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GMAT数学考试Testprep精解

2019-07-10 18:15:00来源:网络

  新东方在线GMAT频道为大家带来“GMAT数学考试Testprep精解”,希望对大家GMAT备考有所帮助。更多精彩尽请关注新东方在线GMAT频道!

  “If I eat nuts, then I break out in hives.” This in turn can be symbolized a

  s N――>H.

  Next, we interpret the clause “there is a blemish on my hand” to mean “hives

  ,“ which we symbolize as H. Substituting these symbolssintosthe argument yie

  lds the following diagram:

  N――>H

  H

  Therefore, N

  The diagram clearly shows that this argument has the same structure as the g

  iven argument. The answer, therefore, is (B)。

  Denying the Premise Fallacy

  A――>B

  ~A

  Therefore, ~B

  The fallacy of denying the premise occurs when an if-then statement is prese

  nted, its premise denied, and then its conclusion wrongly negated.

  Example: (Denying the Premise Fallacy)

  The senator will be reelected only if he opposes the new tax bill. But he wa

  s defeated. So he must have supported the new tax bill.

  The sentence “The senator will be reelected only if he opposes the new tax b

  ill“ contains an embedded if-then statement: ”If the senator is reelected, t

  hen he opposes the new tax bill.“ (Remember: ”A only if B“ is equivalent to

  “If A, then B.”) This in turn can be symbolized as R――>~T. The sentence “But

  the senator was defeated“ can be reworded as ”He was not reelected,“ which

  in turn can be symbolized as ~R. Finally, the sentence “He must have support

  ed the new tax bill“ can be symbolized as T. Using these symbols the argumen

  t can be diagrammed as follows:

  R――>~T

  ~R

  Therefore, T

  [Note: Two negatives make a positive, so the conclusion ~(~T) was reduced to

  T.] This diagram clearly shows that the argument is committing the fallacy

  of denying the premise. An if-then statement is made; its premise is negated

  ; then its conclusion is negated.

  Transitive Property

  A――>B

  B――>C

  Therefore, A――>C

  These arguments are rarely difficult, provided you step back and take a bir

  d‘s-eye view. It may be helpful to view this structure as an inequality in m

  athematics. For example, 5 > 4 and 4 > 3, so 5 > 3.

  Notice that the conclusion in the transitive property is also an if-then sta

  tement. So we don‘t know that C is true unless we know that A is true. Howev

  er, if we add the premise “A is true” to the diagram, then we can conclude t

  hat C is true:

  A――>B

  B――>C

  A

  Therefore, C

  As you may have anticipated, the contrapositive can be generalized to the tr

  ansitive property:

  A――>B

  B――>C

  ~C

  Therefore, ~A

  Example: (Transitive Property)

  If you work hard, you will be successful in America. If you are successful i

  n America, you can lead a life of leisure. So if you work hard in America, y

  ou can live a life of leisure.

  Let W stand for “you work hard,” S stand for “you will be successful in Amer

  ica,“ and L stand for ”you can lead a life of leisure.“ Now the first senten

  ce translates as W――>S, the second sentence as S――>L, and the conclusion as

  W――>L. Combining these symbol statements yields the following diagram:

  W――>S

  S――>L

  Therefore, W――>L

  The diagram clearly displays the transitive property.

  DeMorgan‘s Laws

  ~(A & B) = ~A or ~B

  ~(A or B) = ~A & ~B

  If you have taken a course in logic, you are probably familiar with these fo

  rmulas. Their validity is intuitively clear: The conjunction A&B is false wh

  en either, or both, of its parts are false. This is precisely what ~A or ~B

  says. And the disjunction A or B is false only when both A and B are false,

  which is precisely what ~A and ~B says.

  You will rarely get an argument whose main structure is based on these rules

  ――they are too mechanical. Nevertheless, DeMorgan‘s laws often help simplify

  , clarify, or transform parts of an argument. They are also useful with game

  s.

  Example: (DeMorgan‘s Law)

  It is not the case that either Bill or Jane is going to the party.

  This argument can be diagrammed as ~(B or J), which by the second of DeMorga

  n‘s laws simplifies to (~B and ~J)。 This diagram tells us that neither of th

  em is going to the party.

  A unless B

  ~B――>A

  “A unless B” is a rather complex structure. Though surprisingly we use it wi

  th little thought or confusion in our day-to-day speech.

  To see that “A unless B” is equivalent to “~B――>A,” consider the following s

  ituation:

  Biff is at the beach unless it is raining.

  Given this statement, we know that if it is not raining, then Biff is at the

  beach. Now if we symbolize “Biff is at the beach” as B, and “it is raining”

  as R, then the statement can be diagrammed as ~R――>B.

  CLASSIFICATION

  In Logic II, we studied deductive arguments. However, the bulk of arguments

  on the GMAT are inductive. In this section we will classify and study the ma

  jor types of inductive arguments.

  An argument is deductive if its conclusion necessarily follows from its prem

  ises――otherwise it is inductive. In an inductive argument, the author presen

  ts the premises as evidence or reasons for the conclusion. The validity of t

  he conclusion depends on how compelling the premises are. Unlike deductive a

  rguments, the conclusion of an inductive argument is never certain. The trut

  h of the conclusion can range from highly likely to highly unlikely. In reas

  onable arguments, the conclusion is likely. In fallacious arguments, it is i

  mprobable. We will study both reasonable and fallacious arguments.

  We will classify the three major types of inductive reasoning――generalizatio

  n, analogy, and causal――and their associated fallacies.

  Generalization

  Generalization and analogy, which we consider in the next section, are the m

  ain tools by which we accumulate knowledge and analyze our world. Many peopl

  e define generalization as “inductive reasoning.” In colloquial speech, the

  phrase “to generalize” carries a negative connotation. To argue by generaliz

  ation, however, is neither inherently good nor bad. The relative validity of

  a generalization depends on both the context of the argument and the likeli

  hood that its conclusion is true. Polling organizations make predictions by

  generalizing information from a small sample of the population, which hopefu

  lly represents the general population. The soundness of their predictions (a

  rguments) depends on how representative the sample is and on its size. Clear

  ly, the less comprehensive a conclusion is the more likely it is to be true.

  Example:

  During the late seventies when Japan was rapidly expanding its share of the

  American auto market, GM surveyed owners of GM cars and asked them whether t

  hey would be more willing to buy a large, powerful car or a small, economica

  l car. Seventy percent of those who responded said that they would prefer a

  large car. On the basis of this survey, GM decided to continue building larg

  e cars. Yet during the‘80s, GM lost even more of the market to the Japanese

  ……

  Which one of the following, if it were determined to be true, would best exp

  lain this discrepancy.

  (A) Only 10 percent of those who were polled replied.

  (B) Ford which conducted a similar survey with similar results continued to

  build large cars and also lost more of their market to the Japanese.

  (C) The surveyed owners who preferred big cars also preferred big homes.

  (D) GM determined that it would be more profitable to make big cars.

  (E) Eighty percent of the owners who wanted big cars and only 40 percent of

  the owners who wanted small cars replied to the survey.

  The argument generalizes from the survey to the general car-buying populatio

  n, so the reliability of the projection depends on how representative the sa

  mple is. At first glance, choice (A) seems rather good, because 10 percent d

  oes not seem large enough. However, political opinion polls are typically ba

  sed on only .001 percent of the population. More importantly, we don‘t know

  what percentage of GM car owners received the survey. Choice (B) simply stat

  es that Ford made the same mistake that GM did. Choice (C) is irrelevant. Ch

  oice (D), rather than explaining the discrepancy, gives even more reason for

  GM to continue making large cars. Finally, choice (E) points out that part

  of the survey did not represent the entire public, so (E) is the answer.

  Analogy

  To argue by analogy is to claim that because two things are similar in some

  respects, they will be similar in others. Medical experimentation on animals

  is predicated on such reasoning. The argument goes like this: the metabolis

  m of pigs, for example, is similar to that of humans, and high doses of sacc

  harine cause cancer in pigs. Therefore, high doses of saccharine probably ca

  use cancer in humans.

  Clearly, the greater the similarity between the two things being compared th

  e stronger the argument will be. Also the less ambitious the conclusion the

  stronger the argument will be. The argument above would be strengthened by c

  hanging “probably” to “may.” It can be weakened by pointing out the dissimil

  arities between pigs and people.

  Example:

  Just as the fishing line becomes too taut, so too the trials and tribulation

  s of life in the city can become so stressful that one‘s mind can snap.

  Which one of the following most closely parallels the reasoning used in the

  argument above?

  (A) Just as the bow may be drawn too taut, so too may one‘s life be wasted p

  ursuing self-gratification.

  (B) Just as a gambler‘s fortunes change unpredictably, so too do one‘s caree

  r opportunities come unexpectedly.

  (C) Just as a plant can be killed by over watering it, so too can drinking t

  oo much water lead to lethargy.

  (D) Just as the engine may race too quickly, so too may life in the fast lan

  e lead to an early death.

  (E) Just as an actor may become stressed before a performance, so too may dw

  elling on the negative cause depression.

  The argument compares the tautness in a fishing line to the stress of city l

  ife; it then concludes that the mind can snap just as the fishing line can.

  So we are looking for an answer-choice that compares two things and draws a

  conclusion based on their similarity. Notice that we are looking for an argu

  ment that uses similar reasoning, but not necessarily similar concepts. In f

  act, an answer-choice that mentions either tautness or stress will probably

  be a same-language trap.

  Choice (A) uses the same-language trap――notice “too taut.” The analogy betwe

  en a taut bow and self-gratification is weak, if existent. Choice (B) offers

  a good analogy but no conclusion. Choice (C) offers both a good analogy and

  a conclusion; however, the conclusion, “leads to lethargy,” understates the

  scope of what the analogy implies. Choice (D) offers a strong analogy and a

  conclusion with the same scope found in the original: “the engine blows, th

  e person dies“; ”the line snaps, the mind snaps.“ This is probably the best

  answer, but still we should check every choice. The last choice, (E), uses l

  anguage from the original, “stressful,” to make its weak analogy more tempti

  ng. The best answer, therefore, is (D)。

  Causal Reasoning

  Of the three types of inductive reasoning we will discuss, causal reasoning

  is both the weakest and the most prone to fallacy. Nevertheless, it is a us

  eful and common method of thought.

  To argue by causation is to claim that one thing causes another. A causal ar

  gument can be either weak or strong depending on the context. For example, t

  o claim that you won the lottery because you saw a shooting star the night b

  efore is clearly fallacious. However, most people believe that smoking cause

  s cancer because cancer often strikes those with a history of cigarette use.

  Although the connection between smoking and cancer is virtually certain, as

  with all inductive arguments it can never be 100 percent certain. Cigarette

  companies have claimed that there may be a genetic predisposition in some p

  eople to both develop cancer and crave nicotine. Although this claim is high

  ly improbable, it is conceivable.

  There are two common fallacies associated with causal reasoning:

  Confusing Correlation with Causation.

  To claim that A caused B merely because A occurred immediately before B is c

  learly questionable. It may be only coincidental that they occurred together

  , or something else may have caused them to occur together. For example, the

  fact that insomnia and lack of appetite often occur together does not mean

  that one necessarily causes the other. They may both be symptoms of an under

  lying condition.

  2. Confusing Necessary Conditions with Sufficient Conditions.

  A is necessary for B means “B cannot occur without A.” A is sufficient for B

  means “A causes B to occur, but B can still occur without A.” For example,

  a small tax base is sufficient to cause a budget deficit, but excessive spen

  ding can cause a deficit even with a large tax base. A common fallacy is to

  assume that a necessary condition is sufficient to cause a situation. For ex

  ample, to win a modern war it is necessary to have modern, high-tech equipme

  nt, but it is not sufficient, as Iraq discovered in the Persian Gulf War.

  SEVEN COMMON FALLACIES

  Contradiction

  A Contradiction is committed when two opposing statements are simultaneously

  asserted. For example, saying “it is raining and it is not raining” is a co

  ntradiction. Typically, however, the arguer obscures the contradiction to th

  e point that the argument can be quite compelling. Take, for instance, the f

  ollowing argument:

  “We cannot know anything, because we intuitively realize that our thoughts a

  re unreliable.“

  This argument has an air of reasonableness to it. But “intuitively realize”

  means “to know.” Thus the arguer is in essence saying that we know that we d

  on‘t know anything. This is self-contradictory.

  Equivocation

  Equivocation is the use of a word in more than one sense during an argument.

  This technique is often used by politicians to leave themselves an “out.” I

  f someone objects to a particular statement, the politician can simply claim

  the other meaning.

  Example:

  Individual rights must be championed by the government. It is right for one

  to believe in God. So government should promote the belief in God.

  In this argument, right is used ambiguously. In the phrase “individual right

  s“ it is used in the sense of a privilege, whereas in the second sentence ri

  ght is used to mean proper or moral. The questionable conclusion is possible

  only if the arguer is allowed to play with the meaning of the critical word

  right.

  Circular Reasoning

  Circular reasoning involves assuming as a premise that which you are trying

  to prove. Intuitively, it may seem that no one would fall for such an argume

  nt. However, the conclusion may appear to state something additional, or the

  argument may be so long that the reader may forget that the conclusion was

  stated as a premise.

  Example:

  The death penalty is appropriate for traitors because it is right to execute

  those who betray their own country and thereby risk the lives of millions.

  This argument is circular because “right” means essentially the same thing a

  s “appropriate.” In effect, the writer is saying that the death penalty is a

  ppropriate because it is appropriate.

  Shifting The Burden Of Proof

  It is incumbent on the writer to provide evidence or support for her positio

  n. To imply that a position is true merely because no one has disproved it i

  s to shift the burden of proof to others.

  Example:

  Since no one has been able to prove God‘s existence, there must not be a God

  ……

  There are two major weaknesses in this argument. First, the fact that God‘s

  existence has yet to be proven does not preclude any future proof of existen

  ce. Second, if there is a God, one would expect that his existence is indepe

  ndent of any proof by man.

  Unwarranted Assumptions

  The fallacy of unwarranted assumption is committed when the conclusion of an

  argument is based on a premise (implicit or explicit) that is false or unwa

  rranted. An assumption is unwarranted when it is false――these premises are u

  sually suppressed or vaguely written. An assumption is also unwarranted when

  it is true but does not apply in the given context――these premises are usua

  lly explicit.

  Example: (False Dichotomy)

  Either restrictions must be placed on freedom of speech or certain subversiv

  e elements in society will use it to destroy this country. Since to allow th

  e latter to occur is unconscionable, we must restrict freedom of speech.

  The conclusion above is unsound because

  (A) subversives do not in fact want to destroy the country

  (B) the author places too much importance on the freedom of speech

  (C) the author fails to consider an accommodation between the two alternativ

  es

  (D) the meaning of “freedom of speech” has not been defined

  (E) subversives are a true threat to our way of life

  The arguer offers two options: either restrict freedom of speech, or lose th

  e country. He hopes the reader will assume that these are the only options a

  vailable. This is unwarranted. He does not state how the so-called “subversi

  ve elements“ would destroy the country, nor for that matter, why they would

  want to destroy it. There may be a third option that the author did not ment

  ion; namely, that society may be able to tolerate the “subversives” and it m

  ay even be improved by the diversity of opinion they offer. The answer is (C

  )。

  Appeal To Authority

  To appeal to authority is to cite an expert‘s opinion as support for one‘s o

  wn opinion. This method of thought is not necessarily fallacious. Clearly, t

  he reasonableness of the argument depends on the “expertise” of the person b

  eing cited and whether she is an expert in a field relevant to the argument.

  Appealing to a doctor‘s authority on a medical issue, for example, would be

  reasonable; but if the issue is about dermatology and the doctor is an orth

  opedist, then the argument would be questionable.

  Personal Attack

  In a personal attack (ad hominem), a person‘s character is challenged instea

  d of her opinions.

  Example:

  Politician: How can we trust my opponent to be true to the voters? He isn‘t

  true to his wife!

  This argument is weak because it attacks the opponent‘s character, not his p

  ositions. Some people may consider fidelity a prerequisite for public office

  …… History, however, shows no correlation between fidelity and great politica

  l leadership.

  ――

  I would fly you to the moon and back

  If you‘ll be if you‘ll be my baby

  Got a ticket for a worldswhereswe belong

  So would you be my baby

  Testprep充分性精解转载smth 2001-10-14 10:51:58发信人: ykk (我不说话并不代表我不在乎),信区: EnglishTest

  标题: (GMAT)Testprep充分性精解

  发信站: BBS水木清华站(Fri Oct 12 16:07:05 2001)

  Data Sufficiency

  ----------------------------------------------------------------------------

  ----

  INTRODUCTION DATA SUFFICIENCY

  Most people have much more difficulty with the Data Sufficiency problems tha

  n with the Standard Math problems. However, the mathematical knowledge and s

  kill required to solve Data Sufficiency problems is no greater than that req

  uired to solve standard math problems. What makes Data Sufficiency problems

  appear harder at first is the complicated directions. But once you become fa

  miliar with the directions, you‘ll find these problems no harder than standa

  rd math problems. In fact, people usually become proficient more quickly on

  Data Sufficiency problems.

  THE DIRECTIONS

  The directions for Data Sufficiency questions are rather complicated. Before

  reading any further, take some time to learn the directions cold. Some of t

  he wording in the directions below has been changed from the GMAT to make it

  clearer. You should never have to look at the instructions during the test.

  Directions: Each of the following Data Sufficiency problems contains a quest

  ion followed by two statements, numbered (1) and (2)。 You need not solve the

  problem; rather you must decide whether the information given is sufficient

  to solve the problem.

  The correct answer to a question is

  A if statement (1) ALONE is sufficient to answer the question but statement

  (2) alone is not sufficient;

  B if statement (2) ALONE is sufficient to answer the question but statement

  (1) alone is not sufficient;

  C if the two statements TAKEN TOGETHER are sufficient to answer the question

  , but NEITHER statement ALONE is sufficient;

  D if EACH statement ALONE is sufficient to answer the question;

  E if the two statements TAKEN TOGETHER are still NOT sufficient to answer th

  e question.

  Numbers: Only real numbers are used. That is, there are no complex numbers.

  Drawings: The drawings are drawn to scale according to the information given

  in the question, but may conflict with the information given in statements

  (1) and (2)。

  以上就为大家整理的“GMAT数学考试Testprep精解”,更多精彩内容,请关注新东方在线GMAT频道。

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