Question

In which year was Rahul born?
I) Rahul is 25 years younger to his mother.
II) Rahul's brother, who was born in 1964, is 35 years younger to his mother.

• A. Statement I alone is sufficient to answer the question
• B. Statement II alone is sufficient to answer the question.
• C. Statement I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. Statement I and II together are not sufficient to answer the question and additional data is required.

Hint:

In Data Sufficiency questions, never rush to compute the final answer. First check whether each statement independently gives a unique solution before combining them.

Answer 1

The Correct Option is C

Concept: In Data Sufficiency problems, we check whether the given statements provide enough information to uniquely determine the answer. Each statement is tested individually and then together.
Step 1: Analyze Statement I alone.
Rahul is 25 years younger than his mother: \[ {Rahul's birth year} = {Mother's birth year} + 25 \] Mother's birth year is unknown, so Rahul's birth year cannot be determined.
Statement I alone is NOT sufficient.
Step 2: Analyze Statement II alone.
Rahul's brother was born in 1964 and is 35 years younger than his mother: \[ {Mother's birth year} = 1964 - 35 = 1929 \] But no relation between Rahul and his brother is given, so Rahul's birth year cannot be found.
Statement II alone is NOT sufficient.
Step 3: Use both statements together.
From Step 2, Mother's birth year = 1929.
From Statement I: \[ {Rahul's birth year} = 1929 + 25 = 1954 \] Thus, Rahul's birth year is uniquely determined.
Hence, both statements together are sufficient, but neither alone is sufficient.