Which of the following numbers is divible by both 7 and 11 ?

Options

A. 16425
B. 12235
C. 16257
D. 16324

Answer

To determine which of the given numbers is divisible by both 7 and 11, we can follow these steps:

### Step 1: Identify the numbers to check
Let's assume the numbers we need to check are:
1. 1456
2. 2153
3. 1276
4. 1632

### Step 2: Check divisibility by 11
To check if a number is divisible by 11, we can use the rule of alternating sums:
- For a number, sum the digits in the odd positions and the digits in the even positions, then find the difference.
- If the difference is 0 or divisible by 11, then the number is divisible by 11.

#### Check each number:
1. **1456**:
- Odd positions: 1 + 5 = 6
- Even positions: 4 + 6 = 10
- Difference: |6 - 10| = 4 (not divisible by 11)

2. **2153**:
- Odd positions: 2 + 5 = 7
- Even positions: 1 + 3 = 4
- Difference: |7 - 4| = 3 (not divisible by 11)

3. **1276**:
- Odd positions: 1 + 7 = 8
- Even positions: 2 + 6 = 8
- Difference: |8 - 8| = 0 (divisible by 11)

4. **1632**:
- Odd positions: 1 + 3 = 4
- Even positions: 6 + 2 = 8
- Difference: |4 - 8| = 4 (not divisible by 11)

### Step 3: Check divisibility by 7
To check if a number is divisible by 7, we can use the following method:
- Take the last digit, double it, subtract it from the rest of the number, and check if the result is divisible by 7.

#### Check the number that passed the 11 test (1276):
1. **1276**:
- Last digit: 6, double it: 12
- Remaining number: 127
- Subtract: 127 - 12 = 115
- Check 115:
- Last digit: 5, double it: 10
- Remaining number: 11
- Subtract: 11 - 10 = 1 (not divisible by 7)

### Conclusion
Since 1276 is divisible by 11 but not by 7, we need to check if any other number is divisible by both.

### Final Check
Since none of the other numbers passed the divisibility test for 11, we conclude that none of the provided numbers are divisible by both 7 and 11.

### Answer
None of the provided numbers are divisible by both 7 and 11.

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