GRE閱讀裏竟然還會考數學？

GRE閱讀考察的是邏輯關(guan) 係的梳理，而其中有些題目考察了數學邏輯關(guan) 係。這樣的題目本質上是一道數學題，需要運用數學思維來做題。

大家可能會(hui) 驚呼：什麽(me) ？閱讀題裏還會(hui) 考數學？

數學不好的小夥(huo) 伴們(men) 是不是紮心了呢？

別擔心，GRE閱讀中並不會(hui) 考察複雜的數學計算，隻會(hui) 涉及一些數學基本概念的理解，隻要梳理清楚文章探討對象之間的關(guan) 係，問題便可迎刃而解。

例如下麵這道邏輯題：

1、Belnovia’s government provides health care to all its citizens. Five years ago, with costs incurred from smoking-related health problems accounting for 5 percent of annual government expenditures, Belnovia’s health agency initiated a nationwide antismoking campaign. Although the campaign succeeded in reducing the number of smokers in Belnovia substantially, it clearly failed to reduce the annual costs incurred from smoking-related health problems, since these costs currently account for 6 percent of annual government expenditures.

❓Which of the following is an assumption on which the argument depends?

A. Costs incurred from smoking-related health problems account for a greater portion of the Belnovian government’s overall health expenditures now than they did five years ago.

B. The average cost of treatment for smoking related health problems in Belnovia has not increased significantly over the past five years.

C. Overall health expenditure account for a greater portion of the Belnovian government’s annual expenditures now than they did five years’ ago.

D. Belnovia’s annual government expenditures are not significantly lower now than they were five years ago.

E. Smoking-related health problems usually persist long after a person has quit smoking.

#️⃣ 思路：

邏輯題需要梳理論證的前提和結論，由於(yu) 題幹信息中出現了比例“account for”，因此不妨把文字轉換為(wei) 包含分子分母的數學公式。

#️⃣ 前提：

，即該項花費所占比重增加了1%。

#️⃣ 結論：

5年前的吸煙開支≤今年的吸煙開支，即該項花費金額的數量也增加了。

#️⃣ 題幹：

論證依賴的前提是什麽(me) ？

#️⃣ 解析：

這道題歸根結底是一道數學題，考察的是比例和數量絕對值的關(guan) 係。比重的增加不一定能反映絕對數量的增加，還得看分母是否發生改變。所以本篇論證所依賴的前提是D選項，今年的政府經費和5年前的政府經費相比並沒有大幅下降。

當然，assumption題還可以采取“選項取非，削弱結論”的方式來驗證。D選項取反之後變為(wei) ，今年的政府經費比5年前降低了許多，如此一來，即便吸煙開支的比重增加了1%，那也未必意味著吸煙開支的金額也增加了，如果分母減少的幅度特別大甚至會(hui) 出現吸煙開支的下降。所以，D選項取反之後削弱了原文的結論，該選項即為(wei) 正確選項。

2、再來看考察數學思維的另一道題：

The damage that trucks do to highways escalates dramatically with the weight borne per axle. New regulations increase the maximum permitted vehicle weight; these regulations will therefore allow onto the highway trucks capable of doing even more damage than those currently permitted.

❓The argument is open to criticism on the grounds that it

A. Fails to establish that the level of damage done by trucks is a serious problem

B. Omits evidence about one of the two relevant factors

C. Ignores the possibility that careful driving can lessen damage to highways

D. Presumes that trucks are the only vehicles capable of causing substantial damage to highways

E. Presumes that something is bound to happen just because it is allowed to happen

#️⃣ 前提：

單個(ge) 車軸（per axle）的承重增加，卡車對路麵的損害會(hui) 增加。

#️⃣ 結論：

卡車的總載重量增加會(hui) 導致卡車對路麵損害增加。

#️⃣ 題幹：

這篇論證的漏洞在哪裏？

#️⃣ 解析：

這篇邏輯題同樣也是一道數學題，考察了一個(ge) 最基本的數學公式：

用本題中的具體(ti) 概念套用公式，可記為(wei) ：

因此，總載重量的增加未必意味著單個(ge) 車軸承重量的增加，還得看車軸數量是否改變。既然車軸數量未知，便無法得知單個(ge) 車軸承重量是否上升，因而也不能推斷出卡車對路麵的損害是否會(hui) 增加。所以本篇論證的漏洞就對應B選項“忽略了兩(liang) 個(ge) 相關(guan) 因素中的一個(ge) 因素”，即沒有考慮到車軸數量。

3、同學們(men) 可以再通過下麵這篇文章來體(ti) 會(hui) 一下閱讀中是如何考察數學的。

While most scholarship on women’s employment in the United States recognizes that the Second World War (1939–1945) dramatically changed the role of women in the workforce, these studies also acknowledge that few women remained in manufacturing jobs once men returned from the war. But in agriculture, unlike other industries where women were viewed as temporary workers, women’s employment did not end with the war. Instead, the expansion of agriculture and a steady decrease in the number of male farmworkers combined to cause the industry to hire more women in the postwar years. Consequently, the 1950s saw a growing number of women engaged in farm labor, even though rhetoric in the popular media called for the return of women to domestic life.

❓It can be inferred from the passage that the manufacturing and agricultural sectors in the United States following the Second World War differed in which of the following respects?

A. The rate of expansion in each sector

B. The percentage of employees in each sector who were men

C. The trend in the wages of men employed in each sector

D. The attitude of the popular media toward the employment of women in each sector

E. The extent to which women in each sector were satisfied with their jobs

#️⃣ 解析：

題幹問二戰之後（following the Second World War），農(nong) 業(ye) 和製造業(ye) 在以下哪個(ge) 方麵不同。原文提到，二戰後繼續從(cong) 事製造業(ye) 的女性人數非常少，但是從(cong) 事農(nong) 業(ye) 的女性人數上升，因此二者的差別是女性人數的差別。

隻不過選項當中沒有直接提到女性員工的數量，但可以通過簡單的數學公式得出B選項和原文內(nei) 容是一致的，即

二戰後，製造業(ye) 的女性人數非常少，即絕大部分從(cong) 事製造業(ye) 工作的人員都是男性，男性勞動力在戰後製造業(ye) 的比例非常高，接近100%。而在農(nong) 業(ye) 當中，男性數量持續下降（a steady decrease in the number of male farmworkers），務農(nong) 女性的人數上升，男性勞動力的比例肯定不會(hui) 接近100%。因此可以確定，農(nong) 業(ye) 和製造業(ye) 勞動力當中男性的比例是不同的。

ACE選項中的行業(ye) 的擴張速率（rate of expansion）、行業(ye) 中男性員工工資的趨勢（trend in the wages of men）以及女性對工作的滿意程度（satisfied）均為(wei) 未知信息，因此不選。原文提到大眾(zhong) 媒體(ti) 在戰後對從(cong) 事農(nong) 業(ye) 的女性態度是呼籲她們(men) 回歸家庭生活，但並未提及媒體(ti) 對製造業(ye) 女性的態度，因此D選項“大眾(zhong) 媒體(ti) 對每個(ge) 行業(ye) 當中從(cong) 業(ye) 女性的態度”是否不同也屬未知信息。

總 結

閱讀理解中一旦出現比例（percentage、portion或者account for等詞）一定要意識到比例和數量的絕對值並非等同概念，如果包含如單量、數量、總量三者關(guan) 係時需要理清題幹中相應概念之間的關(guan) 係，必要時可以把題目中探討對象的數學式列出來，以便直觀理解。

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