求解题思路，逻辑大全，比率题

shelvey

19. Recent estimates predict that between 1982 and 1995 the greatest increase in the number of people employed will be in the category of low-paying service occupations. This category, however, will not increase its share of total employment, whereas the category of high-paying service occupations will increase its share.
If the estimates above are accurate, which of the following conclusions can be drawn?
(A) In 1982 more people were working in low-paying service occupations than were working in high-paying service occupations.
(B) In 1995 more people will be working in high-paying service occupations than will be working in low-paying service occupations.
(C) Nonservice occupations will account for the same share of total employment in 1995 as in 1982.
(D) Many of the people who were working in low-paying service occupations in 1982 will be working in high-paying service occupations by 1995.
(E) The rate of growth for low-paying service occupations will be greater than the overall rate of employment growth between 1982 and 1995.

答案是A，求解题思路。总是对这种比例题一筹莫展。

shelvey

我怎么觉得原题是说低收入人群增长数目最多，但所占比例并未增加呢？
因为始终想不通，觉得自己没必要过于纠结此题了。不过，仍期待有人能解惑，一扫我脑中的浆糊一团。

kurtsniper

这道题其实不难么简单的数学
我看想不明白的同学是理解错了“the greatest increase in the number of people employed ” 的意思
这里指的是它自身增长最快的

这道题目就是说低收入的增长最快
增长率高于高收入人群
但是实际增长的数目却要低于高收入的

自然得出结论原本高收入的人就远远超过低收入的
所以即便增长不大
增长的绝对数目还是大于低收入的
所以占总人数的比例进一步增长了

shelvey

再谢！问题是，我不知道A怎么和原文对应了？原文说低收入人数增加最多，A说原来低收入人数比高收入人数多。
可见我是多么的愚钝···

yqhpsyche

If the estimates above are accurate, which of the following conclusions can be drawn?

根据题目这个是must be true题型，也就是所有的信息必须从原文中得到或者推出，不能有new information加入

分析原文的话；
1. Recent estimates predict that between 1982 and 1995 the greatest increase in the number of people employed will be in the category of low-paying service occupations,也就是说在这个时间段里，low paying 的人数增加是最多的（注意这里是人数，而不是百分比）

2.This category, however, will not increase its share of total employment表示虽然low paying的人数增加了，但是其（low pay）相对于total employment的百分比没有增加

3. whereas the category of high-paying service occupations will increase its share---high pay的百分比增加了

因此看
(A) In 1982 more people were working in low-paying service occupations than were working in high-paying service occupations.可以对应原文的（the greatest increase in the number of people employed will be in the category of low-paying service occupations）

(B) In 1995 more people will be working in high-paying service occupations than will be working in low-paying service occupations. 和原文相反了

(C) Nonservice occupations will account for the same share of total employment in 1995 as in 1982. 原文没有给出过这个信息，关于是否non service occupationsxxx，原文的信息也不能作为evidence 能够推出这个结论
(D) Many of the people who were working in low-paying service occupations in 1982 will be working in high-paying service occupations by 1995原文给的信息，也没有提到：工作在low pay的人会work as high pay service

(E) The rate of growth for low-paying service occupations will be greater than the overall rate of employment growth between 1982 and 1995.原文连overall rate of employment growth都不知道，所以这个greater than的比较不成立，原文的信息不能infer

shelvey

先谢！但我仍旧不明白···我问了几个人，都说这题一想就是穷人比富人多，我怎么就一想就想不明白呢。

SMARTCATHYT

我来说下我的想法吧，肯定不是最好的，仅供大家抛砖迎玉的参考：
根据题意，从1982到1995，LP(low-paying)和HP(high-paying)的变化情况我们试着表达如下：（箭头左边是1982年，箭头右边是1995年）
LP ----> (1 +x)LP
HP ----> (1+y)HP
(1 +x)是LP的变化的倍数，(1 +y)是HP的变化的倍数；x*LP是LP的增量部分，y*LP是LP的增量部分

好，现在我们来看市场份额，市场份额这东西很有意思，对于一个公司/群体来说，你要增加你在市场的份额，你必须要增加的比别人快，才能打破原有的市场比例。即使你增加了很多，翻了个倍，但如果大家都翻了个倍，你的市场份额还是一样。

根据题意，HP增加了市场份额而LP没有，所以HP一定增加的比LP快，也就是1+y > 1+x，即y > x; 而文中又说LP的增加人数是最大的，也就是x*LP > y* HP；那么2个不等式可得出LP一定大于HP，即A的答案。

当然我个人也感觉要是这道题这样做肯定超时，还不如用排除法直接把BCDE排除来的更快：
B：错，市场份额增大的多不等于绝对人数增加的多。想象下一家100人组成的大公司和一家1人组成的小公司，即使小公司发展速度比大公司快很多，比如大公司增加0.1倍，小公司增加1倍，小公司的人数还是敌不过大公司
C：错，其他类型的群体的增加减少都可以，不会影响HP和LP之间的比较
D：错，HP人数增加可以来自于外部或新人，未必非要从LP中过去
E：错，假设市场只有LP和HP，如果LP增加1倍，而HP因为市场份额变大，所以肯定增加的比LP快，也就是增加多于1倍；如果LP，HP各自都增加1倍，overall rate也增加1倍，而HP实际增加的要多，导致overall rate也会比1倍要多，所以E也错

虽然说了这么多，我还是觉得我这做法比较费时比较笨的，即使用排除法依然会超时，仅此抛砖引玉引来各位牛人的解答，呵呵~