Common Flaws in GMAT Logic, Sponsored by Manhattan GMAT

SomeCritical Reasoning ("CR") questions will ask you to spot the flawdirectly, but it is more likely that you will need to spot the flaw in order toanswer another question, perhaps regarding assumptions or paradoxes.

Avery common flaw on the GMAT—and in life—is the confusion of absolute numbersand percentages.  For example, which islarger, one-third of x or one-half of y?  Without any information to compare x and y, wecannot answer this question.  It is truethat one-half is larger than one-third when applied to the same quantity, butwhen applied to quantities of different sizes, one-third could be much largerthan one-half.  For example, one-third ofthe population of New York City is a greater quantity than one-half the populationof Boise, Idaho.

Howdoes this play out on the GMAT?  Considerthe following argument:

Atany given time, approximately 15 percent of all homes in Florida are on themarket.  In Texas, however, only sevenpercent of all homes are on the market at any given time.  Therefore, one will have a wider selection ofhomes to choose from if one looks for a home in Florida rather than in Texas.

Thisargument falsely assumes that the number of homes for sale in Florida isgreater than the number of homes for sale in Texas, based on the fact that alarger proportion of homes in Florida are for sale.  Imagine, however, that there are only 100homes in Florida, which means there is 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 argumentwould not hold true.  (Bonus: At leastwhat percentage of the number of homes in Texas would the number of homes inFlorida have to be in order for the argument to hold true?  Answer found at bottom of page.)

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

Morepeople in California own air conditioners than do people in Illinois, Indiana andOhio combined.  Therefore, Californiansare clearly more concerned with their physical comfort than are people in thoseother three states.

Thisargument falsely assumes that the percentage of people who own air conditionersis 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 greaterin California.  Imagine, for example,that the population of California were 10,000,000, of whom 1,000,000 owned airconditioners—representing 10 percent.  Imagine as well that the combined populationof Illinois, Indiana and Ohio were 1,000,000, of whom 900,000 owned airconditioners.  Now, it would indeed betrue that more people owned air conditioners in California, but it wouldrepresent only 10 percent of the population, whereas 90 percent of thepopulation of the other states owned air conditioners.  In these circumstances, it would be difficultto maintain that Californians care more about their physical comfort.  When dealing with arguments that involvecomparisons of quantities and/or percents, be sure you determine whether thecomparison is valid.

Causation

Thisconcept appears regularly on the GMAT and most people taking the exam canexpect to see at least one Critical Reasoning question dealing with the issue.  But if you understand the concept andanticipate it, you should not have much trouble handling causation questionswhen they arise.

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

Let'slook at an example.  Imagine that everytime a bee lands on a certain closed flower, the flower opens and the beeenters to gather pollen.  It would beeasy to assume that the bee's landing somehow spurs the flower to open, thoughit is equally plausible that the flower's opening causes the bee to come landon it.  That is, the bee might know whenthe flower is about to open and come just in time.  The causal connection (between the bee'slanding and the flower's opening) cannot be proven in either direction fromthis simple observation.  How does thisplay out on the GMAT?  Check out thefollowing Critical Reasoning argument:

Researchershave noticed that people whose blood shows abnormally low levels of calciumusually develop laryngeal polyps, which can permanently damage vocal cords andresult in partial or even total loss of voice.  In order to prevent the polyps, theresearchers recommend a diet high in calcium-rich foods such as dairy andgreen, leafy vegetables.

Isthere a clear causal connection between low levels of calcium in the blood andlaryngeal polyps?  No.  Reading the above argument, we are tempted totake for granted that the causal connection is that the lack of calcium causeslaryngeal polyps.  But it is equallyplausible that the causal connection is actually that laryngeal polyps causelack of calcium.  Wondering how thatwould work?  Imagine that the polypssomehow prevent the body from processing calcium, so that it is not the lack ofcalcium causing the polyps but rather the polyps that cause the lack ofcalcium.  In the latter case, increasingone's dietary intake of calcium would likely do little to combat the polyps.

Thesecond major problem with causation on the GMAT is the assumption that thereare no alternate models of causality.  Thatsounds a lot more technical than it really is.  Essentially, this occurs when one assumes thatthere is only one possible cause of a certain outcome.  For example, "The ground is wet,therefore it must have rained."  Inthis case, the faulty assumption is that only rain could have caused the groundto become wet.  It ignores thepossibility that someone could have spilled a bucket of water, someone'ssprinklers 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 aparticular outcome.  How does this playout on the GMAT?  Consider the followingargument:

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

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

Whenevera claim of causation is made in a GMAT Critical Reasoning argument, you need toconsider (a) whether the relationship is causal or correlative and (b) whetherthere are other possible causes for that particular outcome.

Importance of "limiting"words

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

Considerthe following argument:

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

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

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

Here'sanother example:

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

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

Duringyour Critical Reasoning practice, make an effort to spot limiting words in thearguments.  Often, your ability to answercorrectly will depend on this skill.

Disconnect between thefocus of the evidence and the focus of the conclusion

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

Poisonis harmful.

Therefore,cyanide is harmful.

Inthis case, the premise ("Poison is harmful") focuses on poison whilethe conclusion ("Therefore, cyanide is harmful") focuses on cyanide.  Is there a disconnect here?  Yes.  Wehave not been given enough information to make a connection between poison andcyanide.  Since the conclusion is aboutcyanide, we need a premise about cyanide, but instead we have information aboutpoison only.  Of course, in real life weknow that cyanide is a poison, but on the exam you cannot bring outsideknowledge to an argument.  You must judgethe validity of any conclusion only by the strength of given premises.  So here, because the argument provides noinformation about cyanide, it is not valid to draw a conclusion about cyanide.  Notice the difference if we simply insertanother premise:

Poisonis harmful.

Cyanideis poison.

Therefore,cyanide is harmful.

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

Lastyear, the Metropolitan Police Department reported a 10 percent drop in robbery,a 20 percent drop in assault and a 30 percent drop in homicide.  All other categories of crime remained at thesame levels as before.  The PoliceDepartment attributes these decreases to community involvement, includingcitizen patrols and the new crime hotline. Clearly, community involvement canreduce the crime rate in the city.

Noticehow the inclusion of the premise "All other categories of crime remainedat the same levels as before" provides enough information to remedy thedisconnect between the drop in the three specified categories of crime and thedrop in the overall crime rate.

Inaddition to appearing in Assumption questions, this flaw type also appears inStrengthen and Weaken questions.  InStrengthen questions, if the premises and conclusion focus on different things,you can often strengthen the argument by finding a choice that links the twomore clearly.  By the same token, inWeaken questions, you can often weaken the argument by finding a choice thatsevers the potential link between the premises and conclusion.

Asyou practice your Critical Reasoning, pay attention to the focus of thepremises and the focus of the conclusion.  Your skill in this question type shouldimprove as you become more sensitive to the potential disconnect between thetwo.

(Bonusanswer: In order for the argument to be valid, it would have to be true that 15percent of homes in Florida is greater than 7 percent of homes in Texas.  We can represent this as an equation: .15F > .07T.  If we isolate F, we get:

         .15F > .07T

         .15F/.15 > .07T/.15

         F > .47T

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

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