factor (not watching too much TV violence in itself). This argument needs more evidence, like a study showing that violent children are more successfully rehabilitated by cutting out violent shows.

4. Confounding Factors
(also called the "Lurking Variable")

A confounding factor is an additional factor that may be responsible for a correlation. "Con" is a Latin root for "with", so confounding means literally to find with.

Example 1: The Miracle Hospital

A sports injury treatment center in New York has the lowest rate of recovery for sports injuries. A treatment center in rural Pennsylvania has the highest and quickest recovery rate. If you have just been injured while playing softball, should you go to Pennsylvania?

This example seems to indicate that the treatment center in New York is to be avoided at all costs, while the one in rural Pennsylvania is the place to go if you have a sports injury. But the passage provides far too little information for that conclusion to be reliable. For all we know, the New York facility has such a great reputation, doctors from all over the world refer all of their most seriously injured patients to it, while the Pennsylvania facility sees only few, relatively mildly injured locals. A hospital that sees only three slightly injured patients a year is likely to have a higher recovery rate than one that sees 3,000 seriously injured ones. This is the confounding factor. Without the full story, a comparison of the rates of recovery alone is meaningless.

Example 2: The Secret Conspiracy Against Men

At University of California at Berkeley, the school had a much lower acceptance rate for men than for women, and administrators could not determine why since the male applicants had higher SAT scores and grades.
Are the lower admissions rates of men a result of systematic bias?

At first glance, it would seem that someone in the admissions department didn't like men and had systematically rejected their applications. But we don't have enough information to reach that conclusion. Perhaps a high proportion of men applied to the highly-competitive engineering program, while few women did. If men and women were accepted at an equal rate for less competitive programs, this would indicate that gender played no direct role in the admissions process. The confounding factor was the major chosen by the applicants.

Section 4: Question Types

There are four main Critical Reasoning question types on the GMAT:

1. Assumption Questions
2. Strengthen / Weaken Questions
3. Inference Questions
4. Flaw Questions

Section 4-1: Question Types – Assumption Questions

An assumption is an unstated premise that supports the author's conclusion. It's the connection between the stated premises and the conclusion. The author's conclusion will depend upon the assumption being valid. Assumption questions are extremely common and have stems that look like these:

• Which of the following most accurately states a hidden assumption that the author must make in order to advance the argument above?
• Which of the following is an assumption that, if true, would support the conclusion in the passage above?
• Which of the following, if added to the passage, would make the conclusion logical?
• The validity of the argument depends on which of the following?
• Upon which of the following assumptions does the author rely?
• The argument presupposes which one of the following?

How to approach Assumption Questions

1. Look for gaps between the premises and the conclusion. Go on an Assumption Hunt and spend a few seconds finding any holes in the argument.

2. Ask yourself why the conclusion is valid. Before you progress to the answer choices, try to get a feel for which assumptions are necessary to fill the gaps between the premises and the conclusion.

3. Take note of sweeping language or extreme statements.

Example assumption questions:

When doing assumption questions, spend about 10 to 20 seconds trying to think of assumptions underlying the argument.

What ideas or words are in the conclusion, but not stated in any premise or evidence? That's an assumption.

Let's analyze a couple of samples:

Question #1

A study released yesterday by the American Dental Association shows that people who gargle with Berry Pop Soda are 20% less likely to get cavities. We should therefore stock up on Berry Pop Soda and prepare ourselves for increased demand.

Quick! What assumptions are in this argument? Think about it creatively and quickly. The premise is a new report coming out, and the conclusion is that it would lead to increased sales. That's quite a leap!

Let's quickly brainstorm some assumptions:

1. The study was released to major media outlets and people know about it.
2. Berry Pop soda is an attractive product that tastes good. People who try gargling with it will continue gargling with it.
3. Berry Pop is as effective as conventional mouthwashes at cavity prevention.
4. Berry Pop has name recognition. Have you ever heard of Berry Pop?

Question #2

Apartment building owners argue that rent control should be abolished. Although they acknowledge that, in the short term, rents would increase, they argue that the long-term effect would be a reduction in rents. This is because rent increases would lead to greater profitability. Higher profits would lead to increased apartment construction. Increased apartment construction would then lead to a greater supply of residences, and lower prices would result because potential apartment residents would have a better selection. Thus, abolishing rent control would ultimately reduce prices.

Express that complicated argument in your own words:

Premise 1: Abolishing rent control will increase the supply of housing (premise).

Premise 2: Greater supply leads to lower prices (premise).

Conclusion: Abolishing rent control leads to lower rents (conclusion). It is a supply/demand argument.

Try to find gaps between premises and conclusion.

Look at premise 1: Abolishing rent control will increase the supply of housing.
This premise is based on the assumption that higher profits will result in increased supply.

Look at premise 2: Greater supply leads to lower prices.
This is a supply/demand argument; greater supply leads to lower prices. However, there is something missing: supply and demand requires a discussion of demand. Indeed, demand is missing; that is the hidden assumption.

Sample Question

Since the late 1970s and early 1980s, tax incentives and other changes have encouraged increasing numbers of venture capitalists and entrepreneurs to start new enterprises. Since 1980, some one-half million new ventures have been started. Not all have succeeded, of course.
The above statement makes which of the following assumptions?

(A) Success in starting a new business depends in large part on sound financial planning.
(B) Social incentives motivate investors just as much as financial rewards do.
(C) Financial incentives are associated with new business starts.
(D) Most new business ventures succeed initially but fail later on.
(E) Venture capitalists are motivated by non-monetary gains.

Explanation:

This is an "after this, therefore, because of this" argument. It assumes that tax changes since the 1980s have led to an increase in the number of small businesses.

(A) may be true, but there is nothing in the passage to substantiate it.
(B) may be true, however the passage does not allow for social motives to be imputed to investors, let alone that they are as strong as financial motives.
(C) is the correct answer.
(D) can be eliminated because of the word "most."
(E) is not supported by any evidence in the passage.

 Negation Test for Assumption Questions To test if a statement is an assumption required for an argument, try to negate it. If the argument falls apart, it means that the argument requires that assumption. In the above sample question if you got rid of the assumption that people are motivated by financial gain, then the argument falls apart. Therefore, that assumption is likely necessary for the argument.

Section 4-2: Question Types – Strengthen / Weaken Questions

If unstated assumptions are the glue that holds an argument together, then weakening or strengthening the assumptions will weaken or strengthen the argument. Nearly all Strengthen/Weaken questions don't ask you to change the conclusion or the premises, because those are fixed; it is the unstated assumptions that are in flux. The whole trick on a Strengthen/Weaken question is to strengthen or weaken the assumptions.

Strengthening and Weakening is not the same thing as proving something true or false. Instead, the right answer will support (strengthen) or cast doubt upon (weaken) the required assumptions, while also being relevant to the premises.

Here are some examples of Strengthen/Weaken question stems:

Strengthening:

• The conclusion would be more properly drawn if it were made clear that...
• Which of the following, if true, would most strengthen the conclusion drawn in the passage above?
• The argument as it is presented in the passage above would be most strengthened if which of the following were true?

Weakening: (Note that when the stem says "if true," you cannot challenge the statement.)

• Which of the following, if true, most seriously weakens the conclusion drawn above?
• Which of the following, if true, would provide the strongest evidence against the above?
• Which of the following, if true, casts the most serious doubt on the conclusion drawn above?

Tips for Weakening Questions:

1. Try to find one necessary assumption in the passage. This is what the right weakening answer often will target.

2. The All Things are Equal fallacy is very common in these questions. When things are compared over time, the assumption is that background factors remain constant (while they might be changing). A good answer might point out that some background factor did change.

3. When you see a Weakening question that compares two things or tries to show them as similar, look for an underlying factor that makes such a comparison problematic.

4. There likely will be two or more choices that weaken the argument. In this case, re-read the passage carefully and see which one is most directly relevant to the premises, the conclusion and assumptions.

5. Common trap answer choices include:
• A statement that strengthens (and doesn't weaken) the assumptions and the overall argument a trick opposite.
• A statement with information not relevant to the argument.
• A statement that requires additional facts to have value.

6. When you have discarded four out of the five answer choices, the one that remains is the correct answer.

 Use Strong Language to Weaken or Strengthen On most other Verbal questions, you can eliminate potential answers that use strong language. The exception is the Strengthen/Weaken questions. On these questions, sweeping words are more effective: only the most extremely all The reason? Extreme answers will have a more powerful weakening/strengthening effect on assumptions.

Sample Questions

We've discussed this example before. Use the information gained above to generate an answer based on targeting assumptions:

The postal service is badly mismanaged. Thirty years ago, first-class letter delivery cost only three cents. Since then, the price has increased sevenfold, with an actual decrease in the speed and reliability of service.
All of the following would tend to weaken the conclusion of the argument above EXCEPT:

(A) The volume of mail handled by the postal service has increased dramatically over the last thirty years.
(B) Unprecedented increases in the cost of fuel for trucks and planes have put severe upward pressures on postal delivery costs.
(C) Private delivery services usually charge more than does the postal service for comparable delivery services.
(D) The average delivery time for a first-class letter three decades ago was slightly longer than it is today.
(E) The average level of consumer prices overall has increased fourfold over the last thirty years.

 Explanation: The conclusion is that the postal service is poorly managed. This is an EXCEPT stem, so we are looking for something that won't weaken the argument. Premise #1 The price of first-class delivery has increased sevenfold. Premise #2 There has been a decrease in speed and service. Conclusion The postal service is badly mismanaged. Analysis This is the All Things are Equal fallacy. It assumes conditions don't change, thereby making a basis of comparison over time. This compares past performance to the present day. So, of course anything that suggests that business conditions have gotten harder will excuse managerial incompetence. Anything that suggests conditions have gotten easier will not weaken the argument, so that's what we are looking for.

Reviewing Answer Choices

(A) The volume of mail handled by the postal service has increased dramatically over the last thirty years.
This would seem to excuse the poor service/price because the service has had to overcome a massive increase in volume.

(B) Unprecedented increases in the cost of fuel for trucks and planes have put severe upward pressures on postal delivery costs.
This would seem to excuse the poor service/price because costs have increased dramatically.

(C) Private delivery services usually charge more than does the postal service for comparable delivery services.
This would seem to excuse the poor service/price because other services are not as efficient.

(D) The average delivery time for a first-class letter three decades ago was actually slightly longer than it is today.
This indicates that there have been improvements in service.

(E) The average level of consumer prices overall has increased fourfold over the last thirty years.
Since the price of postage has increased seven times over, this suggests that postal prices have increased at a faster rate than inflation. Thus, choice E does support the original argument, making this the correct answer.

1. In many pre-schools, children commonly tend to get colds before their resistance develops and the colds become much less frequent. It is clear that a child requires several colds before white blood cell concentrations rise high enough to effectively deal with colds.
Which of the following, if true, most seriously weakens this theory?

(A) Children commonly spread viruses and bacteria in a small closed environment.
(B) The use of Vitamin C increases resistance to the common cold and decreases its frequency.
(C) Parents stock up on cold medicines that alleviate the symptoms of a cold after a child gets sick.
(D) There are many strains of the cold virus and children develop resistance to individual strains.
(E) White blood cells fight infection and their production is stimulated by high infection levels.

 Explanation: The question is stating that the body's immune system requires numerous infections to be properly stimulated. It is a causal argument that tries to explain an observation. Premise #1 Children tend to get fewer colds as they progress through pre-school. Premise #2 (unstated assumption) Conclusion It takes several colds to activate a child's immune system. Analysis This is After This, Therefore, Because of This fallacy. It observes that as children go through pre-school the number of colds go downs. From this, the creative author develops the theory that a child's immune system requires them to get several colds before it is fully activated. The best way to weaken a causal argument is to suggest an alternative causal factor (find a confounding issue).

Reviewing Answer Choices

(A) Children commonly spread viruses and bacteria in a small closed environment.
Not Relevant

(B) The use of Vitamin C increases resistance to the common cold and decreases its frequency.
Not Relevant

(C) Parents stock up on cold medicine after a child gets sick that alleviate the symptoms of a cold.
This choice seems to present an alternative cause for the observed phenomenon, but the medicine deals with symptoms, not the cold per se. So it is not reducing the incidence of colds, simply their symptoms (no more runny noses!).

(D) There are many strains of the cold virus and children develop resistance to individual strains.
This choice suggests an alternative explanation for the improvement in a child's ability to fight colds: the child simply becomes immune to individual viruses per se. So, the conclusion that a child's immune system needs high white blood cell concentrations isn't sound – it is an issue of exposure to certain strains. By suggesting that a different causal process is at work, this choice weakens the argument.

(E) White blood cells fight infection and their production levels are stimulated by high infection levels.
This choice supports the argument, but the question asks for what weakens it.

 Trick Opposites Trick opposites are sometimes used as junk answer choices on Strengthen/Weaken questions. If the stem asks for what weakens the passage, you'll find a perfect answer choice for what strengthens it, and vice versa. Choice (E) in the above question about colds is an example of a trick opposite.

Two Strengthen / Weaken Questions
http://www.youtube.com/embed/Gx7F0D4ob8Y
Video Courtesy of Kaplan

Section 4-3: Question Types – Inference Questions (Main Point)

These questions ask you to draw conclusions from the passage. While before we analyzed an argument's assumptions, here we analyze its conclusions and implications. The conclusion of an argument in an Inference question is usually not directly stated. To find the conclusion, identify the premises and then identify what conclusion could be drawn from the premises. Inference questions differ from other critical reasoning questions in that the argument in the passage doesn't usually contain flaws. Typical stems for such questions read like this:

• The main point of the passage is that...
• Which of the following statements about... is best supported by the statements above?
• Which of the following best states the author's conclusion in the passage above?
• Which of the following conclusions can be most properly drawn from the data above?
• Which of the following is [implied, must be true, implicit] in the passage above?
• Which of the following conclusions can most properly be drawn if the statements above are true?

How to approach Inference Questions:

1. Analyze scope: Inference junk answers typically will go outside the direct scope of the passage. Be careful to look directly at the scope of the question. Correct inference answers must be within the scope of the passage. Your opinions or knowledge extraneous to the passage are always outside of the scope.
2. Don't jump into the Assumption Hunt. These questions usually don't contain glaring assumptions. Instead, they test your ability to derive a conclusion from stated premises.
3. Knock out answers with extreme wording. Correct inference answers typically do not use only, always, never, best or any strong words that leave little wiggle room. The right answers on Inference questions will generally use more qualifiers and less extreme language.
4. Try to fully understand the passage's point, and the exact reasoning it employs, so that if the question asks you to extend that reasoning, you are able to do so accurately.
5. 5. Use the process of elimination. Inference questions typically have two or three good answers that are semi-plausible. The best way to tackle these questions is to eliminate answers until you have one or two possible answers and then choose the one that best fits the scope.

Sample Questions

1. Although Locke has been hailed as a giant figure in European intellectual history, his ideas were largely borrowed from his predecessors, who are now unfairly neglected by historians. Furthermore, Locke never wrote a truly great book; his most widely-known works are muddy in style, awkwardly constructed and often self-contradictory.
With which of the following would the author most likely agree?

(A) Locke made use of ideas without acknowledging his predecessors as the sources of those ideas.
(B) Current historians are re-evaluating the work of Locke in light of present-day knowledge.
(C) Locke's contributions to the development of European thought have been greatly exaggerated.
(D) Historians should reexamine Locke's place in European intellectual history.
(E) Although Locke's ideas were important, his way of expressing them in writing was sadly inadequate.

Explanation: The author makes two assertions about Locke: that his ideas were not original and that his books were not very good. On the basis of these assertions, the author concludes that Locke's reputation as an intellectual giant is undeserved. Choice (C) accurately summarizes this conclusion.

(A) focuses on a subsidiary point, not the main idea; moreover, it makes an assumption unsupported by the passage namely, that Locke did not acknowledge the sources of his ideas.
(B) is wrong because, although the passage clearly indicates that the author is "re-evaluating" Locke's work, it does not suggest that "current historians" in general are doing so.
(C) best expresses the conclusion that Locke's contributions have been overstated.
(D) is tricky because it seems like a good answer, but it does not necessarily follow from what is in the passage. It implies that the author recommends that other historians re-examine Locke, but there is no such recommendation in the passage.
(E) is not addressed in the passage.

2. In 2008, Gotsland used three-times as much energy from non-renewable sources as renewable sources. Gotsland's proposed ten-year energy plan would result in the country using as much renewable as non-renewable energy by 2018, while using a larger amount of energy than in 2008.
For Gotsland's energy plan to be realized, which of the following will have to occur?

(A) By 2018, Gotsland will have to more than triple its use of energy sources.
(B) Gotsland will have to make a political effort to have a more sustainable energy economy.
(C) By 2018, Gotsland will have to decrease its use of non-renewable energy sources.
(D) By 2018, Gotsland will have to increase its use of renewable energy over 2008 levels.
(E) By 2018, Gotsland will have to more than triple its use of renewable energy sources over 2008 levels.

Explanation: In questions like these where they start throwing around numbers and you scratch your head ("Didn't I already do the quantitative section?"), it might help to use a little Plug-In.

In a quantitative math problem we would translate words to numbers. Let's do that here, looking first at the situation in 2008 and then at what it necessarily has to be in 2018 for Gotsland's plan to be realized:

In 2008, Gotsland used three-times as much energy from non-renewable sources as renewable sources. Well, we can substitute 50 megawatts of renewable energy and 150 megawatts of non-renewable for a total in 2008 of 200 megawatts.

Gotsland's proposed ten-year energy plan would result in the country using as much renewable as non-renewable energy by 2018, while using a larger amount of energy than in 2008. This means that in 2018 more than 200 megawatts has to be used, of which at least half has to be from renewable sources.

Now that we have our facts laid out we can review the answer choices.

(A) No. Gotsland does not need to triple its energy use -- it only needs a marginal increase over 200 megawatts.
(B) Not relevant.
(C) Gotsland can decrease its use of non-renewables, but it doesn't need to. It is mathematically possible for it to keep non-renewable use at 2008 levels, or even to increase non-renewable use, and still to meet both conditions of the plan for 2018 (by a large increase in its use of renewables).
(D) Yes. There is no way for Gotsland to meet both conditions of its 2018 plan without increasing its use of renewables. But at a minimum it only needs to slightly more than double its use of renewables: If total energy use goes up to 201 megawatts, the second condition is met. If this is split 100.5 megawatts each of non-renewables and renewables (i.e. if the former goes down and the latter goes up by just over 100%), the first condition is also met.
(E) No. Gotsland does not have to triple its use of renewables (see the math discussed in the previous answer choice).

 Why is there a math question in my Verbal section?Some inference questions (like the one above) use basic number line analysis or proportions. This is just testing your ability to use numbers in the context of critical reasoning.

Critical Reasoning Strategies
http://www.youtube.com/embed/StL-8Dav1a0
Video Courtesy of Kaplan

Section 4-4: Question Types – Flaw Questions

These questions ask you to recognize what's wrong with an argument. Most of these questions require you to point out a fallacy in the argument. These should be easy if you've studied our extensive section covering the most common logical flaws.

Here are some typical flaw-question stems:

Which one of the following contains a flaw that most closely parallels the flaw contained in the passage?

Which one of the following best identifies the flaw in the above argument?

In presenting her position, the author does which one of the following?

Example 1:
John: We should oppose any attempt to be required to register firearms. Such regulation is the first step to confiscation of all weapons and the elimination of our constitutional right to bear arms.

Ted: This is preposterous. Many things in society have to be registered, such as cars, babies, boats and planes, yet these items have never been confiscated.

What are the flaws in the reasoning above?

Analysis:
Ted is making a faulty analogy between the registration of guns and that of cars and babies. Since guns are frequently used as instruments of intentional violence, registration – which will make them easier to trace – is more likely to make them targets for confiscation.

On the other hand, John is making a slippery slope argument that registration of firearms must invariably lead to the elimination of a constitutional right

Example 2:
John: I don't want to die in an accident. Every few days on the TV news I hear of a major plane crash somewhere in the world. I would never fly planes; they are too dangerous.

Ted: Nonsense. Statistics show that airplanes are the safest mode of transportation on a per-mile basis.

John: The answer then is not to travel such long distances.

Analysis:
John is assuming that, because plane crashes are always in the news, traveling by plane must be very dangerous. The TV news, however, is a biased sample of all accidents. Almost all plane crashes make the news, though traffic fatalities are rarely considered newsworthy.

Ted's point that flying is the safest mode of transport on a per-mile basis takes no account of the fact that flights tend to be much longer than other forms of travel. On the other hand, John's unqualified conclusion that the safest thing is never to travel long distances is mistaking the correlation between long-distance journeys and air crashes for a direct causal connection. This is a little like the person, in our example earlier in this section, who concludes that sending out fewer fire trucks will reduce the ferocity of fires because he has observed a correlation between serious fires and the number of fire trucks attending them.

Section 5: Advanced Question Types

1. Executive Decision Making
2. Paradox Questions
3. Deductive Reasoning
4. Style of Reasoning Questions

Section 5-1: Advanced Question Types – Executive Decision-Making

When reading many of these stems, pretend that you are the CEO of a Fortune 500 company and the GMAT question is a salesman or a manager with a proposal: "Given the advertising costs….. should the new marketing campaign... ?”

These questions ask you to come up with the most effective, efficient or appropriate way to solve real-world problems such as:

• Helping a business improve its profitability
• Dealing with a public health issue
• Improving performance among workers or students
• Fixing a sociological problem
• Making a cost-benefit analysis

The stems will look like this:

Which of the following strategies is most likely to prevent the decline in... ?

Which of the following proposals would be most effective in... ?

 The answer is in the answer choices In Executive Decision questions, don't spend too much time developing a pre-conception of the answer before moving on to the answer choices. For example, if the question asks How could you improve worker productivity?... Well, there could be dozens of ways of doing so. Just develop a general idea of what the right answer will look like. The "right" answer often won't be evident until you see the answer choices.

Examples of Cost Benefit Analysis:

Revenues - Costs = Profits

If you want to boost profits, cut costs or increase revenues.

Cost / Benefit Analysis

If you want to make a sound business decision, evaluate the costs against the potential benefits.

• Is something worth the cost?
• What are the benefits and what are the costs of a course of action?

Section 5-2: Advanced Question Types – Paradox Questions

A paradox is a statement or proposition that seems self-contradictory or absurd, but in reality expresses a possible truth.

These questions present you with a paradox and ask you to resolve it or explain how that contradiction could exist. Paradox questions are rare and more common at the higher difficulty levels. These questions usually contain the keywords explanation, resolve, or account.

Paradox questions often ask you to play the role of a top researcher where you have to reconcile conflicting data.

Here are some examples of the ways in which these questions are worded:

Which of the following, if true, would help to resolve the apparent paradox presented above?

Which of the following, if true, contributes most to an explanation of the apparent discrepancy described above?

Each of the following could help account for this discrepancy, EXCEPT:

Sometimes paradox questions will present two speakers or have some text in bold. The question then asks the user to compare the statements and resolve the conflict.

How to approach paradox questions:

Read the argument and find the apparent paradox, discrepancy or contradiction.

State the apparent paradox, discrepancy or contradiction in your own words.

Use POE (process of elimination). The best answer will explain how both sides of the paradox, discrepancy, or contradiction can be valid. Eliminate answers that are out of scope, or only address one side of the paradox.

Examples
Inflation rose to 5.1% over the 2nd quarter, up from 4.1% during the first quarter of the year, and higher than the 3.3% recorded during the same time last year. However, the higher price index did not seem to alarm Wall Street and stock prices remained steady.
Which of the following, if true, could explain the reaction of Wall Street?

(A) Stock prices were steady because of a fear that inflation would continue.
(B) The president announced that he was concerned about rising inflation.
(C) Economists warned that inflation would persist.
(D) Much of the quarterly increase in the price level was due to a summer drought's effect on food prices.
(E) Other unfavorable economic news had overshadowed the inflation statistics.

Explanation: This is a paradox because the high inflation report would seem to indicate that the stock market should go down.

A fear that inflation would continue (A), an announcement by the president that he was concerned about inflation (B), economists' warnings about inflation (C), and other unfavorable economic news (E) would all tend to cause stock prices to decline and cause alarm on Wall Street.

What we are looking for instead is an explanation that suggests why a high-inflation report would not spook the markets. (D) is most appropriate. If most of the quarterly inflation was due to a rise in food prices caused by a drought, then other prices rose less or no more than in the last quarter. Since the drought is probably a temporary phenomenon, it may be expected that inflation will decline next quarter. This can explain why the stock market was not overly concerned with the high-inflation report.

Section 5-3: Advanced Question Types – Deductive Reasoning

Deductive reasoning questions are the last question type we cover because they are an entirely different species from the rest of the GMAT critical reasoning questions.

Note: these questions are rare on the GMAT. You do not have to memorize the rules; just learn how to apply them.

Deductive vs. Inductive Reasoning

These questions force you to follow highly specific logical rules. Most critical reasoning questions use soft and fuzzy inductive reasoning (with observations, lots of unstated assumptions, etc). Deductive reasoning is what a computer would do: hard logic following rules.Deductive reasoning is often used in the legal profession.

You were on your neighbor's property.

It is against trespassing laws to be on a neighbor's property.

You are therefore guilty of trespassing.

Isaac Inductive says: I've noticed that every time I kick soccer ball up, it comes back down, so I guess this next time when I kick it up, it will come back down again.

Dennis Deductive says: You are merely applying Newton's law of gravity. Everything that goes up must come down. If you kick the ball up, it must come down.

Types of Deductive Reasoning

Which of the following could be answered using pure deductive reasoning:

1. Did the growth of the population of Connecticut slow last year?

2. Do Connecticut residents appreciate access to the ocean?

3. Are Connecticut legal residents also residents of the United States?

4. Does Connecticut have the highest per capita income of any state in the United States?

1. It may seem clear-cut to look at population data, but what about migrant workers, etc. who may not be documented? Answering this question actually involves making assumptions, and therefore an inductive guess.
2.
This relies on surveying popular opinion, which is fraught with assumptions.
3. In 1789, Connecticut became the first signatory to the U.S. Constitution and all Connecticut residents became legal residents of the United States. Thus, this question can be answered using pure deductive reasoning.
4. The income of Connecticut residents is difficult to measure and this is an observational task, not a deductive one. So this question requires inductive reasoning.

Rule #1:
If A, then B
If I press the power button, then the computer will turn off.

Valid Inference: If not B, then not A
If the computer is on, then I didn't press the power button.
(This logic rule is called the Contrapositive)

Invalid Inference: If B, then A
The computer is off; therefore I pressed the power button.
(Just because the computer cannot be on if I've pressed the power button does not mean if it is off I must have pressed the power button. There could be other reasons for it being off.)

Invalid Inference: If not A, then not B
If I did not press the power button, then the computer is not off.
(There are other ways the computer could have shut off. This is called Denying the Antecedent.)

Example: Denying the Antecedent
If it rains, then the grass is wet.
It isn't raining, so the grass must be dry
(There might have a sprinkler system.)

Rule #2: If A, then B, If B, then C
If A, then B: If I press the power button, the computer will turn off.
If B, then C: If the computer is off, then the website will shut down.

Valid Inference: If A, then C
If I press the power button, then the web site will shut down.

Valid Inference: If not C, then not A
If the website is not shut down, then I did not press the power button.

Invalid Inference: If C, then A
If website is shut down, then I must have pressed the power button.
(There may be other reasons for the computer being off (and the website shutting down as a result) and also reasons other than the computer being off for the website shutting down.)

Rule #3: All A are B
All GMATs are adaptive tests.

Valid Inference: All non-B's are non-A's.
A test that is not adaptive is not a GMAT.

Valid Inference: No non-B is an A.
No test that is not adaptive is a GMAT.

Invalid Inference: No non-A's are B's.
No non-GMAT tests are adaptive.
(Try the GRE.)

Invalid Inference: All B are A.
All adaptive tests are GMAT tests.
(Try the GRE.)

Rule #4: All A are B, All B are C.
All A are B: All GMATs are adaptive
All B are C: All adaptive tests are computerized tests.

Valid Inference: All A are C
All GMAT tests are computerized.

Valid Inference: No non-C is an A
No non-computerized test is a GMAT.

Invalid Inference: No non-A is a C
No non-GMAT test is computerized.
(Try the GRE).

Invalid Inference: All C are A
All computerized tests are GMAT tests.
(Try the GRE).

Rule #5: Some A are B.
Some MBA programs are part-time programs.

Valid Inference: Some B are A.
Some part-time programs are MBA programs.

Invalid Inference: Some A are not B.
Some MBA programs are not part-time.

Invalid Inference: Some B are not A.
Some part-time programs are not MBA programs.

Rule #6: Some A are B and Some B are C
Some A are B: Some MBA programs are part-time programs.
Some B are C: Some part-time programs are poetry degrees.

Valid Inference: Some B are A.
Some part-time programs are MBA programs.

Valid Inference: Some C are B.
Some poetry degrees are part-time programs.

Invalid Inference: Some A are C.
Some MBA programs are poetry degrees.

Invalid Inference: Some C are A.
Some poetry degrees are MBA programs.

(Why are C and D invalid? Although A and C have B in common, there does not need to be any overlap between MBA programs and poetry degrees.)

Rule #7: Some A are B and All B are C.
Some A are B: Some MBA programs are accounting programs.
All B are C: All accounting programs are math-intensive programs
.

Valid Inference: Some B are A.
Some accounting programs are MBA programs.

Valid Inference: Some A are C.
Some MBA programs are math-intensive programs.

Valid Inference: Some C are A.
Some math-intensive programs are MBA programs.

Invalid Inference: All C are A.
All math-intensive programs are MBA programs.

Invalid Inference: All C are B.
All MBA programs are math-intensive programs.

Rule #8: Either A or B, but not both
Either a dog or a cat.

Valid Inference: If A, then not B.
If a dog, then not a cat.

Valid Inference: If B, then not A.
If a cat, then not a dog.

Valid Inference: If not B, then A.
If a not a cat, then a dog.

Valid Inference: If not A, then B.
If a not a dog, then a cat.

There are two main types of Deductive Reasoning (Must Be True) Questions:

1. Make a deduction: extend the premises to make a direct logical conclusion?

If the statements above are true, which of the following must also be true?

Which of the following may be correctly inferred?

Which of the following inferences (inference means the same thing as "must be true" on the test) is best supported by the statement made above?
(Conclusions differ from inferences in that conclusions are the result of premises and inferences must be true if the premises are true.)

2. What's the missing premise? (Here you find out what premise would be necessary to make the argument logically valid.)

The passage's conclusion is only true if which of the following statements is also true?

Which of the following, if introduced into the argument as a premise, makes the argument logically correct?

 Most critical reasoning questions are about what may or may not be true based on assumptions. For example: Which of the following is the best, the most, or the least likely to satisfy the question? Deductive questions will never use those indicators. They are written in terms of certainty: must be true, required, necessary, etc...

How to tackle Deductive Reasoning (Must Be True Questions):

1. Read the passage and look for the argument. Note that Must Be True questions may not be an argument. They may just be a series of facts. Nevertheless, try to find the argument.

2. Must Be True questions always should be tackled using POE (process of elimination). Go through every answer choice systematically and check if it is ALWAYS true. If you can find a situation where it is not true, eliminate it. Gradually eliminate answer choices until you have one left.

Example

Every store on Main Street in Summitville has an awning. All of these awnings are either green or red.

If the statements above are true, which one of the following must also be true?

I. Some awnings in Summitville are green.
II. If a store in Summitville does not have an awning, then it is not on Main Street .
III. If a store in Summitville has a red awning, then it is on Main Street .

(A) I only

(B) II only

(C) I and II only

(D) I and III only

(E) I, II, and III

Explanation: The correct answer is B. Note that this question is not an argument per se because it requires deductive reasoning.

Statement I may not be true. The question states that all of the awnings on Main Street are either green or red, but this does not preclude the possibility that all of the awnings on Main Street are red.

Statement III may not be true either. The question states that every store on Main Street has either a red awning or a green awning, but this does not preclude the possibility that a store on some other street has a red awning.

Statement II must be true. If every store on Main Street has an awning, then a store without an awning cannot be on Main Street . The correct answer is B.

Example

The mathematical constant "e" ( the base of the natural logarithm) is transcendental and therefore irrational. In 1882, the mathematician Johann Heinrich Lambert proved that the number pi is irrational. Pi must therefore be transcendental.

Which of the following statements, if true, most weakens the conclusion drawn above about the number pi?

(A) The exact value of transcendental numbers cannot be given.

(B) The number √2 is irrational but not transcendental.

(C) The mathematician Fernard von Lindermann used the fact that e is transcendental to prove that pi is transcendental.

(D) The number √3 is transcendental but not irrational.

(E) It is extremely difficult to prove that a number is transcendental.

Explanation: The correct answer is B. This question asks you to weaken the conclusion, which states that pi must be transcendental. The key phrase here is “must be.” We know "e" to be transcendental and therefore irrational, but all we’re told about pi is that it is irrational, so the conclusion that pi must therefore be transcendental is unfounded. Pi might be transcendental (and in fact is), but the information in the passage can’t logically lead us to that conclusion. A statement weakening the conclusion will show that pi is not necessarily transcendental. Choices (A), (C) and (E) are irrelevant. Choice (B) states that a number can be irrational and not transcendental. This shows that pi is not necessarily transcendental. Choice (D) gives us the reverse of what we want since it tells us that a number can be transcendental and not irrational.  We already know that pi is irrational, so this doesn’t weaken the conclusion. Choice (B) does, and is the best answer.

Section 5-4: Advanced Question Types – Style of Reasoning Questions (uncommon)

Style of Reasoning questions ask you to describe how the argument was made, not necessarily what it says. You will compare the reasoning in two arguments or choose the answer choice that uses the most similar deductive process.

Here are some examples of the ways in which the stems to such questions are worded:

• How does the author make his point?
• A's response has which of the following relationships to B's argument?

How to approach Style of Reasoning Questions

1. Read the argument and find the conclusion.

2. State the reasoning in your own words. Describe how the author gets from the premises to the conclusion.

3. Use POE. The best answer will describe the reasoning used in the argument. Eliminate answer choices that don't match the reasoning used in the argument.

Examples

1. There is a piece of folk wisdom expressed in the saying, "If it is not broken, don't fix it." A factory manager who accepted that saying would be least likely to:

(A) Agree to union demands, in the interest of safety, for better lighting in the stairwells and storage areas.

(B) Respond to the difficulty of retaining skilled electronic technicians by establishing an on-site day-care center for small children.

(C) Order the immediate replacement of windows broken in a strike.

(D) Replace the quality control supervisor after receiving several complaints about defective units in recent shipments from the factory.

(E) Institute a program of preventive maintenance for major pieces of production machinery.

Explanation: The point of the proverb, "If it is not broken, don't fix it" is that tampering with something which is not an urgent problem is unnecessary. All of the alternatives involve the manager's making some change or taking some action. But the first four represent the manager's action as being a response to a particular existing problem. They are not against the spirit of the proverb. But preventive maintenance seems to be just what the proverb advises against. (E) is the best answer.

2. Despite recent rumors of a new and improved building, employees should not expect renovations.
Without the support of the building's supervisor, the committee's plan usually fails. Two years ago, a plan to renovate the meeting rooms went under after the supervisor changed his mind and withdrew his support.

The bolded extracts play which of the following roles in the argument above?

(A) The first extract offers advice and the second extract states a conclusion.

(B) The first extract states the conclusion and the second extract supports that conclusion with an analogy.

(C) The first extract states a conclusion and the second extract provides evidence that weakens the conclusion.

(D) The first extract states a position and the second extract contains unrelated information.

(E) The first extract states a premise on which the conclusion is based and the second extract states the conclusion.

Explanation: This question asks you to identify the parts of an argument. The argument's structure is as follows: The expected outcome of a situation is presented; followed by a general rule for predicting the outcome of situations like these; followed by a specific instance of the general rule. The conclusion is in the beginning, while the argument in support of the conclusion follows after it.

Looking at the answer choices, we see that only two answer choices, (B and C), put the conclusion first.

Choice (A)'s description of the first extract as an offer of advice could be correct, but as the second extract is not the conclusion. Choice (A) is incorrect.

Choice (D) inaccurately describes the first extract's function as stating a position.

Choice (E) describes the first extract's function as a premise, which is incorrect.

Choices (B) and (C) are identical in their description of the first extract as a conclusion, but differ in their descriptions of the second extract. Choice (B) describes the second extract as an analogy supporting the conclusion. Is this accurate? Yes. The use of another, similar situation to illustrate the outcome of this situation constitutes an analogy, and it supports the conclusion. Choice (C) suggests that the second phrase weakens the conclusion, which it does not. Choice (B) is the best answer.

 Double Bold Critical Reasoning Questions are typically deductive arguments and demonstrate how two arguments interact.

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