如何在GMAT邏輯推理（Critical Reasoning）部分拿到滿分

本文作者： 本質教育創始人 李澤宇老師

GMAT的邏輯推理部分(Critical Reasoning)對於很多學生來說是難點。然而，這一部分和數學，閱讀一樣，是可以爭取拿到滿分的（在GMAT中唯一不太可能拿到滿分的只有Sentence

Correction，畢竟我們不是語言學家，不可能知曉所有的idioms，但90%以上正確率是做得到的）。接下來，我們就通過幾個實際的例子，來談談如何在GMAT Critical Reasoning中拿到滿分。（本文的思路也適用於LSAT的考生）

Example 1 （Difficulty Level: 700）.

Whenever a major airplane accident occurs, there is a dramatic increase in the number of airplane mishaps reported in the media, a phenomenon that may last for as long as a few months after the accident. Airline officials assert that the publicity given the gruesomeness of major airplane accidents focuses media attention on the airline industry, and the increase in the number of reported accidents is caused by an increase in the number of news sources covering airline accidents, not by an increase in the number of accidents.

Which of the following, if true, would seriously weaken the assertions of the airline officials?

A. The publicity surrounding airline accidents is largely limited to the country in which the crash occurred.

B. Airline accidents tend to occur far more often during certain peak travel months.

C. News organizations do not have any guidelines to help them decide how severe an accident must be for it to receive coverage.

D. Airplane accidents receive coverage by news sources only when the news sources find it advantageous to do so.

E. Studies by government regulations show that the number of airplane flight miles remains relatively constant from month to month.

所有的CR題目由三個部分組成：

1. Question 「Which of the following, if true, would seriously weaken the assertions of the airline officials? 」

2. Argument: 「Whenever a … accident」(問題前面的整段話)

3. Choices

我們解題，第一步看Question。這題，問的是weaken. 90%的GMAT題目都是在問如何weaken（削弱）, support（支持）, evaluate（評估） the argument 或者是這 argument的assumption (假設)是什麼

一旦題目問的是weaken, support, evaluation or assumption，我們接下來第二步就是需要閱讀argument並且找出其line of reasonings (也叫作logical tree)

任何推理(reasoning)都是由前提(premises/evidence)和結論(conclusion)兩個部分構成，一般我們用橫線隔開，例如大家非常熟悉的假言推理（常用於數學證明）：

If p, then q (前提1)

P （前提2）

_________________

q（結論）

要在GMAT Critical Reasoning拿到滿分，同學們應該對形式邏輯中常見的推理形式（例如簡單歸納法，由因到果的推理，由果到因的推理（溯因推理，假說演繹推理，求異法，求同法），類比推理等）十分熟悉。一個argument往往由1個甚至數個reasoning構成，同學們在快速閱讀理解後，應該在頭腦中（也可藉助草稿紙簡單標註）形成作者的推理形式並分析出他用了哪一（幾）種推理形式。例如本題就用到了溯因推理(Abduction)。

溯因推理是常見的由果（通常是有一個事實和現象，例如蘋果從樹上掉下來）找因的推理。其形式如下：

q

if p, then q

____________________

q is because of p

例如：

今年的收成不好（一個現象，事實）

如果天不下雨，莊稼收成不好

—————————————————————

因此今天收成不好是因為雨量不足

注意這個推理並不是演繹推理，即所有前提為真，結論不一定為真。例如上面的這個例子，雨水過多也可能導致莊稼收成不好，這就是C à q (別的原因可以解釋這個現象)，這是溯因推理5種削弱方式的一種。本題，其實和上面的例子非常類似，作者的推理如下：

q: Whenever a major airplane accident occurs, the number of reported airplane mishaps increases for a few months

if p (publicity focuses media attention to the industry), then q (more mishaps are reported, not a real increase in the number)

____________________________________________________________________________________________ q is because of p

正確答案是B，airline

accidents tend to occur together (in peak travel months)，這解釋了reported airplane mishaps在幾個月中增加，B à q(別的原因可以解釋這個現象)，從而削弱了原來的推理。

正如這題顯示出來的，一旦你能夠1）分析出argument的line

of reasonings並找出其使用的推理形式；2）掌握該推理形式的weaken的方法；那麼所有weaken和assumption的題目從此就應該駕輕就熟了(assumption是用weaken來定義的，後講)

Exercise 1 (Difficulty Level: 700):

M: It is almost impossible to find a person between the ages of 85 and 90 who primarily uses the left hand.

Q: Seventy to ninety years ago, however, children were punished for using their left hands to eat or to write and were forced to use their right hands.

Qs response serves to counter any use by M of the evidence about 85 to 90 year olds in support of which one of the following hypotheses?

(A) Being born right-handed confers a survival advantage.

(B) Societal attitudes toward handedness differ at different times.

(C) Forcing a person to switch from a preferred hand is harmless.

(D) Handedness is a product of both genetic predisposition and social pressures.

(E) Physical habits learned in school often persist in old age.

做出來了嗎？「It is almost impossible to find a person between the ages of 85 and 90 who primarily uses the left hand.」這是一個現象（phenomenon）。這題就是叫你找Q追溯的這個現象的原因(hypothesis = theory = model = explanation = cause!)。這個原因應該和Q指出來的原因不同，這樣Q才weaken了M(counter)，正如我們上面的公式C à q。學會了溯因推理，這道只有24%正確率的題目簡單吧，選A。(B,C,D,E都不能解釋這個現象)

接下來，我們看一道更難的題目：

Example 2 (Difficulty Level: 750) :

Roland: The alarming fact is that 90 percent of the people in this country now report that they know someone who is unemployed.

Sharon: But a normal, moderate level of unemployment is 5 percent, with 1 out of 20 workers unemployed. So at any given time if a person knows approximately 50 workers, 1 or more will very likely be unemployed.

Sharons argument relies on the assumption that

(A) normal levels of unemployment are rarely exceeded

(B) unemployment is not normally concentrated in geographically isolated segments of the population

(C) the number of people who each know someone who is unemployed is always higher than 90% of the population

(D) Roland is not consciously distorting the statistics he presents

(E) knowledge that a personal acquaintance is unemployed generates more fear of losing ones job than does knowledge of unemployment statistics

這題問的是Assumption。我們先學習下Assumption的定義：

Assumption is an unstated premise such that if we negate it, it weakens the reasoning.

也就是說假設（assumption）必須滿足兩個條件：

1）沒有在argument中提到過(unstated)

2) 對假設取非後變成weaken

我們還是先來看看這一題的Line of reasonings:

q: 90% of people know someone who is unemployed (一個現象)

if p (5% unemployment rate) à(if someone knows 50 people) 50*5%=2.5, i.e. everyone should know someone who is unemployed(q)

____________________________________________________________________________________

q is because of p

仍然是溯因推理（假說演繹推理）。接下來我們來談談溯因推理（假說演繹推理）的別的削弱方式。If p, then q這個前提實際上包含了由因到果的推理。因此，必須符合因果關係的三大性質：

1）有因必有果

2）有果必有因

3）因先於果

因此，當我們得出p且非q（和性質1矛盾）, 非p且q（和性質2矛盾），p後於q（和性質3矛盾）時，我們就削弱了If p, then q，從而削弱了整個溯因推理。

這題之所以是難題，在於這裡If p, then q不僅僅是從因到果的推理，同時也是統計三段論(statistical syllogism)：

總體A有某種統計性質P(例如平均數，中位數，眾數等)

a是總體的一個樣本（一部分）

———————————————————————————

a有性質P

例如：

中國人的平均年齡是45歲

小明是中國人

—————————————————————

小明是45歲

這個推理當且樣本很好的代表了（typical of, representative of）總體才成立，當樣本有偏(biased, atypical of ,not representative of)時，結論是不成立的。例如上面的例子，如果小明是小學生（樣本有偏），結論明顯是錯誤的。

回到我們的Critical Reasoning問題, Sharon實際上用了如下的推理（unstated）5% unemployment rate – Statistical Property for the country!

A is city of the country

________________________________________________

A』s unemployment rate is also 5%

正確的選項是B, 當我們對B取非後，B變成了：

unemployment is concentrated in geographically isolated segments of the population

換句話說，假如這個國家有10個城市，每個城市人口相同，所有失業人員全部集中在城市X（失業率50%），剩下的9個城市失業率為0%。這時我們滿足了p(失業率5%)，然而生活在剩下9個城市的人，哪怕認識50個人，恐怕裡面失業的也幾乎應該是0%，即我們找出了統計三段論的問題，得出了p且非q，因此削弱了原文的溯因推理。

今天我用溯因推理舉例，說明了GMAT邏輯推理題目應該如何拿到滿分：

同學們需要具備：

1. 形式邏輯的相關知識（例如溯因推理以及其5種削弱方式）

2. 能夠用好「澤宇閱讀法」，即讀出argument的line of reasoning並分析出其使用了什麼樣的邏輯推理形式

那麼隨著你不斷練習，對1,2越發熟練掌握，你會發現，GMAT Critical Reasoning變成小菜一碟了。

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