GMAT考试Testprep数学精解

　　-Testprep数学精解

　　ARGUMENTS INTRODUCTION

　　An argument， as used on the GMAT， is a presentation of facts and opinions in　order to support a position. Many arguments will be fallacious. And many correct answers will be false! This often causes students much consternation;they feel that the correct answer should be true. But the arguments are intended to test your ability to think logically. Now logic is the study of the　relationships between statements， not of the truth of those statements. Being overly concerned with finding the truth can be ruinous to your GMAT argument score.

　　2 OUT OF 5 RULE

　　Creating a good but incorrect answer-choice is much harder than developing the correct answer. For this reason， usually only one attractive wrong answer-choice is presented. This is called the 2 out of 5 rule. That is， only two of the five answer-choices will have any real merit. Hence， even if you dont fully understand an argument， you probably can still eliminate the three　fluff choices， thereby greatly increasing your odds of answering the question correctly.

　　LOGIC I

　　Although in theory the argument questions are designed to be answered without any reference to formal logic， the section is essentially a logic test. So　me knowledge of the fundamentals of logic， therefore， will give you a definite advantage. Armed with this knowledge， you should quickly notice that the　arguments are fundamentally easy and that most of them fallsintosa few basic　categories. In this section， we will study the logical structure of arguments. In Logic II， we will symbolize and diagram arguments in much the same way as we did with games.

　　Conclusions

　　Most argument questions hinge， either directly or indirectly， on determining　the conclusion of the argument. The conclusion is the main idea of the argument. It is what the writer tries to persuade the reader to believe. Most of　ten the conclusion comes at the end of the argument. The writer organizes the facts and his opinions so that they build up to the conclusion. Sometimes，however， the conclusion will come at the beginning of an argument， rarely does it come in the middle， and occasionally， for rhetorical effect， the conclusion is not even stated.

　　Example：

　　The police are the armed guardians of the social order. The blacks are the chief domestic victims of the American social order. A conflict of interest exists， therefore， between the blacks and the police.――Eldridge Cleaver， Soul

　　on Ice

　　Here the first two sentences anticipate or set up the conclusion. By changing the grammar slightly， the conclusion can be placed at the beginning of the　argument and still sound natural：

　　A conflict of interest exists between the blacks and the police because the　police are the armed guardians of the socialsgroupsand the blacks are the chief domestic victims of the American social order.

　　The conclusion can also be forcedsintosthe middle：

　　The police are the armed guardians of the social order. So a conflict of interest exists between the blacks and the police because the blacks are the chief domestic victims of the American social order.

　　It is generally awkward， as in the previous paragraph， to place the conclusion in the middle of the argument because then it cannot be fully anticipated by what comes before nor fully explained by what comes after. On the rare occasion when a conclusion comes in the middle of an argument， most often either the material that comes after it or the material that comes before it is　not essential.

　　In summary： To find the conclusion， check the last sentence of the argument.

　　If that is not the conclusion， check the first sentence. Rarely does the conclusion come in the middle of an argument.

　　When determining the meaning of a conclusion， be careful not to read any moresintosit than what the author states. Although arguments are not worded as　precisely as games， you still need to read them with more care than you would use in your everyday reading.

　　As with games， read the words and sentences of an argument precisely， and use their literal meaning.

　　For example， consider the meaning of some in the sentence Some of Marys friends went to the party. It would be unwarranted， based on this statement，to assume that some of Marys friends did not go to the party. Although it may seem deceiving to say that some of Marys friends went to the party when　in fact all of them did， it is nonetheless technically consistent with the meaning of some.

　　Some means at least one and perhaps all.

　　As mentioned before， the conclusion usually comes at the end of an argument，sometimes at the beginning， and rarely in the middle. Writers use certain words to indicate that the conclusion is about to be stated. Following is a list of the most common conclusion indicators：

　　Conclusion Indicators

　　hence therefore

　　so accordingly

　　thus consequently

　　follows that shows that

　　conclude that implies

　　as a result means that

　　Most often the conclusion of an argument is put in the form of a statement.

　　Sometimes， however， the conclusion is given as a command or obligation.

　　Example：

　　All things considered， you ought to vote.

　　Here， the author implies that you are obliged to vote.

　　The conclusion can even be put in the form of a question. This rhetorical technique is quite effective in convincing people that a certain position is correct. We are more likely to believe something if we feel that we concluded　it on our own， or at least if we feel that we were not told to believe it.

　　A conclusion put in question form can have this result.

　　Example：

　　The Nanuuts believe that they should not take from Nature anything She cannot replenish during their lifetime. This assures that future generations can　enjoy the same riches of Nature that they have. At the current rate of destruction， the rain forests will disappear during our lifetime. Do we have an obligation to future generations to prevent this result?

　　Here the author trusts that the power of her argument will persuade the reader to answer the question affirmatively.

　　Taking this rhetorical technique one step further， the writer may build up to the conclusion but leave it unstated. This allows the reader to make up his own mind. If the build-up is done skillfully， the reader will be more likely to agree with the author， without feeling manipulated.

　　Example：

　　He who is without sin should cast the first stone. There is no one here who　does not have a skeleton in his closet.

　　The unstated but obvious conclusion here is that none of the people has the　right to cast the first stone.

　　When determining the conclusions scope be careful not to read any more or lesssintosit than the author states. GMAT writers often create wrong answer-choices by slightly overstating or understating the authors claim. Certain words limit the scope of a statement. These words are called quantifiers――pay　close attention to them. Following is a list of the most important quantifiers：

　　Quantifiers

　　all except likely

　　some most many

　　only could no

　　never always everywhere

　　probably must alone

　　Example：

　　Whether the world is Euclidean or non-Euclidean is still an open question.

　　However， if a stars position is predicted based on non-Euclidean geometry，then when a telescope is pointed toswheresthe star should be it will be there. Whereas， if the stars position is predicted based on Euclidean geometry，then when a telescope is pointed toswheresthe star should be it wont be there. This strongly indicates that the world is non-Euclidean.

　　Which one of the following best expresses the main idea of the passage?

　　 The world may or may not be Euclidean.

　　 The world is probably non-Euclidean.

　　 The world is non-Euclidean.

　　 The world is Euclidean.

　　 The world is neither Euclidean nor non-Euclidean.

　　Choice understates the main idea. Although the opening to the passage states that we dont know whether the world is non-Euclidean， the author goes　on to give evidence that it is non-Euclidean. Choice overstates the main　idea. The author doesnt say that the world is non-Euclidean， just that evidence strongly indicates that it is. In choice ， the word probably properly limits the scope of the main idea， namely， that the world is probably non-Euclidean， but we cant yet state so definitively. The answer is 。

　　Premises

　　Once youve found the conclusion， most often everything else in the argument　will be either premises or noise. The premises provide evidence for the conclusion; they form the foundation or infrastructure upon which the conclusion depends. To determine whether a statement is a premise， ask yourself whether it supports the conclusion. If so， its a premise. Earlier we saw that　writers use certain words to flag conclusions; likewise writers use certain　words to flag premises. Following is a partial list of the most common premise indicators：

　　Premise Indicators

　　because for

　　since is evidence that

　　if in that

　　as owing to

　　suppose inasmuch as

　　assume may be derived from

　　Example：

　　Since the incumbents views are out of step with public opinion， he probably　will not be reelected.

　　Here since is used to flag the premise that the incumbents positions are　unpopular.

　　Suppressed Premises

　　Most arguments depend on one or more unstated premises. Sometimes this indicates a weakness in the argument， an oversight by the writer. More often， however， certain premises are left tacit because they are too numerous， or the　writer assumes that his audience is aware of the assumptions， or he wants the audience to fill in the premise themselves and therefore be more likely to　believe the conclusion.

　　Example：

　　Conclusion： I knew he did it.

　　Premise： Only a guilty person would accept immunity from prosecution.

　　The suppressed premise is that he did， in fact， accept immunity. The speaker　assumes that his audience is aware of this fact or at least is willing to believe it， so to state it would be redundant and ponderous. If the unstated　premise were false ， the argument would　not technically be a lie; but it would be very deceptive. The unscrupulous　writer may use this ploy if he thinks that he can get away with it. That is，his argument has the intended effect and the false premise， though implicit， is hard to find or is ambiguous. Politicians are not at all above using this tactic.

　　A common question on the GMAT asks you to find the suppressed premise of an　argument. Finding the suppressed premise， or assumption， of an argument can　be difficult. However， on the GMAT you have an advantage――the suppressed premise is listed as one of the five answer-choices. To test whether an answer-choice is a suppressed premise， ask yourself whether it would make the argument more plausible. If so， then it is very likely a suppressed premise.

　　Example：

　　American attitudes tend to be rather insular， but there is much we can learn　from other countries. In Japan， for example， workers set aside some time each day to exercise， and many corporations provide elaborate exercise facilities for their employees. Few American corporations have such exercise programs. Studies have shown that the Japanese worker is more productive than the　American worker. Thus it must be concluded that the productivity of American　workers will lag behind their Japanese counterparts， until mandatory exercise programs are introduced.

　　The conclusion of the argument is valid if which one of the following is assumed?

　　 Even if exercise programs do not increase productivity， they will improve the American workers health.

　　 The productivity of all workers can be increased by exercise.

　　 Exercise is an essential factor in the Japanese workers superior productivity.

　　 American workers can adapt to the longer Japanese work week.

　　 American corporations dont have the funds to build elaborate exercise facilities.

　　The unstated essence of the argument is that exercise is an integral part of　productivity and that Japanese workers are more productive than American workers because they exercise more. The answer is 。

　　Counter-Premises

　　When presenting a position， you obviously dont want to argue against yourself. However， it is often effective to concede certain minor points that weaken your argument. This shows that you are open-minded and that your ideas are well considered. It also disarms potential arguments against your position For instance， in arguing for a strong， aggressive police department， you may concede that in the past the police have at times acted too aggressively.

　　Of course， you will then need to state more convincing reasons to support y　our position.

　　Example：

　　I submit that the strikers should accept the managements offer.Admittedly，　it is less than what was demanded. But it does resolve the main grievance――　inadequate health care. Furthermore， an independent study shows that a wage　increase greater than 5% would leave the company unable to compete against Japan and Germany， forcing itsintosbankruptcy.

　　The conclusion， the strikers should accept the managements offer， is stated in the first sentence. Then Admittedly introduces a concession; namely，that the offer was less than what was demanded. This weakens the speakerscase， but it addresses a potential criticism of his position before it can be made. The last two sentences of the argument present more compelling reasons to accept the offer and form the gist of the argument.

　　Following are some of the most common counter-premise indicators：

　　Counter-Premise Indicators

　　but despite

　　admittedly except

　　even though nonetheless

　　nevertheless although

　　however in spite of the fact

　　As you may have anticipated， the GMAT writers sometimes use counter-premises　to bait wrong answer-choices. Answer-choices that refer to counter-premises　are very tempting because they refer directly to the passage and they are in part true. But you must ask yourself Is this the main point that the auth　or is trying to make? It may merely be a minor concession.

　　Logic II

　　Most arguments are based on some variation of an if-then statement. However，　the if-then statement is often embedded in other equivalent structures. Diagramming brings out the superstructure and the underlying simplicity of arguments.

　　If-Then

　　A――B

　　By now you should be well aware that if the premise of an if-then statement　is true then the conclusion must be true as well. This is the defining characteristic of a conditional statement; it can be illustrated as follows：

　　A――B

　　A

　　Therefore， B

　　This diagram displays the if-then statement A――B， the affirmed premise A， and the necessary conclusion B. Such a diagram can be very helpful in showing the logical structure of an argument.

　　Example：

　　If Jane does not study for the GMAT， then she will not score well. Jane， in　fact， did not study for the GMAT; therefore she scored poorly on the test.

　　When symbolizing games， we let a letter stand for an element. When symbolizing arguments， however， we may let a letter stand for an element， a phrase， a　clause， or even an entire sentence. The clause Jane does not study for the

　　GMAT can be symbolized as ~S， and the clause she will not score well can　be symbolized as ~W. Substituting these symbolssintosthe argument yields the following diagram：

　　~S――~W

　　~S

　　Therefore， ~W

　　This diagram shows that the argument has a valid if-then structure. A conditional statement is presented， ~S―― its premise affirmed， ~S; and then the conclusion that necessarily follows， ~W， is stated.

　　Embedded If-Then Statements

　　Usually， arguments involve an if-then statement. Unfortunately， the if-then　thought is often embedded in other equivalent structures. In this section， we study how to spot these structures.

　　Example：

　　John and Ken cannot both go to the party.

　　At first glance， this sentence does not appear to contain an if-then statement. But it essentially says： if John goes to the party， then Ken does not.

　　Example：

　　Danielle will be accepted to graduate school only if she does well on the GRE.

　　Given this statement， we know that if Danielle is accepted to graduate school， then she must have done well on the GRE. Note： Students often wrongly interpret this statement to mean：

　　If Danielle does well on the GRE， then she will be accepted to graduate school.

　　There is no such guarantee. The only guarantee is that if she does not do well on the GRE， then she will not be accepted to graduate school.

　　A only if B is logically equivalent to if A， then B.

　　Affirming the Conclusion Fallacy

　　A――B

　　B

　　Therefore， A

　　Remember that an if-then statement， A――B， tells us only two things： If　A is true， then B is true as well. If B is false， then A is false as well 。 If， however， we know the conclusion is true， the if-then　statement tells us nothing about the premise. And if we know that the premise is false ， then the if-then statement tells us nothing about the conclusion.

　　Example：

　　If he is innocent， then when we hold him under water for sixty seconds he will not drown. Since he did not die when we dunked him in the water， he must　be innocent.

　　The logical structure of the argument above is most similar to which one of　the following?

　　 To insure that the remaining wetlands survive， they must be protected by　the government. This particular wetland is being neglected. Therefore， it will soon perish.

　　 There were nuts in that pie I just ate. There had to be， because when I　eat nuts I break out in hives， and I just noticed a blemish on my hand.

　　 The president will be reelected unless a third candidate enters the race A third candidate has entered the race， so the president will not be reelected.

　　 Every time Melinda has submitted her book for publication it has been rejected. So she should not bother with another rewrite.

　　 When the government loses the power to tax one area of the economy， it just taxes another. The Supreme Court just overturned the sales tax， so we can expect an increase in the income tax.

　　To symbolize this argument， let the clause he is innocent be denoted by I，and let the clause when we hold him under water for sixty seconds he will not drown be denoted by ~D. Then the argument can be symbolized as

　　I――~D

　　~D

　　Therefore， I

　　Notice that this argument is fallacious： the conclusion he is innocent is　also a premise of the argument. Hence the argument is circular――it proves what was already assumed. The argument affirms the conclusion then invalidly uses it to deduce the premise. The answer will likewise be fallacious.

　　We start with answer-choice 。 The sentenceTo insure that the remaining wetlands survive， they must be protected by the government　contains an embedded if-then statement：

　　If the remaining wetlands are to survive， then they must be protected by the government.This can be symbolized as S――P. Next， the sentence This particular wetland　is being neglected can be symbolized as ~P. Finally， the sentence It will　soon perish can be symbolized as ~S. Using these symbols to translate the　argument gives the following diagram：

　　S――P

　　~P

　　Therefore， ~S

　　The diagram clearly shows that this argument does not have the same structure as the given argument. In fact， it is a valid argument by contraposition.

　　Turning to ， we reword the statement when I eat nuts， I break out in hives as