Direction(Question 1 to 3) : Read the information given below to answer these questions :
(i) Aarti is older than Sanya
(ii) Muskan is elder than Aarti but younger than kashish
(iii) Kashish is elder than Sanya
(iv) Sanya is younger than Muskan
(v) Gargi is the eldest
Which of the given statments is / are superfluous and can be dispensed with while answering the above questions ?

Options

A. Either (i) or (iii)
B. Only (iv)
C. Either (i) or (iv)
D. both(iii) and(iv)

Explanation

To determine which statements are superfluous and can be dispensed with while answering the question, we will analyze the given statements step by step.

### Step-by-Step Solution:

1. **List the Statements**:
- (i) Aarti is older than Sanya.
- (ii) Muskan is elder than Aarti but younger than Kashish.
- (iii) Kashish is elder than Sanya.
- (iv) Sanya is younger than Muskan.
- (v) Gargi is the eldest.

2. **Analyze the Relationships**:
- From statement (i): Aarti > Sanya
- From statement (ii): Kashish > Muskan > Aarti
- From statement (iii): Kashish > Sanya
- From statement (iv): Muskan > Sanya
- From statement (v): Gargi > All

3. **Establish the Order**:
- From (ii), we can deduce: Kashish > Muskan > Aarti > Sanya.
- Since Gargi is the eldest, we can place her at the top: Gargi > Kashish > Muskan > Aarti > Sanya.

4. **Identify Superfluous Statements**:
- Now, we need to check if any statements can be removed without losing the ability to determine the order.
- Statements (iii) and (iv) provide information about Sanya's relationship with Kashish and Muskan, respectively. However, we already know from statement (ii) that Kashish is older than Muskan and Aarti, which implies that Kashish is also older than Sanya.
- Similarly, statement (iv) is also redundant because Muskan being older than Aarti (from statement ii) already implies that Muskan is older than Sanya.

5. **Conclusion**:
- Therefore, statements (iii) and (iv) are superfluous as they do not add any new information that is necessary to establish the order of ages.

### Final Answer:
The superfluous statements are (iii) and (iv).