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一题数字相关的逻辑,麻烦给用数学推导一下,谢谢拉。

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楼主
发表于 2007-3-5 01:28:00 | 只看该作者

一题数字相关的逻辑,麻烦给用数学推导一下,谢谢拉。

Thirty years ago, the percentage of their income that single persons spent on food was twice what it is today. Given that incomes have risen over the past thirty years, we can conclude that incomes have risen at a greater rate than the price of food in that period.

Which one of the following, if assumed, helps most to justify the conclusion drawn above?

(A) The amount of food eaten per capita today is identical to the amount of food eaten per capita thirty years ago

 (B) In general, single persons today eat healthier foods and eat less than their counterparts of thirty years ago.

(C) Single persons today, on average, purchase the same kinds of food items in the same quantities as they did thirty years ago.

(D) The prices of nonfood items single person purchase have risen faster than the price of food over the past thirty years.

(E) Unlike single persons, families today spend about the same percentage of their income on food as they did thirty years ago.

答案为C。该题为LSAT逻辑,出自大全。本题可用排除法用,其余4个选项都无关,全本题不知用数学公式该如何推导,请数学的NN们给推导一下啊!谢谢!

附:官方给的解释:

When arguments deal with percent/number comparisons, study scope carefully.

From the fact that single people today spend 50% less of their income on food than they did 30

years ago, and the fact that incomes rose over that period, the author draws a conclusion in the form of a

comparison: Incomes have risen faster than food prices. But this is only true if the nature and amount of

food that single people buy has stayed the same, (C). If for instance they are buying much more food now,

or caviar instead of corned beef hash, then it is quite possible that food prices have risen slower, or faster,

than incomes.

Those baffled by arguments involving economic data could have taken heart from the fact that all

four wrong choices deviate markedly from the scope. Amount of food eaten is irrelevant, which knocks out

(A) and (B); (B)’s reference to “healthier food” is even further afield. Nonfood items, (D), and food

purchased by families, (E), are in the same way not part of the author’s equations.


[此贴子已经被作者于2007-3-5 1:28:58编辑过]
沙发
发表于 2007-3-5 10:07:00 | 只看该作者

同问。

这题很诡异嘛。我推出来是一个恒等式哦

设原来和现在的收入分别是X和Y。花在食物的百分比是2K和K。那么题目的结论是(Y-X)/X>(YK-2XK)/2XK问这里需要的假设:是2KX=YK就是C选项。

我们推导一下结论(Y-X)/X>(YK-2XK)/2XK可以推出Y/X>Y/2X.这是一个恒等式呀,不需要任何假设的嘛。

请问我理解的对不对?牛人来说说嘛!

板凳
发表于 2007-3-5 17:23:00 | 只看该作者

(YK-2XK)/2XK

这是花在食物上的钱的增长率

但不是price of the food

------------------------

但是如果买的食物的量是一样的话,那么(YK-2XK)/2XK上下都除以相同的量,就是单价price了

从而结论成立。黄色部分是选项C


[此贴子已经被作者于2007-3-5 17:25:06编辑过]
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