Finding Fault: Common Flaws in GMAT Logic

[Kevin]

PART ONE:
This week, we begin a new series on common flaws in GMAT Critical Reasoning arguments. Some Critical Reasoning ("CR") questions will ask you to spot the flaw directly, but it is more likely that you will need to spot the flaw in order to answer another question, perhaps regarding assumptions or paradoxes.

A very common flaw on the GMAT, and in life, is the confusion of absolute numbers and percentages. For example, which is larger, one-third of x or one-half of y? Without any information to compare x and y, we cannot answer this question. It is true that one-half is larger than one-third when applied to the same quantity, but when applied to quantities of different sizes, one-third could be much larger than one-half. For example, one-third of the population of New York City is a greater quantity than one-half the population of Boise, Idaho.

How does this play out on the GMAT? Consider the following argument:

At any given time, approximately fifteen percent of all homes in Florida are on the market. In Texas, however, only seven percent of all homes are on the market at any given time. Therefore, one will have a wider selection of homes to choose from if one looks for a home in Florida rather than in Texas.

This argument falsely assumes that the number of homes for sale in Florida is greater than the number of homes for sale in Texas, based on the fact that a larger proportion of homes in Florida are for sale. Imagine, however, that there are only 100 homes in Florida, yielding an available housing stock of 15 homes. And imagine that there are 1000 homes in Texas, yielding an available housing stock of 70 homes. In this case, the conclusion of the argument would not hold true. (Bonus: At least what percentage of the number of homes in Texas would the number of homes in Florida have to be in order for the argument to hold true? Answer found at bottom of page.)

The relationship between number and percent can also go the other way. Consider the following argument:

More people in California own air conditioners than do people in Illinois, Indiana, and Ohio combined. Therefore, Californians are clearly more concerned with their physical comfort than are people in those other three states.

This argument falsely assumes that the percentage of people who own air conditioners is higher in California than it is in Illinois, Indiana, and Ohio together, based on the fact that the number of people who own air conditioners is greater in California. Imagine, for example, that the population of California were 10,000,000, of whom 1,000,000 owned air conditioners - representing 10%. Imagine as well that the combined population of Illinois, Indiana, and Ohio were 1,000,000, of whom 900,000 owned air conditioners. Now, it would indeed be true that more people owned air conditioners in California, but it would represent only 10% of the population, whereas 90% of the population of the other states owned air conditioners. In these circumstances, it would be difficult to maintain that Californians care more about their physical comfort. When dealing with arguments that involve comparisons of quantities and/or percents, be sure you determine whether the comparison is valid.

(Bonus answer: In order for the argument to be valid, it would have to be true that 15% of homes in Florida is greater than 7% of homes in Texas. We can represent this as an equation: . If we isolate F, we get:

Therefore, the number of homes in Florida has to be greater than 47% of the number of homes in Texas.)

Next week, we will look at flaws in arguments involving claims of causation.



PART TWO:
This week, we continue our discussion of common GMAT logic flaws with a look at causation. This concept appears regularly on the GMAT and most people taking the exam can expect to see at least one Critical Reasoning question dealing with the issue. But if you understand the concept and anticipate it, you should not have much trouble handling the question when it arises.

Two problems generally crop up when the GMAT tests the concept of causation. The first is a false assumption that the causal connection is possible in one direction only. This is basically the confusion of causation with correlation. What does that mean? Causation is, as the term implies, a direct causal link: x causes y. Correlation, however, is essentially coincidence: x and y occur simultaneously so often that a causal relationship is assumed. The problem with this confusion is that with correlation, it is difficult to know whether x causes y or y causes x. It may be that neither causes the other and they are truly coincidental.

Let's look at an example: Imagine that every time a bee lands on a certain closed flower, the flower opens and the bee enters to gather pollen. It would be easy to assume that the bee's landing somehow spurs the flower to open, though it is equally plausible that the flower's opening causes the bee to come land on it. That is, the bee might know when the flower is about to open and come just in time. The causal connection (between the bee's landing and the flower's opening) cannot be proven in either direction from this simple observation. How does this play out on the GMAT? Imagine the following Critical Reasoning argument:

Researchers have noticed that people whose blood shows abnormally low levels of calcium usually develop laryngeal polyps, which can permanently damage vocal cords and result in partial or even total loss of voice. In order to prevent the polyps, the researchers recommend a diet high in calcium-rich foods such as dairy and green, leafy vegetables.

Is there a clear causal connection between low levels of calcium in the blood and laryngeal polyps? No. Reading the above argument, we are tempted to take for granted that the causal connection is lack of calcium -> laryngeal polyps. But it is equally plausible that the causal connection is actually laryngeal polyps -> lack of calcium. How? Imagine that the polyps somehow prevent the body from processing calcium, so that it is not the lack of calcium causing the polyps but rather the polyps that cause the lack of calcium. In the latter case, increasing one's dietary intake of calcium would likely do little to combat the polyps.

The second major problem with causation on the GMAT is the assumption that there are no alternate models of causality. That sounds a lot more technical than it really is. Essentially, this occurs when one assumes that there is only one possible cause of a certain outcome. For example, "The ground is wet, therefore it must have rained." In this case, the faulty assumption is that only rain could have caused the ground to become wet. It ignores the possibility that someone could have spilled a bucket of water, someone's sprinklers could be on, a garden hose could be leaking, etc. In the absence of direct proof of causation, one cannot assume that any particular thing is necessarily the cause of a particular outcome. How does this play out on the GMAT? Consider the following argument:

The recent boom in new home construction has finally begun to taper off. Developers are not buying land, contractors are finding themselves going without work for longer periods, and banks are issuing fewer mortgages. People must not be as interested in buying new homes as they were even six months ago.

Is this conclusion ("People must not be as interested in buying new homes as they were even six months ago.") valid? Not necessarily. It may be, for example, that all of the observations made in the argument were caused by a sudden, steep increase in interest rates, which made buying a home too expensive for most people even though they remained as interested in buying a home as ever. So the cause here is not lack of interest but rather lack of money.

Whenever a claim of causation is made in a GMAT Critical Reasoning argument, you need to consider (a) whether the relationship is causal or correlative; or (b) whether there are other possible causes for that particular outcome.

Next week, we will look at flaws involving "limiting words" in GMAT arguments.

[800guy]

awesome article, kevin!!

[Kevin]

PART THREE:
This week, we continue our discussion of common GMAT flaws with a look at a different type of mistake. Instead of a mistake in the logic of a GMAT argument, it is a mistake in the way many test takers interpret GMAT arguments. Specifically, we will look at ways in which test takers fail to grasp the importance of "limiting" words.

By "limiting" words, we mean those words that serve to limit the scope of an argument. For example, "always," "none," "some," and "only" are all limiting words in that they set boundaries for the logic of an argument. Because these words are so common and easily understood, however, they fail to register with many test takers, who often skim past them in their rush to read the argument. But often these words are the key to understanding the argument and, by extension, finding the correct answer.

Consider the following argument:

In order to save money, some of Company X's manufacturing plants converted from oil fuel to natural gas last year, when the cost of oil was more than the cost of natural gas. Because of a sudden, unexpected shortage, however, natural gas now costs more than oil, the price of which has fallen steeply over the past year. The cost of conversion back to oil would more than negate any cost savings in fuel. So Company X's fuel costs this year will be significantly higher than they were last year.

On first read, this argument probably seems valid: gas is now more expensive than oil, but converting back to oil will cost more than sticking with gas, so Company X will have to spend more on fuel this year. But is this really a valid conclusion based on the information in the argument? How many of Company X's plants converted to gas last year? All we know is that some of the plants converted to gas. It is possible, therefore, that the vast majority stuck with oil, which is now cheaper than gas, plausibly reducing Company X's overall fuel costs for the year. The validity of the conclusion depends on the easily missed word "some". If you caught it, good job! If not, remember to read carefully.

Limiting words are especially important in questions where you are asked to decide which of the five choices is a valid conclusion that could be drawn from the information given in the passage. It is crucial in these questions to remember that the correct answer (i.e., the valid conclusion) cannot go beyond the scope of the information in the text. In fact, the wrong answers in these questions are usually wrong for that very reason: they go beyond the information in the text. If the argument does not provide extreme information, you cannot draw an extreme conclusion. For example, if it is true that many people like pizza, then it is true that some people like pizza. But, in contrast, if it is true that some people like pizza, it is not necessarily true that many people do.

Consider the following:

Scientists have determined that an effective way to lower cholesterol is to eat three servings of whole grains every day. Studies have shown that the cholesterol levels of people who did so were significantly lower after six months than were those of people who did not, even though the cholesterol levels of the two groups were the same before the studies began.

If the statements above are taken as true, can we conclude that eating three servings of whole grains every day is the best way to lower cholesterol? No. Can we conclude that it is one of the best ways? No. Can we conclude that it always works? No. Can we conclude that it usually works? No. Can we conclude that it sometimes works? Yes! Finally, a valid conclusion! It may not seem earth-shattering, but that is probably because you already knew as much from reading the text (which is what makes it a valid conclusion). Do not expect the correct answer in such questions necessarily to be something you would never have thought of on your own. Usually, in fact, test takers get such questions wrong when they reach too far, wanting to conclude more than the information has already told them.

During your Critical Reasoning practice, make an effort to spot limiting words in the arguments. Often, your ability to answer correctly will depend on this skill.

Next week, we will look at flaws involving a disconnect between the focus of the evidence and the focus of the conclusion.

[Kevin]

PART FOUR:
This is the final installment in our series on common logic flaws on the GMAT. This week, we will discuss disconnects between the stated premises and the conclusion of an argument. This flaw type is very common in Assumption and Strengthen/Weaken questions. It also comes into play in the AWA (Analytical Writing Assessment) portion of the exam.

First, let's define what we mean by "disconnect" between the premises and the conclusion. The premises are those facts or opinions that the author uses to support his or her final position (i.e., conclusion). In order for the argument to be valid, the premises must provide a logical basis for the conclusion, otherwise the conclusion has no foundation. When the conclusion focuses on something different from the focus of the premises, we have a "disconnect" and the argument is flawed. Consider the following example:

Poison is harmful.
Therefore, cyanide is harmful.

In this case, the premise ("Poison is harmful") focuses on poison while the conclusion ("Therefore, cyanide is harmful") focuses on cyanide. Is there a disconnect here? Yes. We have not been given enough information to make a connection between poison and cyanide. Since the conclusion is about cyanide, we need a premise about cyanide, but instead we have information about poison only. Of course, in real life we know that cyanide is a poison, but on the exam you cannot bring outside knowledge to an argument. You must judge the validity of any conclusion only by the strength of given premises. So here, because the argument provides no information about cyanide, it is not valid to draw a conclusion about cyanide. Notice the difference if we simply insert another premise:

Poison is harmful.
Cyanide is poison.
Therefore, cyanide is harmful.

The argument is now valid: the premises provide enough information to support the conclusion. The term "poison" no longer simply disappears, only to be replaced with the term "cyanide." Now there is an intermediate step that links the two terms and allows us to draw a valid conclusion. This flaw crops up primarily in Assumption questions, where the correct answer is often the choice that connects the focus of the premises and the focus of the conclusion, because that choice provides information that has to be assumed in order to link the two. Let's look at another example:

Last year, the Metropolitan Police Department reported a ten percent drop in robbery, a twenty percent drop in assault, and a thirty percent drop in homicide. All other categories of crime remained at the same levels as before. The Police Department attributes these decreases to community involvement, including citizen patrols and the new crime hotline. Clearly, community involvement can reduce the crime rate in the city.

Notice how the inclusion of the premise "All other categories of crime remained at the same levels as before" provides enough information to remedy the disconnect between the drop in the three specified categories of crime and the drop in the overall crime rate.

In addition to appearing in Assumption questions, this flaw type also appears in Strengthen and Weaken questions. In Strengthen questions, if the premises and conclusion focus on different things, you can often strengthen the argument by finding a choice that links the two more clearly. By the same token, in Weaken questions, you can often weaken the argument by finding a choice that severs the potential link between the premises and conclusion.

As you practice your Critical Reasoning, pay attention to the focus of the premises and the focus of the conclusion. Your skill in this question type should improve as you become more sensitive to the potential disconnect between the two.