Most kindergarteners appear to have a desire to learn, but kindergarte

Isn't it idiomatically wrong to say "abilities for..."?

You're right. Ability for sitting still is not correct.

GMATNinja VeritasKarishma please explain B vs E?

The non underlined part talks in present tense - they appear to have a desire.
So when we talk about some specific kindergarteners, it should be in the present tense too. So present perfect is the correct tense - the determination has happened but it has relevance to the present.
Also, the determination has happened so we can say that "an increased ability" has been noticed. But increasing ability would need regular determination.
So the correct answer is (B)

STEP 1 - UNDERSTANDING INTENDED MEANING

Most kindergarteners appear to have a desire to learn, but kindergarteners with specifically planned diets were determined to have increased abilities for sitting still for extended periods.

1. The first clause of the sentence “Most ….. learn” has the verb in the simple present tense - “appear”.
2. Thus, the second clause should be parallel to the first clause in terms of tense and meaning.
3. Hence, the use of the simple past “were determined” is incorrect. We need to use the present perfect “have been determined” to indicate an action that is over but whose effect is still visible.
4. Since we are talking about a particular ability, the use of the plural "abilities" is incorrect.

INTENDED MEANING

• The above construction tells us two things that have been observed about kindergarteners.
• It appears that most of them have a desire to learn
• However, it has been determined that kindergarteners with specifically planned diets have an increased ability for sitting still for extended periods.

STEP 2 - ELIMINATE CHOICES WITH IDENTIFIED ERRORS

Choice C has the same error as choice A.
Choice D uses the incorrect past perfect “had determined”, and the plural "abilities"

STEP 3: EVALUATE MEANING OF REMAINING CHOICES

CHOICE B

Most kindergarteners appear to have a desire to learn, but kindergarteners with specifically planned diets have been determined to have an increased ability for sitting still for extended periods.

1. Logical
2. Clear
3. Same as the intended meaning
Correct Choice.

CHOICE E

Most kindergarteners appear to have a desire to learn, but kindergarteners with specifically planned diets have been determined to have increasing abilities for sitting still for extended periods.

• The task of determining is over. Thus, the result of “have been determined” should not be in any current increasing/progressive measure.
Incorrect Choice.

Note: The correct idiomatic expression is “ability to do something” or “ability of someone/ something”.