A remembers that P's first appointment to the job is after 17th but before 20th March. Whereas B remembers that P's first appointment to the job is after 18th but before 22nd March. Assuming both are correct, which date is most likely to be P's first appointment to the job?

Given:  

Two people's memories about P's appointment date:

A remembers:
The date is after 17th March but before 20th March → Possible dates: 18th, 19th March
B remembers:
The date is after 18th March but before 22nd March → Possible dates: 19th, 20th, 21st March

Finding the Common Date:
A says : 18th, 19th
B says: 19th, 20th, 21st
Common date: 19th March
Thus, the correct option is (d) 19th March