'His or Her' Vs 'Their'

A/B - no chance of seems idiomatically right, moreover to recognize is wrong tense in choice B.
D - wrong tense, we need simple past.
E - his/her is not necessary as the subject is plural adult survivors. His or her is applicable when the subject is singular as in everyone, anyone, everybody etc.

IMO C.

Adult survivors should match with "they"

(C) is the choice

'His' and 'her' are used to refer to a singular entity.

The person who wins can have his or her name inscribed on a plaque.

In this case, 'his' or 'her' refer to the person. As we don't know who the person is - that person could be a boy or a girl - we don't want to only use his, so to be gender neutral we use his/her.

The people who win can have their names inscribed on a plaque.

In this example, 'person' is plural. 'People' - and for that matter any plural subject - never go together with his/her or he/she but always take plural pronouns, e.g. them/their.

One last point:

The person who wins can have his or her name inscribed on a plaque. He or she will also be featured in the local paper.

Notice that I used he or she, and not they. Colloquially, 'they' would be fine. But in standard English/GMAT, we want to keep the pronoun number consistent. In the above sentence, we've already established that 'person' is singular. Therefore that person could be either a he or she (but not a they).

Hope that helps!