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Data Sufficiency — Birthday date: On which day in April is Gautam's birthday? Statement I: Gautam was born exactly 28 years after his mother was born. Statement II: His mother will be 55 years, 4 months, and 5 days on August 18 of this year. Decide which statement(s) are sufficient to determine the April date. Choose the correct sufficiency option.

Difficulty: Medium

Statement I alone is sufficient, but Statement II alone is not sufficient.
Statement II alone is sufficient, but Statement I alone is not sufficient.
Both statements I and II together are sufficient, but neither alone is sufficient.
Either statement I or statement II alone is sufficient.
Even both statements I and II together are not sufficient.

Correct Answer: Both statements I and II together are sufficient, but neither alone is sufficient.

Explanation:

From Statement II
Mother's birthday = Aug 18 − 4 months − 5 days = April 13 (same calendar year).II alone gives only the mother’s April date, not Gautam’s.

From Statement I
Gautam is born exactly 28 years after his mother ⇒ same date of the month, 28 years later.I alone gives a relative offset but no concrete April date.

Combine I + II
Mother's birthday is April 13 ⇒ Gautam's birthday is also April 13 (28 years later).
Final Answer
Both statements together are sufficient.

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