Anisha and Amit study in class VII. Anisha told Amit that if the marks in Mathematics of each student in the class are increased by 5, the average would go up by 5. She further says that it is true for all numbers. Amit does not agree and Anisha proves it by taking the case n, instead of 5. Anisha is using

Options

A. deductive logic
B. common sense
C. estimation
D. inductive logic

Answer

To solve the question regarding Anisha and Amit's discussion about the average marks in mathematics, we need to analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Problem**: Anisha claims that if the marks of each student in the class are increased by a certain number (in this case, 5), the average marks will also increase by that same number (5). She asserts that this principle holds true for any number, not just 5.

**Hint**: Think about how averages work when all values in a dataset are uniformly increased.

2. **Defining the Average**: The average of a set of numbers is calculated by dividing the sum of those numbers by the count of the numbers. If we denote the current average marks as \( A \) and the number of students as \( n \), then the total marks can be expressed as \( n \times A \).

**Hint**: Recall the formula for calculating the average.

3. **Increasing Marks**: If each student’s marks are increased by 5, the new total marks will be \( n \times A + 5n \) (since each of the \( n \) students has their marks increased by 5).

**Hint**: Consider how the total changes when each individual score is modified.

4. **Calculating the New Average**: The new average after increasing the marks will be:
\[ \text{New Average} = \frac{n \times A + 5n}{n} = A + 5 \]
This shows that the average has indeed increased by 5.

**Hint**: Simplify the expression to see how the average changes.

5. **Generalizing the Argument**: Anisha states that this principle holds for any number \( n \) instead of just 5. If we replace 5 with \( n \), the same logic applies:
- New total marks = \( n \times A + n \times n \)
- New average = \( A + n \)

**Hint**: Think about how changing the number from 5 to \( n \) affects the calculations.

6. **Conclusion**: Anisha is using a method of reasoning that involves assuming a variable (in this case, \( n \)) to generalize her statement. This method is known as **estimation**, as it allows her to demonstrate that the principle holds true for any number.

**Hint**: Identify the reasoning technique that allows for generalization from a specific case.

### Final Answer:
Anisha is using **estimation** to prove her point.