求教 prep07- Q23 一道 Paradox 的题（屡做屡错）

teddybearj4

From 1978 to 1988, beverage containers accounted for a steadily decreasing percentage of the total weight of household garbage in the United States. The increasingly widespread practice of recycling aluminum and glass was responsible for most of this decline. However, although aluminum recycling was more widely practiced in this period than glass recycling, it was found that the weight of glass bottles in household garbage declined by a greater percentage than the weight of aluminum cans.

Which of the following, if true of the United States in the period 1978 to 1988, most helps to account for the finding?

(A) Glass bottles are significantly heavier than aluminum cans of comparable size.
(B) Recycled aluminum cans were almost all beverage containers, but a significant fraction of the recycled glass bottles had contained products other than beverages.
(C) Manufacturers replaced many glass bottles, but few aluminum cans, with plastic containers.
(D) The total weight of glass bottles purchased by households increased at a slightly faster rate than the total weight of aluminum cans.
(E) In many areas, glass bottles had to be sorted by color of the glass before being recycled, whereas aluminum cans required no sorting.

OA：C

各位童鞋们、NN们能不能帮忙分析一下这道题啊，每次看到都选A。查了以前的帖子也不懂，实在是想不明白！
Thx in advance！！！

babybearmm

这题我也做错了，选了C. 不过现在明白了，整理了我个人的思路见附件。
[attachimg]98808[/attachimg]
或者你参考这里
http://www.manhattangmat.com/forums/from-1978-to-1988-beverage-containers-accounted-for-t8333.html

本来我在纠结weight到底理解为物理学的mass（质量）还是统计学意义的weight（权重?），后来发现两者就解题来说没有区别，"garbage"那一项可以消掉的。

From 1978 to 1988, beverage containers accounted for a steadily decreasing percentage of the total weight of household garbage in the United States. The increasingly widespread practice of recycling aluminum and glass was responsible for most of this decline. However, although aluminum recycling was more widely practiced in this period than glass recycling, it was found that the weight of glass bottles in household garbage declined by a greater percentage than the weight of aluminum cans.

Which of the following, if true of the United States in the period 1978 to 1988, most helps to account for the finding?

(A) Glass bottles are significantly heavier than aluminum cans of comparable size.
(B) Recycled aluminum cans were almost all beverage containers, but a significant fraction of the recycled glass bottles had contained products other than beverages.
(C) Manufacturers replaced many glass bottles, but few aluminum cans, with plastic containers.
(D) The total weight of glass bottles purchased by households increased at a slightly faster rate than the total weight of aluminum cans.
(E) In many areas, glass bottles had to be sorted by color of the glass before being recycled, whereas aluminum cans required no sorting.

OA：C

各位童鞋们、NN们能不能帮忙分析一下这道题啊，每次看到都选A。查了以前的帖子也不懂，实在是想不明白！
Thx in advance！！！

-- by 会员 teddybearj4 (2012/4/10 19:39:50)

teddybearj4

哇谢谢baby姐呀！图图看不清楚耶！我先看看你给的link~~

猪王山

这个weight应该说的就是重量。我觉得关键是在于comparable size：万一玻璃瓶都是小型饮料瓶（比如说口服液。。。），而铝罐都是大易拉罐，那不就解决不了了。
而C选项，只要居民产生的glass少了，无论如何必然导致pencentage下降

babybearmm

我是觉得size根本没关系，关键在于percentage change.
就是我用绿色框住的两个式子，文中说(1)这两个ratio的大小比较，(2)分子的大小比较，(1)和(2)相反。那么就可以推出，问题的关键是分母。正确选项恰好是给出了分母大小的比较，能够justify the conclusion.

weight不管理解为mass还是statistical weight，都没关系。如果理解为后者，数学表达上要复杂一些，但是到最后可以纯数学运算抵消掉，所以两种理解是等效的。

这个weight应该说的就是重量。我觉得关键是在于comparable size：万一玻璃瓶都是小型饮料瓶（比如说口服液。。。），而铝罐都是大易拉罐，那不就解决不了了。
而C选项，只要居民产生的glass少了，无论如何必然导致pencentage下降

-- by 会员 猪王山 (2012/4/12 14:49:46)

teddybearj4

姐姐，明白了你的weight的意思，但是我对你的那两个绿色框框的公式的大于小于号有些疑问呀！我觉得好像应该反过来。(那两个公式从word实在没办法复制过来，编辑的太丑了。公式跟姐姐的一样，就是方向变了~)



1、percentage change：
aluminum recycling was more widely practiced。意思是AL的回收比例比glass要高。
   >     (这里分母的glass和AL指的是总个数)

2、numerical change
the weight of glass bottles in household garbage declined by a greater percentage than the weight of aluminum cans.（RON的解释是the NUMERICAL CHANGE in aluminum in the trash was lower than the NUMERICAL CHANGE in glass in the trash）

      <        (这里指的是recycle的个数)

只有glass的总个数<AL的总个数（即第一个式子的分母的glass和AL）。才能同时解释1、2


而C的话说了plastic代替的glass的数量比代替AL的数量要多，所以glass瓶子的个数就比AL要少，这样就满足了。

teddybearj4

我也觉得跟size没有关系哦~
A我现在明白为什么不选了，是因为同一个比值上下都有单个的glass weight或者是单个的AL weight。

这个weight应该说的就是重量。我觉得关键是在于comparable size：万一玻璃瓶都是小型饮料瓶（比如说口服液。。。），而铝罐都是大易拉罐，那不就解决不了了。
而C选项，只要居民产生的glass少了，无论如何必然导致pencentage下降

-- by 会员 猪王山 (2012/4/12 14:49:46)

babybearmm

我觉得是咱俩定义的量不同。
我的recycling对应的是Delda(x), 然后percentage of weight decline对应的是 Delta (x) / x。而生产总量是影响了x，也就是分母。
Anyway，答案一样就行。

(这里指的是recycle的个数)
这点我同意，"recycle的个数"=Delta(x)
不过我关注的是percentage of "recycle的个数": Delta(x) / x *100%

姐姐，明白了你的weight的意思，但是我对你的那两个绿色框框的公式的大于小于号有些疑问呀！我觉得好像应该反过来。(那两个公式从word实在没办法复制过来，编辑的太丑了。公式跟姐姐的一样，就是方向变了~)



1、percentage change：aluminum recycling was more widely practiced。意思是AL的回收比例比glass要高。
   >     (这里分母的glass和AL指的是总个数)
2、numerical change：the weight of glass bottles in household garbage declined by a greater percentage than the weight of aluminum cans.（RON的解释是the NUMERICAL CHANGE in aluminum in the trash was lower than the NUMERICAL CHANGE in glass in the trash）

      <        (这里指的是recycle的个数)

只有glass的总个数<AL的总个数（即第一个式子的分母的glass和AL）。才能同时解释1、2


而C的话说了plastic代替的glass的数量比代替AL的数量要多，所以glass瓶子的个数就比AL要少，这样就满足了。

-- by 会员 teddybearj4 (2012/4/12 16:17:19)

teddybearj4

哦哦~~谢谢姐姐！懂了哇！
这道题真的把我给绕的！~~~

我觉得是咱俩定义的量不同。
我的recycling对应的是Delda(x), 然后percentage of weight decline对应的是 Delta (x) / x。而生产总量是影响了x，也就是分母。
Anyway，答案一样就行。

(这里指的是recycle的个数)
这点我同意，"recycle的个数"=Delta(x)
不过我关注的是percentage of "recycle的个数": Delta(x) / x *100%

姐姐，明白了你的weight的意思，但是我对你的那两个绿色框框的公式的大于小于号有些疑问呀！我觉得好像应该反过来。(那两个公式从word实在没办法复制过来，编辑的太丑了。公式跟姐姐的一样，就是方向变了~)



1、percentage change：aluminum recycling was more widely practiced。意思是AL的回收比例比glass要高。
   >     (这里分母的glass和AL指的是总个数)
2、numerical change：the weight of glass bottles in household garbage declined by a greater percentage than the weight of aluminum cans.（RON的解释是the NUMERICAL CHANGE in aluminum in the trash was lower than the NUMERICAL CHANGE in glass in the trash）

      <        (这里指的是recycle的个数)

只有glass的总个数<AL的总个数（即第一个式子的分母的glass和AL）。才能同时解释1、2


而C的话说了plastic代替的glass的数量比代替AL的数量要多，所以glass瓶子的个数就比AL要少，这样就满足了。

-- by 会员 teddybearj4 (2012/4/12 16:17:19)

-- by 会员 babybearmm (2012/4/12 16:23:42)

双色鹿

mark一下晚上看啦~