A) so gradual as to be indistinguishable
"so... as to be..." is a correct idiom.

B) so gradual so that they can be indistinguishable
"so... so that..." is not a correct idiom

C) so gradual that they are unable to be distinguished
This one is tough, because it's not grammatically or idiomatically incorrect. "So... that" is a correct idiom. It's certainly wordier than A, and there also seems to be a disconnect in meaning. If something is "indistinguishable," then people are not able to distinguish it. Here, saying that the "shifts... are unable to be distinguished," then the lack of ability is on the part of the shifts, and not on the people distinguishing. This is a case in which passive voice alters the meaning slightly, and therefore makes less sense.

D) gradual enough not to be indistinguishable
"gradual enough" means something different from "so gradual." "Enough" implies a sufficient quantity, above a certain threshold - "I have enough money to by the new laptop." "So" is a qualifier meaning "to such a degree that." For example, "I have so much money that I could buy all of the laptops in the world." It doesn't imply any threshold.

E) gradual enough so that one cannot distinguish them
Same issue as in D.

The correct answer is A.

所以需判断主句的发生对状语事件的发生与否是否有直接影响。主句的发生对状语事件的发生与否在题中有直接影响，因此必须用不定式
另关于C我的理解是economic shifts不是人，不应用“能力able”来衡量。

we start to have trouble when using "not" with "enough". although it makes sense to say that i am tall enough to reach the ceiling, it's much trickier to assert that i am short enough NOT to reach the ceiling. there are lots of ways i could avoid reaching the ceiling without having to be short..
the takeaway here is that you should be wary of a construction that combines "enough" with "not" in this way..

"enough" usually means that something has a sufficient amount of a property that it can achieve some goal that was otherwise unattainable. for instance, perhaps i am tall enough to reach the ceiling. if i weren't tall enough, i could not reach the ceiling..

这里总结一下关于so as to和so that在字面上的区别。so…that可以用作多个主语时，so前面的主语和that后面的主语可以不一样，例如：
I set up the computer so that they could work from home.（我把电脑设置好，这样他们就可以在家办公了。）
so as to要求so前的主语和as to身后动作的主语相同。例如：
I set up the computer so as to do my work. （我把电脑设置好以便完成我的工作）
此时，do my work的主语必须是I。

be able to 不能用做被动语态。表示能力，不能说他没有被区分的能力

我觉得C选项不好再be able to do 是表示能力的，用在这里不好，还有就是被动语态的用法明显没有A选项要好用

in general, "so [adj/adverb] that [complete sentence]" is used when "[complete sentence]" has a DIFFERENT SUBJECT than the original sentence.
e.g., When I came back from vacation, I was so tan that my friends didn't even recognize me.
(subject changes from "i" to "my friends")

if the subject is still the same, then "so [adj] as to [verb]" is a more efficient way to write the construction.

C) so gradual that they are unable to be distinguished
This one is tough, because it's not grammatically or idiomatically incorrect. "So... that" is a correct idiom. It's certainly wordier than A, and there also seems to be a disconnect in meaning. If something is "indistinguishable," then people are not able to distinguish it. Here, saying that the "shifts... are unable to be distinguished," then the lack of ability is on the part of the shifts, and not on the people distinguishing. This is a case in which passive voice alters the meaning slightly, and therefore makes less sense.

积累：
so as to，前后需要保持主语一致
so thta，可以是不同主语
enough for sb
enough to do sth
C选项的错误在于they指代shifts，而shifts不能用able to do来描述
A correct

※主语1+so…that+主语2：
可以用作多个主语时，so前面的主语和that后面的主语可以不一样，例如：
【I--主语1】 set up the computer so that 【they--主语2 】could work from home.（我把电脑设置好，这样他们就可以在家办公了。）

※同个主语+so as to+同个主语：
要求so前的主语和as to身后动作的主语相同。例如：
【I--同个主语】 set up the computer so as to do my work. （我把电脑设置好以便完成我的工作）
此时，do my work的主语必须是I。

选项A（√）
Often major economic 【shifts】 are 【so gradual as to be indistinguishable 】at first from ordinary fluctuations in the financial markets.
通常，重大的经济转变是如此缓慢，以至于起初与金融市场的普通波动无法区分。

※ 能……
人+ ABLE / ABILITY / CAPABLE / CAPABILITY ..., （√）
人/ 物 + “Can / could” （√）
able/unable+被动语态（×）

选项C（×）
Often major economic 【shifts--主语不是人】 are so gradual that they are 【unable to be distinguished（×）冗余 = indistinguishable，且able/unable+被动语态错误】 at first from ordinary fluctuations in the financial markets.

People cannot hear this sound.（√）
This sound cannot be heard by humans. (√)

People are unable to hear this sound. （√）
【This sound--不是人】 is unable to 【be heard by humans 被动语态】. (×)

Sound waves are able to 【shatter glass 主动语态】. （√）

when "one" is used to mean "a random person", it doesn't need an antecedent.

THIS kind of "one" couldn't possibly have an antecedent, anyway -- the whole point is that it could refer to anyone at all.
when you are talking about antecedents, i think you're confusing this kind of "one" with a totally different kind of thing (e.g., This store has large bottles of my favorite soda in the cooler, so I will buy one for the drive.)

“Should The subject of "can" and "be able to" be animate?please certify,thanks!”

I'm not totally sure what you mean by "animate" here. Sounds to me like 'person or animal', but that's just a guess.

In any case, not necessarily, because it's possible for an inanimate object to have capabilities. (This bullet is able to pierce Kevlar. Because the snow reflects incoming sunlight, the Siberian landscape is unable to retain much heat. Etc.)

The question you should really ask yourself is, "Are we talking about something that X can do?"
If the answer to this question is yes -- regardless of whether X is a person or an animal -- then "(un)able" / "(in)ability" should be fine.

If you're talking about something that someone can do to or with X, then you shouldn't use those words.
That's definitely the case here -- we're talking about whether people can distinguish the shifts, not about what the shifts themselves can do.

(b) "so gradual so that..." is not a correct idiom. instead you should say "so gradual that..."

(c) is substantially more wordy than the correct answer (a).
i don't see anything strictly ungrammatical in (c).

as i said upthread, i don't see anything ungrammatical about choice (c), so i don't think splitting is going to do you any good here.
the only difference i see between (a) and (c) is a somewhat substantial difference in wordiness / concision. (i.e., "unable to be distinguished" is 4 words that mean the exact same thing as the 1 word "indistinguishable")

i also find something a bit awkward about the use of "unable" to describe something that's not actually an inability of the subject. here's what i mean:

this plant is unable to perform photosynthesis.
legitimate, because this actually describes an inability of the plant itself.

this sentence:
they (= major economic shifts) are unable to be distinguished...
i don't like this, because we're not actually talking about an "inability" possessed by the economic shifts themselves.
if we'd said something like "economic shifts are unable to destroy your equity", then i'd find that more appealing.

(e) is unidiomatic. you can't mix "enough" and "so that".
the correct idiom is "enough to...". you can't "double up" with another idiom.

as for (d), i'm not sure whether you're allowed to insert "not" between "enough" and "to".
i don't think that you are.

C选项：本选项在语法上没有问题。但在逻辑上，应将so gradual that改为so gradual as to be。这点考查了不定式和从句的区别。用之于本题，由于变化部分是状语，所以需判断主句的发生对状语事件的发生与否是否有直接影响。显然地，主句“主要经济变化是如此的逐渐”这个事件会直接影响“主要经济变化不能在最开始被检测出来”这个事件的发生与否。显然地，经济变化只要具有逐渐这个特点，则其就会具有难以被检测这个特点。因此，只能用不定式短语。

be able to表示主观能力，不用被动

1.Idiom：强调句型so that或者so...as to，注意so ...as to的逻辑主语前后一致。
BE错
2.措辞，unable一般用于人，这里C用法错误，C错
3.简洁,enough not to be表达很奇怪，而且enough主要用于表示主观满足，书面表达中很少用。
关于enough：
enough的固定搭配：
enough for sb. 对某人来说足够了
enough to do something 足够做某事
错误搭配：(X) enough + ”that / so as to / so to / so that”。

I set up the computer so that they could work from home.（我把电脑设置好，这样他们就可以在家办公了。）
so as to要求so前的主语和as to身后动作的主语相同。例如：
I set up the computer so as to do my work. （我把电脑设置好以便完成我的工作）
此时，do my work的主语必须是I。

be able to 不能用做被动语态。表示能力，不能说他没有被区分的能力

另外注意区分so ... as to ...和so ... to ...
so ... as to ...是一种平行结构。
如：
Major economic shifts are so gradual as to be indistinguishable.
are gradual 和 be indistinguishable平行

而 so ... to ...表示目的，to 后面加动词（包括被动式）
这种情况下 so ... to ...本身具有“太难去做……”的意思，本身就是否定，所以按照上面的语义不需要加否定
如：
Major economic shifts are to gradual to be distinguished.

B so ... so that... 表述错误，应该是 so ... that...
C unable 发出动作应该是人
D adj + (not) to...后面应该加动词表示目的，可以这样表达：Major economic shifts are gradual enough not to be distinguished. 这里的adj是gradual， enough 不是固定搭配表示，实际是 adj后的副词，这样是OK的
E so that 表示主观能动，题目中的economic shift 到 发现 实际是一种客观现象/状态，一般so that 我们这样使用：I got up early so that I could get there on time.

C中they are unable to be distinguished, 能力在economic shifts。而实际上应该是人有没有这个ability，indistinguishable是说人无法distinguish它

主句“主要经济变化是如此的逐渐”这个事件会直接影响“主要经济变化不能在最开始被检测出来”这个事件的发生与否。显然地，经济变化只要具有逐渐这个特点，则其就会具有难以被检测这个特点。
---那么 so gradual that 在句中就表现不出这个直接影响的意思了？