GMT考试--Testprep数学精解（1）

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 CO

RRECT ANSWERS WILL BE FALSE! THIS OFTEN CAUSES STUDENTS MUCH CONSTERNATION;

THEY FEEL THAT THE CORRECT ANSWER SHOULD BE TRUE. BUT THE ARGUMENTS ARE INTE

NDED TO TEST YOUR ABILITY TO THINK LOGICALLY. NOW LOGIC IS THE STUDY OF THE

RELATIONSHIPS BETWEEN STATEMENTS, NOT OF THE TRUTH OF THOSE STATEMENTS. BEIN

G OVERLY CONCERNED WITH FINDING THE TRUTH CAN BE RUINOUS TO YOUR GMAT ARGUME

NT SCORE.

"2 OUT OF 5" RULE

CREATING A GOOD BUT INCORRECT ANSWER-CHOICE IS MUCH HARDER THAN DEVELOPING T

HE 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 TW

O OF THE FIVE ANSWER-CHOICES WILL HAVE ANY REAL MERIT. HENCE, EVEN IF YOU DO

N’T FULLY UNDERSTAND AN ARGUMENT, YOU PROBABLY CAN STILL ELIMINATE THE THREE

FLUFF CHOICES, THEREBY GREATLY INCREASING YOUR ODDS OF ANSWERING THE QUESTI

ON CORRECTLY.

LOGIC I

ALTHOUGH IN THEORY THE ARGUMENT QUESTIONS ARE DESIGNED TO BE ANSWERED WITHOU

T 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 DEFINI

TE 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 ARGUMEN

TS. IN LOGIC II, WE WILL SYMBOLIZE AND DIAGRAM ARGUMENTS IN MUCH THE SAME WA

Y 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 ARGU

MENT. 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 TH

E 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 D

OES IT COME IN THE MIDDLE, AND OCCASIONALLY, FOR RHETORICAL EFFECT, THE CONC

LUSION IS NOT EVEN STATED.

EXAMPLE:

THE POLICE ARE THE ARMED GUARDIANS OF THE SOCIAL ORDER. THE BLACKS ARE THE C

HIEF DOMESTIC VICTIMS OF THE AMERICAN SOCIAL ORDER. A CONFLICT OF INTEREST E

XISTS, THEREFORE, BETWEEN THE BLACKS AND THE POLICE.--ELDRIDGE CLEAVER, SOUL

ON ICE

HERE THE FIRST TWO SENTENCES ANTICIPATE OR SET UP THE CONCLUSION. BY CHANGIN

G 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 CH

IEF 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 INT

EREST EXISTS BETWEEN THE BLACKS AND THE POLICE BECAUSE THE BLACKS ARE THE CH

IEF DOMESTIC VICTIMS OF THE AMERICAN SOCIAL ORDER.

IT IS GENERALLY AWKWARD, AS IN THE PREVIOUS PARAGRAPH, TO PLACE THE CONCLUSI

ON 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 O

CCASION WHEN A CONCLUSION COMES IN THE MIDDLE OF AN ARGUMENT, MOST OFTEN EIT

HER 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 CO

NCLUSION COME IN THE MIDDLE OF AN ARGUMENT.

WHEN DETERMINING THE MEANING OF A CONCLUSION, BE CAREFUL NOT TO READ ANY MOR

ESINTOSIT 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 WOUL

D USE IN YOUR EVERYDAY READING.

AS WITH GAMES, READ THE WORDS AND SENTENCES OF AN ARGUMENT PRECISELY, AND US

E THEIR LITERAL MEANING.

FOR EXAMPLE, CONSIDER THE MEANING OF SOME IN THE SENTENCE "SOME OF MARY’S FR

IENDS WENT TO THE PARTY." IT WOULD BE UNWARRANTED, BASED ON THIS STATEMENT,

TO ASSUME THAT SOME OF MARY’S FRIENDS DID NOT GO TO THE PARTY. ALTHOUGH IT M

AY SEEM DECEIVING TO SAY THAT SOME OF MARY’S FRIENDS WENT TO THE PARTY WHEN

IN FACT ALL OF THEM DID, IT IS NONETHELESS TECHNICALLY CONSISTENT WITH THE M

EANING 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 W

ORDS TO INDICATE THAT THE CONCLUSION IS ABOUT TO BE STATED. FOLLOWING IS A L

IST 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 TE

CHNIQUE IS QUITE EFFECTIVE IN CONVINCING PEOPLE THAT A CERTAIN POSITION IS C

ORRECT. 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 CANNO

T REPLENISH DURING THEIR LIFETIME. THIS ASSURES THAT FUTURE GENERATIONS CAN

ENJOY THE SAME RICHES OF NATURE THAT THEY HAVE. AT THE CURRENT RATE OF DESTR

UCTION, THE RAIN FORESTS WILL DISAPPEAR DURING OUR LIFETIME. DO WE HAVE AN O

BLIGATION TO FUTURE GENERATIONS TO PREVENT THIS RESULT?

HERE THE AUTHOR TRUSTS THAT THE POWER OF HER ARGUMENT WILL PERSUADE THE READ

ER TO ANSWER THE QUESTION AFFIRMATIVELY.

TAKING THIS RHETORICAL TECHNIQUE ONE STEP FURTHER, THE WRITER MAY BUILD UP T

O THE CONCLUSION BUT LEAVE IT UNSTATED. THIS ALLOWS THE READER TO MAKE UP HI

S OWN MIND. IF THE BUILD-UP IS DONE SKILLFULLY, THE READER WILL BE MORE LIKE

LY 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 CONCLUSION’S SCOPE BE CAREFUL NOT TO READ ANY MORE OR L

ESSSINTOSIT THAN THE AUTHOR STATES. GMAT WRITERS OFTEN CREATE WRONG ANSWER-C

HOICES BY SLIGHTLY OVERSTATING OR UNDERSTATING THE AUTHOR’S CLAIM. CERTAIN W

ORDS LIMIT THE SCOPE OF A STATEMENT. THESE WORDS ARE CALLED QUANTIFIERS--PAY

CLOSE ATTENTION TO THEM. FOLLOWING IS A LIST OF THE MOST IMPORTANT QUANTIFI

ERS:

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 STAR’S POSITION IS PREDICTED BASED ON NON-EUCLIDEAN GEOMETRY,

THEN WHEN A TELESCOPE IS POINTED TOSWHERESTHE STAR SHOULD BE IT WILL BE THER

E. WHEREAS, IF THE STAR’S POSITION IS PREDICTED BASED ON EUCLIDEAN GEOMETRY,

THEN WHEN A TELESCOPE IS POINTED TOSWHERESTHE STAR SHOULD BE IT WON’T BE TH

ERE. THIS STRONGLY INDICATES THAT THE WORLD IS NON-EUCLIDEAN.

WHICH ONE OF THE FOLLOWING BEST EXPRESSES THE MAIN IDEA OF THE PASSAGE?

(A) THE WORLD MAY OR MAY NOT BE EUCLIDEAN.

(B) THE WORLD IS PROBABLY NON-EUCLIDEAN.

(C) THE WORLD IS NON-EUCLIDEAN.

(D) THE WORLD IS EUCLIDEAN.

(E) THE WORLD IS NEITHER EUCLIDEAN NOR NON-EUCLIDEAN.

CHOICE (A) UNDERSTATES THE MAIN IDEA. ALTHOUGH THE OPENING TO THE PASSAGE ST

ATES THAT WE DON’T KNOW WHETHER THE WORLD IS NON-EUCLIDEAN, THE AUTHOR GOES

ON TO GIVE EVIDENCE THAT IT IS NON-EUCLIDEAN. CHOICE (C) OVERSTATES THE MAIN

IDEA. THE AUTHOR DOESN’T SAY THAT THE WORLD IS NON-EUCLIDEAN, JUST THAT EVI

DENCE STRONGLY INDICATES THAT IT IS. IN CHOICE (B), THE WORD "PROBABLY" PROP

ERLY LIMITS THE SCOPE OF THE MAIN IDEA, NAMELY, THAT THE WORLD IS PROBABLY N

ON-EUCLIDEAN, BUT WE CAN’T YET STATE SO DEFINITIVELY. THE ANSWER IS (B).

PREMISES

ONCE YOU’VE FOUND THE CONCLUSION, MOST OFTEN EVERYTHING ELSE IN THE ARGUMENT

WILL BE EITHER PREMISES OR "NOISE." THE PREMISES PROVIDE EVIDENCE FOR THE C

ONCLUSION; THEY FORM THE FOUNDATION OR INFRASTRUCTURE UPON WHICH THE CONCLUS

ION DEPENDS. TO DETERMINE WHETHER A STATEMENT IS A PREMISE, ASK YOURSELF WHE

THER IT SUPPORTS THE CONCLUSION. IF SO, IT’S 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 PREMI

SE 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 INCUMBENT’S VIEWS ARE OUT OF STEP WITH PUBLIC OPINION, HE PROBABLY

WILL NOT BE REELECTED.

HERE "SINCE" IS USED TO FLAG THE PREMISE THAT THE INCUMBENT’S POSITIONS ARE

UNPOPULAR.

SUPPRESSED PREMISES

MOST ARGUMENTS DEPEND ON ONE OR MORE UNSTATED PREMISES. SOMETIMES THIS INDIC

ATES A WEAKNESS IN THE ARGUMENT, AN OVERSIGHT BY THE WRITER. MORE OFTEN, HOW

EVER, 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 TH

E 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 B

ELIEVE IT, SO TO STATE IT WOULD BE REDUNDANT AND PONDEROUS. IF THE UNSTATED

PREMISE WERE FALSE (THAT IS, HE DID NOT ACCEPT IMMUNITY), 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 TH

IS 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 PRE

MISE 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 ARGUM

ENT 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 EA

CH DAY TO EXERCISE, AND MANY CORPORATIONS PROVIDE ELABORATE EXERCISE FACILIT

IES FOR THEIR EMPLOYEES. FEW AMERICAN CORPORATIONS HAVE SUCH EXERCISE PROGRA

MS. 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 EXERCI

SE PROGRAMS ARE INTRODUCED.

THE CONCLUSION OF THE ARGUMENT IS VALID IF WHICH ONE OF THE FOLLOWING IS ASS

UMED?

(A) EVEN IF EXERCISE PROGRAMS DO NOT INCREASE PRODUCTIVITY, THEY WILL IMPROV

E THE AMERICAN WORKER’S HEALTH.

(B) THE PRODUCTIVITY OF ALL WORKERS CAN BE INCREASED BY EXERCISE.

(C) EXERCISE IS AN ESSENTIAL FACTOR IN THE JAPANESE WORKER’S SUPERIOR PRODUC

TIVITY.

(D) AMERICAN WORKERS CAN ADAPT TO THE LONGER JAPANESE WORK WEEK.

(E) AMERICAN CORPORATIONS DON’T HAVE THE FUNDS TO BUILD ELABORATE EXERCISE F

ACILITIES.

THE UNSTATED ESSENCE OF THE ARGUMENT IS THAT EXERCISE IS AN INTEGRAL PART OF

PRODUCTIVITY AND THAT JAPANESE WORKERS ARE MORE PRODUCTIVE THAN AMERICAN WO

RKERS BECAUSE THEY EXERCISE MORE. THE ANSWER IS (C).

COUNTER-PREMISES

WHEN PRESENTING A POSITION, YOU OBVIOUSLY DON’T WANT TO ARGUE AGAINST YOURSE

LF. HOWEVER, IT IS OFTEN EFFECTIVE TO CONCEDE CERTAIN MINOR POINTS THAT WEAK

EN YOUR ARGUMENT. THIS SHOWS THAT YOU ARE OPEN-MINDED AND THAT YOUR IDEAS AR

E WELL CONSIDERED. IT ALSO DISARMS POTENTIAL ARGUMENTS AGAINST YOUR POSITION

.. FOR INSTANCE, IN ARGUING FOR A STRONG, AGGRESSIVE POLICE DEPARTMENT, YOU M

AY 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 MANAGEMENT’S 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 J

APAN AND GERMANY, FORCING ITSINTOSBANKRUPTCY.

THE CONCLUSION, "THE STRIKERS SHOULD ACCEPT THE MANAGEMENT’S OFFER," IS STAT

ED IN THE FIRST SENTENCE. THEN "ADMITTEDLY" INTRODUCES A CONCESSION; NAMELY,

THAT THE OFFER WAS LESS THAN WHAT WAS DEMANDED. THIS WEAKENS THE SPEAKER’S

CASE, BUT IT ADDRESSES A POTENTIAL CRITICISM OF HIS POSITION BEFORE IT CAN B

E MADE. THE LAST TWO SENTENCES OF THE ARGUMENT PRESENT MORE COMPELLING REASO

NS 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 I

N 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 (DIAGRAMMING)