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T-9-Q4.
In the years following an eight-cent increase in the federal tax on a pack of cigarettes, sales of cigarettes fell ten percent. In contrast, in the year prior to the tax increase, sales had fallen one percent. The volume of cigarette sales is therefore strongly related to the after-tax price of a pack of cigarettes.
(Pretax price + tax)*volume=sale
The argument above requires which of the following assumptions?
A. During the year following the tax increase, the pretax price of a pack of cigarettes did not increase by as much as it had during the year prior to the tax increase. 是税前价和税后价比较而不是两年间价格增幅的比较。A极具迷惑性
B. The one percent fall in cigarette sales in the year prior to tax increases was due to a smaller tax increase. Strengthen
C. The pretax price of a pack of cigarettes gradually decreased throughout the year before and the year after the tax increase. Stregnthen
D. For the year following the tax increase, the pretax price of a pack of cigarettes was not eight or more cents lower than it had been the previous year. 那么税前裸价的下降抵消了税的增长,括号部分没有变化。不是括号的部分,也就是税后价格导致了Sales的变化。(排除此消彼长的可能)
E. As the after-tax price of a pack of cigarettes rises, the pretax price also rises.
论题是税费增加第二年香烟销量减少10%和税后价格增加有关,题目给出信息是税费每合增加8分,但税前裸价变化没有信息,而税后价和这2者都有关系。于是D中给出了补充信息:第二年税前裸价并不比前年低8美分或以上,也就是说税前裸价没有下降到足以抵消税费增加的幅度,可能是降了5美分,甚至也可能是裸价提高了。这样得出的结论是第二年每合税后总价格(裸价+税费)确实是增加了,从而引起香烟销量剧降。
首先把选项取非, 也就是说价格的增加超过税率增加前的价格增加. 可以发现, 税率增加后的情况是税率增加了, 价格也增加了, 他们共变导致了10%的销售量的下降; 由于A默认了价格的增加会导致销售量的下降, 所以如果我现在假设一种情况, 即销售价格增幅很大, 达到可以几乎不考虑税率的区区8分, 而这个大幅增加导致了销售量的大幅减少, 这样, 无法确定这区区8分税率的变化究竟是否有影响.
提炼一步:
税率*裸价=价格---销售量(中间的"---"表示"推倒出")
简化就是:
{税率*裸价}---销售量
答案A给出的以上三者同方向变化, 无法证明任何东西.
推广一步: <物理学实验证明方法论>里面有一条: 等式量变如果存在相同方向的共变, 无法证明不变的其它因素是否产生影响.
注意谁跟谁比:是“加税以后的税前价”跟“加税前的税前价”比较,
而不是“加税后的税前价的增幅”跟“加税前的税前价的增幅”进行比较
For the year following the tax increase, the pretax price of a pack of cigarettes was not eight or more cents lower than it had been the previous year. —>取非:税前价格比前一年要低八分钱,那么加上增加的税收八分钱,则今年加税的税后价格与去年的税后价格相同,那么今年的销售下降10%的原因就不一定是加税后的税后价格了 |
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