Jue
When it comes to remembering numbers or binary digits,
each competitor in the World Memory Championships has its own systems for converting these items into images.
A) each competitor in the World Memory Championships has its
B) each competitor in the World Memory Championships has their
C) each competitor in the World Memory Championships have their
D) all of the competitors in the World Memory Championships have its
E) all of the competitors in the World Memory Championships have their
--Source: Erica L. Meltzer / GMAT SC Guide
The competitors are presumably people, so we can't say "each competitor... has its", because "it" can't refer to a person, and A and D are wrong. C is wrong because "each competitor" is singular, so the plural "have" is the wrong verb choice.
But both B and E are acceptable in contemporary language, and these days, I'd be surprised if a GMAT question preferred one answer to the other (so the GMAT wouldn't ask a question like this). We use "they" in the singular in everyday speech all the time when gender is unknown or irrelevant ("someone left their watch on the table", for example). If you go back in time a few decades, strict grammarians would insist on using "his" or "her" or "his or her" when referring to a singular person (so they would argue you need to say something like "someone left his or her watch on the table", which sounds a bit ridiculous). But these days, most professional style guides not only consider "they" and "them" perfectly acceptable in situations like this, these guides actually consider it preferable to "his" or "her" (which, as a factual matter, are incorrect if you don't know the gender of the person involved) or "his or her", which is more awkward than necessary.
I'm sure the source justifies E here because it insists you need to say "the competitors... have their" and not "each competitor... has their", but that's a dated way to look at English usage. Both are perfectly fine in modern English, though if I was forced to choose between the two on a standardized test, I'd choose E just because of the strict plural/plural agreement.