Step 1: Approach this as a triage exercise. Ask which option, if delayed, will cause the worst irreversible damage in the shortest time.
Step 2: Rank the threats. A black, dusky finger means the artery feeding it is occluded - a vascular emergency where the clock is measured in hours before gangrene sets in. That makes option a the most urgent escalation.
Step 3: Compare with the rest. Loss of arm extension is a neuromuscular or tendon deficit that can be assessed without instant intervention. A 10 cm abrasion is a clean-and-dress soft-tissue issue. An intra-articular elbow fracture will need surgery on a planned list but does not threaten limb survival in the next hour.
Step 4: Because preserving blood supply takes precedence over deformity, wounds or joint involvement, the blackening finger goes to the orthopaedic PG first.
\[\boxed{\text{Patient's finger is blackening}}\]