GMAT考試Testprep數學精解
-Testprep數學精解
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：
