Scholars have little doubt whether the latter years of Egypt's Old Kin

OFFICIAL EXPLANATION

Solution

In general, use doubt that.
Always avoid doubt if.
As long as the statement is affirmative, doubt whether is usually okay.
If the statement is negative or you are asking a question, use doubt that.

-- If a statement / main clause is negative, use doubt that:
I do not doubt that you are telling the truth. = I am certain that you are telling the truth.
I have no doubt that foreigners interfered with U.S. elections in 2016. = I am certain that foreigners interfered with elections.
I have little doubt that foreigners interfered with U.S. elections in 2016. = I am certain that foreigners interfered with elections.

I have no doubt = I am certain
When we use the verb to doubt in the negative, we are not expressing doubt.
In fact, we are expressing certainty. We are confident about our belief.
I do not doubt = I am not uncertain = I am certain
Use doubt that.

-- When asking a question, use doubt that:
Do you doubt that foreigners interfered with U.S. elections in 2016?
Does she doubt that you fought in Afghanistan?

If a statement / main clause is positive and expresses skepticism, use doubt that or doubt whether.
Do not use doubt if.
I doubt that he will be on time. = I am pessimistic; I think he will be late.
I doubt whether he will be on time. = I am pessimistic; I think he will be late.

But if the statement is in the negative then the following is true:

I have little doubt that ≈ I have no doubt that

We have a statement in the negative.
The sentence means that scholars are almost completely certain that changes in the flow of the Nile River brought about economic and governmental "disasters" that plagued the last years of Egypt's old kingdom.

• Split #1: subject-verb agreement

→ In option E because the plural noun years does not agree with the singular verb was.
Eliminate E

• Split #2: negative doubt statements cannot take whether

Options A, B, and E incorrectly use doubt whether, doubt as to whether, and doubt about whether.
The scholars are confident that changes in the flow of the Nile caused disasters in the last years of Egypt's Old Kingdom and led to the demise of that Old Kingdom.
The scholars do not doubt that changes in the flow of the Nile caused disasters in the last years of Egypt's Old Kingdom.

Options A, B, and E incorrectly use some form of whether.
In negative sentences, use doubt that.
ELIMINATE A and B (option E is already eliminated.)

• Split #3 - Use that for negative statements; avoid awkward phrasing

Option D uses having been marked, phrasing that makes an already passive sentence more passive.
Because option D does not use whether, it may not seem as incorrect as the other three options.
But SC is often a comparison between the better option and the worse option.
Option C is better than option D: (C) is straightforward and does not use awkward phrasing.
(If you disagree, argue your case: why is D better than C?)
Eliminate D

The best answer is C.

COMMENTS

vipulshahi , welcome to SC Butler.

This question is hard.
GMAC has tested this rule on a couple of occasions (and probably on occasions I have not yet seen.)

One reason I posted this question stems from non-native speakers' tendency to say, "I have a doubt."
That sentence usually goes further to: "I have a doubt about . . ."
I have a doubt about is not wrong—I hope that people continue to ask questions.
(The only dumb question is the one that goes unasked.)

Just know that if you express doubt in a negative statement—use that.

vipulshahi , you were brave. And your answer is very good. Well done.