According to the PMBOK® Guide, specifically the Develop Schedule process within the Project Schedule Management knowledge area, the project duration is determined by the total length of the Critical Path.

Understanding Parallel Activities: When two activities (B and C) are performed in " parallel, " they occur simultaneously. The total time required for this parallel segment is determined by the activity with the longest duration.

Duration of B = 3 days.

Duration of C = 2 days.

Time for parallel block = $\max(3, 2) = 3$ days.

Calculating Activity A: The project is stated to have a total duration of 10 days. Assuming A is the sequential component of the project (either preceding or following the parallel block), we use the following formula:

$\text{Total Project Duration} = \text{Duration of A} + \text{Duration of Parallel Block (B and C)}$

$10 \text{ days} = \text{Duration of A} + 3 \text{ days}$

$\text{Duration of A} = 10 - 3 = 7$ days.

Why other options are incorrect:

Option A: 3 days: This is the duration of the parallel segment. If A were 3 days, the total project duration would only be 6 days (3 for A + 3 for the block).

Option B: 5 days: This would be the result if you added the durations of B and C together ($3 + 2$). However, the question specifies they are in parallel, not in sequence (series).

Option D: 10 days: If A were 10 days, the total project duration would be at least 13 days (10 for A + 3 for the block), which contradicts the " 10-day project " constraint given in the prompt.