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QUICK ANSWER
"Quien" is a form of "quien", a pronoun which is often translated as "who". "La que" is a phrase which is often translated as "the one that". Learn more about the difference between "quien" and "la que" below.
quien()
A pronoun is a word that stands in for a noun (e.g., she).
1. (relative)
2. (indefinite)
a. anyone
Puedes elegir a quien quieras siempre y cuando levanten la mano.You can choose anyone you like as long as they raise their hand.
la que
A phrase is a group of words commonly used together (e.g., once upon a time).
a. the one that
No me gusta esta bufanda. La que compré en el mercado de pulgas es más linda.I don't like this scarf. The one that I bought at the flea market is prettier.
b. whichever
¿Qué tarea elijo? - La que elijas te enseñara algo nuevo.What task do I choose? - Whichever you choose will teach you something new.