定位句： The large volume of transactions associated with these activities seems to have necessitated hierarchical management structures well before the advent of modern communications and transportation.

B选项，they were brilliant 和 G.H.Hardy alone recognized是两个independent句子，两个independent句子不能使用逗号直接连接，需使用分号或连词FANBOYS。C选项，but only one，one 是代词，就近指代 these theorems，这改变了原句的逻辑意思。D选项their brilliance中的their指代不明，是指代theorems还是指代mathematician，且分号后的整个句子在逻辑意义和语法上存在很大问题。E选项，but these theorems were brilliant thanks to Hardy’s recognition，“因为H的recognition，these theorems很brilliant”逻辑意义严重错误。

A选项，like A，so B ...是错误的表达方式，在Manhattan SC中有相关的描述。Just as ... so ... 是正确的习惯用语。

A选项at least 和 more 表意重复；而some places 表示的是“有些地方”，因而画线部分应该是表示相反的方面，即"其他地方"，即应该使用others。

x*0.5 + y*0.25 and x+y=300.

stat 1 tells us y, and we can figure out x, and therefore total amount of milk

stat 2 tells us x, and we can find y and therefore total amount of milk

LCM : 2 x 2 x 3 x 3 x 5 x 5 x 7 x 7 = M
A. 600 : 2 x 3 x 2 x 5 x 2 x 5 [ uses three 2's --> Not a Factor ]

一个问题，A中可否理解为percent have be been attacked逻辑不对

B 选项 原命题成立 否命题不一定成立

B中的argument不是应该是关于政治领导的学说而不是关于美国的历史的吧？

B 使用了while表示句义的对比，外延和内涵， 因为变化在主语，优势群体，所以选了doing结构？ 急需老师解答。

It can be inferred from the above line that regardless of the amount of refuse collected, the city services will only send half the truckloads. Hence, the amount of refuse collected does not matter. Even if 10X the refuse is collected this year, still the # of truckloads sent for incineration will be half of last year's number.

这题不该错， per capita和per person 重复

A 里面 customer demand growth, 3个名词放在一起很奇怪，按照就近原则我觉得解释更好吧， unexpected 应该修饰growth,

Follow-up for the rest of the choices D&E, from Ron:
--
It's nonsense, because "$xxxx in yyyyy" would mean that yyyy is something that can actually be measured in dollars.
E.g.,
By driving a hybrid car, I will save thousands of dollars in fuel costs.
Your business can save over $10,000 per month in shipping costs by using XYZ Courier Service.

Hungary不是匈牙利么

排除他因：葡萄牙人和Ife联系的可能

和描述社交能力的准确性无关，和社交能力的高低有关

C和E的split可以由平行来排除 ：and to pinpoint the most affected areas within two hours of the event.前面要有与之相平行的成分，故选C

Although the first pulsar, or rapidly spinning collapsed star, to be sighted was in the summer of 1967 by graduate student Jocelyn Bell, it had not been announced until February, 1968.提取从句主干：the first pulsar was in the summer 这句话逻辑不成立呀

D.an achievement attempted later in the century by other Scandinavian kings that was not successful 把这句话还原就很容易看出错误来：an achievement was not successful （这句话啥意思没懂）