Though he declared himself eligible for the National Basketball...

Hi AdityaHongunti , daspri2809 , saarthakkhanna04
vyascd , this question is hard.
It is similar to two official questions, which I link to.

The player is the he.

In options A and C, the word "though" and "an agent to retain his status" make the sentence confusing:
Both A and C can be read in two ways:

1) if a college player wants to keep his amateur status, he should not hire an agent. Hiring an agent = player loses his amateur status.

2) if a college player wants to keep his amateur status, he should hire an agent "to retain" his amateur status. The agent is the person who helps a player to retain amateur status (maybe the agent files special papers and knows about a lot of other rules that would compromise amateur status).

• Overview

We need an idiom of purpose. What motivates the player to avoid hiring an agent?
Correct: X so that Y

Correct but often not preferred: X so as to Y

First, please do not confuse the second idiom of purpose with the idiom of emphasis SO X as to Y.**

Second, although that GMAC seems to prefer X so that Y,
X so as to Y is not wrong, and
in two instances in which that idiom was incorrect,
the problem lay in meaning.

So as to is a commonly accepted idiom of purpose in formal writing.
GMAC has offered it as a choice pitted against so that.
After looking through many official questions:
1) so as to is not part of any correct answer I have seen, and
2) all answers with so as to have something else wrong with them.

Call so as to "suspect," but be open to the idea that you may see so as to in the correct answer on the test.
I worry that GMAC will write a question in which so as to is used correctly—I would try to find another error if I saw "so as to."

In other words, X so as to Y is NOT automatically wrong. GMAC may have a preference. A preference is not a prohibition.

• Eliminate B
Verb tenses are incorrect. AND is a conjunction that signals parallelism. (SO is also a conjunction. The construction is odd.)
In a compound predicate, if one subject (player) is attached to two verbs that are joined by and,
the verbs must be parallel.
college player avoided and could retain are not parallel.

• Eliminate E
--in order that is allowed, but not with would in this case.
Would is too certain.
-- compared to (D), (B) is not nearly as concise

• Option A has two meanings, a fact that is easier to see in option (C)

Scenario #1: If you are a player who wants to retain amateur status, you must
1) declare yourself ineligible for the draft and
2) hire [an agent so as to retain = who will help you retain] the option of amateur status.
-- in this case, the player needed to hire an agent, an agent who would have helped the player retain his option of amateur status—the player just failed to do so.

Scenario #2 (logically, the more likely one, but we cannot be sure because of "though" and uncertainty about whom "to retain" modifies).
If you are a player who wants to retain amateur status, you must
1) declare yourself ineligible for the draft and
2) AVOID hiring an agent so as to retain the option of amateur status—because having an agent means that you are NOT an amateur.

The word "though" creates a mess. Though the player did good thing #1, _______
The next thing we expect to read about is a contrast statement such as "the player avoided doing good thing #2."

This contrast word, though, makes it seem as if the player got one thing right and a second thing wrong.

We still do not know whether an agent helps or hurts your chances of keeping your option of amateur status.

• Option C is ambiguous
In Option (C), whom does "to retain" modify? Does to retain modify
-- the agent? If so, then the agent gets hired in order to retain a player's status.
-- or the player? If so, then the player must not hire an agent. Hiring an agent = player loses his status.

Option C in the shortened sentence:
... the college basketball player avoided hiring an agent to retain the option of keeping his amateur status.

Meaning #1 (emphasis on avoided): The college basketball player did not care whether he lost his amateur status.
He avoided hiring an agent who would have helped him keep that status.

Meaning #2 (emphasis on avoided one thing to get another): A college basketball player who hires an agent becomes a "professional" and loses his amateur status.

This college player avoided hiring a person because to do so would strip the athlete of his status.

Option (A) is not much different from (C); (A), too, is ambiguous.
(A) merely emphasizes purpose a little more by using so as.

Both A and C are ambiguous.

What cures the ambiguity? Option (D), in which the pronoun HE is attached to SO THAT. "To retain" refers to the player.

• Option D solves the problem with its usage of that + HE

HE can only be the college player. In the non-underlined portion, the pronoun HE is the college player[/i].

In option D, replace the second HE with "the college player":
... The college player avoided hiring an agent so that the college player could retain the option of amateur status.

The subordinate clause beginning with so that is clear. The agent does not retain the option FOR the player.
"To retain" modifies and belongs to the player (who will lose the option if he hires an agent).

The inclusion of he and the presence of "could retain" after the word THAT clear things up.

The college player avoided X so that [the college player] could keep his amateur status.

Option (D) is better than options A and C.

This question strongly resembles this official quesiton, here. and this official question, here.

Spoiler alert: The answer to the second official question is revealed

Takeaways:
1) GMAC appears to have a strong preference for so that, but
2) so as to is an acceptable idiom of purpose if the meaning is conveyed correctly, especially in the negative.
: I spoke quietly so as not to disturb the skittish birds.

Answer D is correct.

All, I hope that analysis helps.

*Do not confuse two nearly identical idioms.
The idiom of purpose begins with X so
The idiom of emphasis behind with with So X
PURPOSE: X so as to Y
and
EMPHASIS: so X as to Y (this rendition of the emphasis idiom is incorrect)
To emphasize an adjective or adverb, for example, use SO X THAT Y
Wrong:The curry was so spicy as to make my eyes water. (Do not confuse with purpose, e.g. I whispered so as not to wake the sleeping kittens.)

Correct: The curry was so spicy that it made my eyes water.
Again, the second idiom is of emphasis, not of purpose.