Let's analyze the given Data Sufficiency question to determine if the provided statements are sufficient to find Mrinal's age.

Understanding the Question: How Old is Mrinal?

The goal is to find the specific numerical value of Mrinal's age. To answer this question, we need information that leads to a unique age for Mrinal.

Analyzing Statement 1: Mrinal's Mother's Age Relation

Statement 1 says: "Mrinal’s mother is 20 years older than him."

• Let Mrinal's age be represented by $M$ years.
• According to Statement 1, the mother's age is $M + 20$ years.

This statement establishes a relationship between Mrinal's age and his mother's age. However, it does not give us a specific number for either age. If Mrinal is 10, his mother is 30. If Mrinal is 15, his mother is 35. Since we can find many possible ages for Mrinal that satisfy this statement, Statement 1 alone is not sufficient to determine Mrinal's age.

Analyzing Statement 2: Mrinal's Brother's Age Relation

Statement 2 says: "Mrinal’s brother is 3 years younger than him."

• Let Mrinal's age be represented by $M$ years.
• According to Statement 2, the brother's age is $M - 3$ years.

This statement establishes a relationship between Mrinal's age and his brother's age. Similar to Statement 1, it gives an age difference but no specific age. If Mrinal is 10, his brother is 7. If Mrinal is 15, his brother is 12. Since we can find many possible ages for Mrinal that satisfy this statement, Statement 2 alone is not sufficient to determine Mrinal's age.

Combining Statements 1 and 2: Are They Sufficient Together?

Now, let's consider both statements together.

• From Statement 1: Mother's age = $M + 20$.
• From Statement 2: Brother's age = $M - 3$.

We have two relationships involving Mrinal's age ($M$), but we still do not have any equation or direct information that gives a specific numerical value for $M$. For example:

• If Mrinal is 10, his mother is 30 and his brother is 7. Both statements are satisfied.
• If Mrinal is 25, his mother is 45 and his brother is 22. Both statements are satisfied.

Even when combined, the statements only provide age differences relative to Mrinal. They do not fix Mrinal's age to a single value. To find Mrinal's age, we would need additional information, such as:

• The mother's age
• The brother's age
• The sum or difference of any two people's ages (e.g., the sum of Mrinal's and his mother's age, or the difference between his mother's and brother's age)

Since neither statement alone, nor both statements combined, provide enough information to find a unique value for Mrinal's age, both statements together are not sufficient.

Conclusion on Data Sufficiency for Mrinal's Age

Based on the analysis:

• Statement 1 alone is not sufficient.
• Statement 2 alone is not sufficient.
• Statements 1 and 2 together are not sufficient.

Therefore, additional data is needed to answer the question "How old is Mrinal?".

Revision Table: Assessing Statement Sufficiency

Additional Information on Data Sufficiency Questions

Data sufficiency questions test your ability to determine if the given information is adequate to answer a specific question, not necessarily to solve the question itself. Here are key points:

• Goal: The primary goal is to assess if the data provided is sufficient, not to calculate the final answer numerically (unless the calculation proves or disproves sufficiency).
• Independence of Statements: When evaluating statements individually, always assume the other statement is not given.
• Combining Statements: Only combine statements if neither statement alone is sufficient. When combined, use information from both statements simultaneously.
• Keywords: Look for keywords like "sufficient," "alone," "together," and "additional data needed."
• Types of Sufficiency: The options typically cover scenarios where one statement alone is sufficient, both are needed, neither is sufficient, or additional data is required.

In this problem about Mrinal's age, even knowing the age differences related to two other people isn't enough; you need at least one actual age or another relationship that creates a solvable system.