As neptune28 has noted, to learn and to play are not prepositional phrases but INFINITIVES.
An infinitive -- TO + VERB -- can serve as a noun.
Infinitive as DIRECT OBJECT:
John learned TO PLAY.
Here, to play serves as the DIRECT OBJECT of learned.
WHAT did John learn?
He learned TO PLAY.
Infinitive as COMPLEMENT:
In the construction X is Y, Y is called the COMPLEMENT.
The complement essentially is the equivalent of the subject.
An infinitive can serve as the complement of a sentence.
The goal is to raise revenue.
Here, to raise revenue is the complement of the goal.
WHAT is the goal?
TO RAISE REVENUE.
This usage is rare.
I would be skeptical of this construction on the GMAT.
Infinitive as SUBJECT:
There are two primary ways -- one rare, one far more common -- that an infinitive will serve as the SUBJECT.
RARE: INFINITIVE + VERB
TO ERR is human.
Here, TO ERR is the subject of is.
Generally, this construction is used to express a GENERAL PRINCIPLE.
I would be skeptical of this construction on the GMAT.
COMMON: IT + TO BE + MODIFIER + INFINITIVE
It is easy TO LIKE MARY.
In this construction, it serves as an EXPLETIVE: a pronoun serving to delay the subject.
Here, the delayed subject is TO LIKE MARY.
The conveyed meaning is as follows:
To like Mary is easy.
But positioning the infinitive-as-subject before the verb results in a construction that is awkward and to be avoided.
In 99% of cases, an infinitive serving as the subject will be preceded by an expletive such as IT:
IT is easy to like Mary.
This is the sort of construction that the GMAT is likely to use when an infinitive serves as the subject of a clause or sentence.
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