In the country of Veltria, the past two years' broad economic recession has included a business downturn in the clothing trade, where sales are down by about 7 percent as compared to two years ago. Clothing wholesalers have found, however, that the proportion of credit extended to retailers that was paid off on time fell sharply in the first year of the recession but returned to its prerecession level in the second year. Which of the following, if true, most helps to explain the change between the first and the second year of the recession in the proportion of credit not paid off on time? (A) The total amount of credit extended to retailers by clothing wholesalers increased between the first year of the recession and the second year. (B) Between the first and second years of the recession, clothing retailers in Veltria saw many of their costs, rent and utilities in particular, increase. (C) Of the considerable number of clothing retailers in Veltria who were having financial difficulties before the start of the recession, virtually all were forced to go out of business during its first year. (D) Clothing retailers in Veltria attempted to stimulate sales in the second year of the recession by discounting merchandise. (E) Relatively recession-proof segments of the clothing trade, such as work clothes, did not suffer any decrease in sales during the first year of the recession. 这道题错选了A。 思路如下： 题目问的是为什么在经济不好，衣服卖不动的情况下，第一年零售商还不上钱第二年就能还上了。讲的是零售商还钱的问题。 当时留下的是A,C,D 排除D是因为觉得，即使刺激销售量衣服打折也不能说明能还上钱。可能打折卖1块，纵使家当全卖了也不够。 排除C是因为觉得， 那些本身经济状况就很差的在第一年被淘汰掉以后，剩下的那些没说经济状况如何啊，如果也不咋地，第二年还是得淘汰啊。 A选项当时觉得，即使credit extended，对pay off on time也无太大用处，但最起码跟原文意思接近。所以选了A。

调查1200人对A B C 的喜好，喜欢A的40%，喜欢B的58%，喜欢C的40%，同时喜欢AB的30%，求喜欢C但不喜欢A B的人

问题：在“数的整除性质小节中”，第一段写到，如果a能被b整除，记作aΙb. 但如果照这么理解的话，为什么在性质3: 如果b、c都能整除a且b和c互质，那么b与c的积能整除a。以上说法化成公式的表示为：bΙa 。但如果根据上面的被整除表达，这里不应该写为aΙb嘛？

G（x）表示x的取整且是小于x的，L（x）表示x取整且是大于x的，问L（x）-G（x）的所有可能值的的集合？ （-1,0） （1,0）等

题目：1993年的元旦是星期五，1994年的元旦是星期几。 问题：在文字解释中提到，问题的实质是求用7去除某一天的天数后所得的余数。然后引出，因为15与365除以7后，余数都是1，所以15与365对于模7同余。但15这个数字是怎么推到出来的呢？

问题：由于以前完全没有学习过“同余”的概念，因此书中的解释完全不明白。还烦请MAY老师帮忙讲解一下。

题目：求143∧89（143的89次方）除以7的余数 问题：（1）如何利用同余的概念推出最后的结果的？ （2） 如果可以不用同余概念，还有什么其他方法可以处理此类题型嘛？

题目：A Printer numbered consecutively the pages of a book, beginning with 1 on the first page. In numbering the pages, he printed a total of 189 digits. How many pages are there in the book? 问题：看了中文翻译并听了管老师的讲解，我都没弄明白这个题目的解题思路。的别是对“a total of 189 digits”的处理。

DS：已知半径为7，求ABR 的周长？ 条件1：∠x=120 度 条件2：△ABR 的面积为(49/9) π 图片附件

题目：If n is a prime number greater than 3, what is the remainder when n的平方is divided by 12? 问题：当管老师解题时，他出了3个方程式，分别是： 1） n=3A+1, n的平方=9A(square)+6A+1 2) n=3A+2, n的平方=9A(square)+12A+4 3) n=2A+1, n的平方=4A(square)+4A+1 我不明白的点是：这3个方程式是怎么推到或者是一看到题目就这么设出来的？

有图。