its a choice between 2 alternatives, why isn't 'between' being used?

The sense of between is given by word 'alternate' in this question. Also use of being is correct in 2 cases- when it is used as a noun at the start of the sentence and when it is used used in perfect tense.

Hope this helps!

Meaning issue , proper verb.

A. between periods that were lethargic and withdrawal: It was not the periods that was lethargic and withdrawal but rather the person. Wrongly gives the impression that the periods were Lethargic and withdrawal and not the person.INCORRECT

B.with periods of lethargy and withdrawal : Correctly refers to the person.CORRECT

C. those that were of lethargy and of withdrawal: " those that were of " is passive and pronoun " those " does not refer to periods as clear as in option B. INCORRECT

D.withdrawal with periods of lethargy: cleary incorrect.INCORRECT

E. between periods of being lethargic and withdrawn: use of being is incorrect here.INCORRECT

Hope it's clear.
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After Woodrow Wilson had a massive right-hemisphere stroke, he could not read more than a few lines at a time, he was subject to outbursts of temper and tears, and his periods of alertness alternated between periods that were lethargic and withdrawal.

"X alternate with Y" is the correct idiom, in which X and Y are similar elements.

Hence, "periods of alertness alternated with periods of lethargy and withdrawal" make the most sense. The answer is B

VeritasKarishma GMATNinja
Why the use of "being" in option E is wrong?
Meaning is more clearer in option E than B.
use of "with" doesn't give the intended meaning.
alternate between is much better than alternate with.
Kindly explain

The problem with (E) is the meaning. It's okay to say, "his periods of alertness alternated between [x] and [y]." And it's also probably okay to alternate between (1) periods of being [x] and (2) periods of being [y].

But in choice (E), are his periods of alertness alternating between (1) periods of being lethargic and (2) withdrawn?? Again, it's probably okay to alternate between (1) periods of being lethargic and (2) periods of being withdrawn. But it doesn't make sense to have "withdrawn", by itself, alternating with "periods of being lethargic".

At this point you might be thinking, "Well, the entire prepositional phrase 'of being lethargic and withdrawn' modifies the word 'period' right before it, so what you just said doesn't matter!" But if that's the case, what are we alternating between?? We have, "his periods of alertness alternated between (1) periods of being lethargic and withdrawn ... (umm, wait, where's the 2nd thing??)". We need to alternate between [x] and [y], but in this case we only get an [x].

Most importantly, think about the logical meaning here: we are not trying to say that his periods of alertness, themselves, alternated between [x] and [y]. Instead, we are trying to say that his periods of alertness alternated with periods of lethargy and withdrawal.

You could say, for example, that his mental state alternated between (1) periods of alertness and (2) periods of lethargy and withdrawal. But we don't have that structure in this question. Instead we have [x] alternated with [y], so (B) is the best choice.

I hope that helps!
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The use of with/between is different

A alternates with B - The red light alternates with the green light.

He is alternating between A and B - Choosing between 2 options
We are going to alternate between the lead and the understudy.

Here, we have A alternated with B.
So periods of alertness alternated with the periods of lethargy.
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Here's the official explanation provided by the GMAC for this question:

The original version can be read as illogically indicating that Wilson’s withdrawal and periods of lethargy comprised the entire times in which Wilson was alert. In principle, one could be alert and at the same time lethargic or withdrawn (from other people). However, the earlier part of the sentence says that he had outbursts of temper and tears. These would necessarily have been during times when he was alert and neither lethargic nor withdrawn. Thus, the original wording is contradictory. The phrase periods that were lethargic is indirect and illogical, appearing to claim that the periods, rather than the person, were lethargic.

Option A: This can be read as illogically claiming that Wilson’s alert times consisted of alternating periods of lethargy and withdrawal. The phrase periods that were lethargic is indirect and illogical, appearing to claim that the periods, rather than the person, were lethargic.

Option B: Correct. This logically, directly, and concisely expresses the relationship between the periods of alertness and the periods with which those are contrasted. The phrase alternated with clearly indicates that the periods of alertness were not themselves periods of lethargy and withdrawal.

Option C: This illogically treats alternated as a transitive verb; it says that periods of lethargy and periods of withdrawal were things that the periods of alertness alternated, as if the periods of alertness acted to bring about those effects. The phrases that were of lethargy and [that were] of withdrawal are unidiomatic, awkward, verbose, and jarringly indirect.

Option D: This illogically treats alternated as a transitive verb; it says that withdrawal and periods of lethargy were things that the periods of alertness alternated, as if the periods of alertness acted to bring about those effects.

Option E: This illogically claims that Wilson’s alert times consisted of alternating periods during each of which he was both lethargic and withdrawn.

The correct answer is B.

Please note that I'm not the author of this explanation. I'm just posting it here since I believe it can help the community.
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VeritasKarishma,

Suppose we had a choice that said "between periods of lethargy and withdrawal." Would this be fine?

My understanding is that A and E are wrong not because of the use of 'between', but because of the use of "lethargic and withdrawal" in A and "of being" in E.
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basshead

Both 'between' and 'with' are acceptable but used differently.

... alternates between A and B...
A alternates with B...

Since 'periods of alertness' are already given, they will alternate with 'periods of lethargy and withdrawal'.
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Thank you for clarifying!

Much appreciated.
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