Help me crack three questions please

ca3ltoys

There are three questions from PPrep, help me crack them
1. However much United States voters may agree that there is waste in government and that the government as a whole spends beyond its means, it is difficult to find broad support for a movement toward a minimal state.
(A) However much United States voters may agree that
(B) Despite the agreement among United States voters to the fact
(C) Although United States voters agree
(D) Even though United States voters may agree
(E) There is agreement among United States voters that

answer is (A), I wondered whether or not "MUCH" can modify voters?

2. Based on accounts of various ancient writers, scholars have painted a sketchy picture of the activities of an all-female cult that, perhaps as early as the sixth century B.C., worshipped a goddess known in Latin as Bona Dea, " the good goddess."
(A) Based on accounts of various ancietn writers
(B) Basing it on various ancient writers' accounts
(C) With accounts of various ancient writers used for a basis
(D) By the accounts of various ancient writers they used
(E) Using accounts of various ancient writers

answer is E, I don't know why answer B and C is wrong.

3. Astronomers at the Palomar Observatory have discovered a distant supernova explosion, one that they believe is a type previously unknown to science.
(A) that they believe is
(B) that they believe it to be
(C) they believe that it is of
(D) they believe that is
(E) they believe to be of

the answer is E, I wondered why this sentence eliminate "THAT"? and why the answer A is wrong?

sbbi

1. MUCH is to modify "agree"

2.
B, "it" does not have a valid referent
C. is redundant

3. 'that' is extra.

ca3ltoys

Thanks for your kind help. while for the 3rd one, "that" is redundant? how to distinguish whether  I should eliminate "that" or not?

sbbi

I think it is not idiomatic to say 'one that ...'. I remember that i read from og.

dxwei2008

第一个题目太有价值了，however的用法从来没有仔细看过，刚查了一下字典（金山词霸）：
不管用什么方法；无论什么方式
"However abundant certain natural resources may be, they cannot reproduce themselves and are bound to be used up ultimately."
上面这个例句也第一题基本上是一样的，however就是修饰much。刚看到题目的时候我还以为C对呢，结果C把意思表达得不够贴切。
这个问题建议重点关注。（斑竹还是斑竹，果然比一般人要厉害，佩服佩服！）

第三题刘振民的语法书里有解释。
一个supernova explosion是一种未知类型这样的说法是不正确的。只能说一个supernova explosion属于某种未知类型，所以必须用be of a type的表达方式。再使用简洁原则一过滤，答案就出来了。