Read the following statements.
Statement-1: A number for which sum of all its factors is equal to twice the number is called a perfect number.
Statement-2: If two numbers are divisible by a number, then their sum and difference are also divisible by that number.
Which of the following options holds?

Options

A. Both Statement-1 and Statement-2 are true.
B. Statement-1 is true but Statement-2 is false.
C. Statement-1 is false but Statement-2 is true.
D. Both Statement-1 and Statement-2 are false

Answer

To solve the question, we need to evaluate the two statements provided and determine their truthfulness.

### Step-by-Step Solution:

**Step 1: Analyze Statement 1**
- Statement 1 claims: "A number for which the sum of all its factors is equal to twice the number is called a perfect number."
- To verify this, we can take the example of the number 6.
- The factors of 6 are: 1, 2, 3, and 6.
- The sum of these factors is: 1 + 2 + 3 + 6 = 12.
- Twice the number 6 is: 2 × 6 = 12.
- Since the sum of the factors (12) is equal to twice the number (12), Statement 1 is true.

**Step 2: Analyze Statement 2**
- Statement 2 claims: "If two numbers are divisible by a number, then their sum and difference are also divisible by that number."
- Let's denote two numbers as n1 and n2, and let k be the number they are divisible by.
- If n1 is divisible by k, we can write n1 = k × a (for some integer a).
- If n2 is divisible by k, we can write n2 = k × b (for some integer b).
- Now, consider the sum:
- n1 + n2 = (k × a) + (k × b) = k × (a + b), which is divisible by k.
- Now, consider the difference:
- n1 - n2 = (k × a) - (k × b) = k × (a - b), which is also divisible by k.
- Therefore, Statement 2 is also true.

**Step 3: Conclusion**
- Both statements are true.

### Final Answer:
Both Statement 1 and Statement 2 are true.