Question : On which date of the month was Anjali born in February 2004 ?…
2026
Question : On which date of the month was Anjali born in February 2004 ?
Statements :
I. Anjali was born on an even date of the month.
II. Anjali's birth date was a prime number.
- A.
I alone is sufficient while II alone is not sufficient
- B.
II alone is sufficient while I alone is not sufficient
- C.
Either I or II is sufficient
- D.
Both I and II are sufficient
Attempted by 17 students.
Show answer & explanation
Correct answer: D
Concept: In a data-sufficiency question, a statement (or combination of statements) is 'sufficient' only if it narrows the answer to exactly one value consistent with every constraint in the question - not if it merely narrows the range. Test each statement alone first, then in combination, stopping as soon as a stage yields a unique value.
Application: February 2004 is a leap year (2004 is divisible by 4 and not a century year), so the month has 29 days, meaning the date lies in the range 1 to 29.
Statement I alone: the date is even, giving the candidates {2, 4, 6, ..., 28} - fourteen possible dates, so Statement I alone is NOT sufficient.
Statement II alone: the date is a prime number, giving the candidates {2, 3, 5, 7, 11, 13, 17, 19, 23, 29} - ten possible dates, so Statement II alone is NOT sufficient.
Statements I and II together: the date must be both even AND prime. The only even prime number is 2, because every other even number is divisible by 2 and hence composite. Intersecting the two candidate sets above leaves exactly one value, 2, so the date is uniquely determined as 2nd February 2004.
Cross-check: 2 is indeed even (2 = 2 x 1) and prime (divisors are only 1 and 2), and no other date from 1 to 29 satisfies both properties at once, confirming the intersection is unique.
Result: Neither statement alone is sufficient, but the two statements together are sufficient - both I and II are required.