Read the given statements carefully and select the correct option.
Statement-1: If a number is divisible by both 3 and 6, then it must be divisible by 18.
Statement-2 : If 295x4 is divisible by 11, then the least value of x is 2.

Options

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

Answer

To solve the given problem, we need to evaluate both statements separately.

### Statement 1:
"If a number is divisible by both 3 and 6, then it must be divisible by 18."

**Step 1:** Understand the divisibility rules.
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 6 if it is divisible by both 2 and 3.

**Step 2:** Analyze the relationship between the numbers.
- If a number is divisible by 6, it is also divisible by 3. Therefore, if a number is divisible by both 3 and 6, it must be divisible by 6.

**Step 3:** Check if divisibility by 3 and 6 implies divisibility by 18.
- The least common multiple (LCM) of 3 and 6 is 6, not 18.
- For a number to be divisible by 18, it must be divisible by both 2 and 9 (since 18 = 2 * 9).

**Step 4:** Find a counterexample.
- Consider the number 12. It is divisible by 3 (12 ÷ 3 = 4) and by 6 (12 ÷ 6 = 2), but it is not divisible by 18 (12 ÷ 18 = 0.67).

**Conclusion for Statement 1:**
The statement is **false** because a number can be divisible by both 3 and 6 without being divisible by 18.

### Statement 2:
"If 295x4 is divisible by 11, then the least value of x is 2."

**Step 1:** Understand the divisibility rule for 11.
- A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is either 0 or a multiple of 11.

**Step 2:** Identify the positions of the digits in 295x4.
- Odd positions: 2 (1st), 5 (3rd), 4 (5th) → Sum = 2 + 5 + 4 = 11
- Even positions: 9 (2nd), x (4th) → Sum = 9 + x

**Step 3:** Set up the equation based on the divisibility rule.
- The difference should be:
\[ \text{Sum of odd positions} - \text{Sum of even positions} = 11 - (9 + x) = 11 - 9 - x = 2 - x \]
- For the number to be divisible by 11, \(2 - x\) should be 0 or a multiple of 11.

**Step 4:** Solve for x.
- Setting \(2 - x = 0\) gives \(x = 2\).
- The next multiple of 11 would be \(2 - x = 11\), which gives \(x = -9\) (not valid since x must be a digit).

**Conclusion for Statement 2:**
The least value of x that makes the number divisible by 11 is indeed **2**, making this statement **true**.

### Final Conclusion:
- Statement 1 is **false**.
- Statement 2 is **true**.