On which date of the month was Anjali born in February 2004 ?
I. Anjali was born on an even date of the month.
II. Anjali's birth date was a prime number
If the data in both statements I and II together are necessary to answer the question
From I and II, we conclude that Anjali was born in February 2004 on a date which is an even prime number. Since the only even prime number is 2, so Anjali was born on 2nd February, 2004.