You are given a question and three statements. Identify which of the statements is/are necessary/sufficient to answer the question:
Question:
In which year was Aarti born?
Statements:
I. Aarti is six years older than Pranavi.
II. Pranavi's sister was born in 1982.
III. Aarti's sister is two-years younger than Pranavi's sister, who is eight years younger than Pranavi.

Options

A. Only II and III are sufficient
B. Only I and III are sufficient
C. All, II and III are necessary
D. Only I is sufficient

Answer

To determine the year Aarti was born, let's analyze the statements step by step.

### Step 1: Analyze Statement I
**Statement I:** Aarti is six years older than Pranavi.

- Let’s denote Pranavi's birth year as \( P \).
- Therefore, Aarti's birth year can be expressed as \( A = P - 6 \).

### Step 2: Analyze Statement II
**Statement II:** Pranavi's sister was born in 1982.

- If Pranavi's sister was born in 1982 and she is 8 years younger than Pranavi, we can find Pranavi's birth year.
- Thus, Pranavi was born in \( 1982 + 8 = 1990 \).

### Step 3: Calculate Aarti's Birth Year Using Statement I
Using the information from Statement I and the birth year of Pranavi:

- From Step 2, we found that Pranavi was born in 1990.
- Now, substituting into the equation from Step 1:
\[ A = 1990 - 6 = 1984 \]

### Step 4: Analyze Statement III
**Statement III:** Aarti's sister is two years younger than Pranavi's sister, who is eight years younger than Pranavi.

- We already know Pranavi's sister was born in 1982.
- Therefore, Aarti's sister must be born in \( 1982 - 2 = 1980 \).

### Step 5: Confirm Aarti's Birth Year
Now, we can confirm Aarti's birth year using the information from Statement III:

- Since Pranavi is 8 years older than her sister (born in 1982), Pranavi was born in 1990.
- Aarti is 6 years older than Pranavi, so:
\[ A = 1990 - 6 = 1984 \]

### Conclusion
From the analysis of all three statements, we can conclude that Aarti was born in 1984.