GRE阅读里竟然还会考数学？

GRE阅读考察的是逻辑关系的梳理，而其中有些题目考察了数学逻辑关系。这样的题目本质上是一道数学题，需要运用数学思维来做题。

大家可能会惊呼：什么？阅读题里还会考数学？

数学不好的小伙伴们是不是扎心了呢？

别担心，GRE阅读中并不会考察复杂的数学计算，只会涉及一些数学基本概念的理解，只要梳理清楚文章探讨对象之间的关系，问题便可迎刃而解。

例如下面这道逻辑题：

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：

逻辑题需要梳理论证的前提和结论，由于题干信息中出现了比例“account for”，因此不妨把文字转换为包含分子分母的数学公式。

#️⃣ 前提：

，即该项花费所占比重增加了1%。

#️⃣ 结论：

5年前的吸烟开支≤今年的吸烟开支，即该项花费金额的数量也增加了。

#️⃣ 题干：

论证依赖的前提是什么？

#️⃣ 解析：

这道题归根结底是一道数学题，考察的是比例和数量绝对值的关系。比重的增加不一定能反映绝对数量的增加，还得看分母是否发生改变。所以本篇论证所依赖的前提是D选项，今年的政府经费和5年前的政府经费相比并没有大幅下降。

当然，assumption题还可以采取“选项取非，削弱结论”的方式来验证。D选项取反之后变为，今年的政府经费比5年前降低了许多，如此一来，即便吸烟开支的比重增加了1%，那也未必意味着吸烟开支的金额也增加了，如果分母减少的幅度特别大甚至会出现吸烟开支的下降。所以，D选项取反之后削弱了原文的结论，该选项即为正确选项。

2、再来看考察数学思维的另一道题：

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：

单个车轴（per axle）的承重增加，卡车对路面的损害会增加。

#️⃣ 结论：

卡车的总载重量增加会导致卡车对路面损害增加。

#️⃣ 题干：

这篇论证的漏洞在哪里？

#️⃣ 解析：

这篇逻辑题同样也是一道数学题，考察了一个最基本的数学公式：

用本题中的具体概念套用公式，可记为：

因此，总载重量的增加未必意味着单个车轴承重量的增加，还得看车轴数量是否改变。既然车轴数量未知，便无法得知单个车轴承重量是否上升，因而也不能推断出卡车对路面的损害是否会增加。所以本篇论证的漏洞就对应B选项“忽略了两个相关因素中的一个因素”，即没有考虑到车轴数量。

3、同学们可以再通过下面这篇文章来体会一下阅读中是如何考察数学的。

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：

题干问二战之后（following the Second World War），农业和制造业在以下哪个方面不同。原文提到，二战后继续从事制造业的女性人数非常少，但是从事农业的女性人数上升，因此二者的差别是女性人数的差别。

只不过选项当中没有直接提到女性员工的数量，但可以通过简单的数学公式得出B选项和原文内容是一致的，即

二战后，制造业的女性人数非常少，即绝大部分从事制造业工作的人员都是男性，男性劳动力在战后制造业的比例非常高，接近100%。而在农业当中，男性数量持续下降（a steady decrease in the number of male farmworkers），务农女性的人数上升，男性劳动力的比例肯定不会接近100%。因此可以确定，农业和制造业劳动力当中男性的比例是不同的。

ACE选项中的行业的扩张速率（rate of expansion）、行业中男性员工工资的趋势（trend in the wages of men）以及女性对工作的满意程度（satisfied）均为未知信息，因此不选。原文提到大众媒体在战后对从事农业的女性态度是呼吁她们回归家庭生活，但并未提及媒体对制造业女性的态度，因此D选项“大众媒体对每个行业当中从业女性的态度”是否不同也属未知信息。

总 结

阅读理解中一旦出现比例（percentage、portion或者account for等词）一定要意识到比例和数量的绝对值并非等同概念，如果包含如单量、数量、总量三者关系时需要理清题干中相应概念之间的关系，必要时可以把题目中探讨对象的数学式列出来，以便直观理解。

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