Which of the following is divisible by 88 ?

Options

A. a) 4987316
B. b) 4897136
C. c) 4987136
D. d) 4978136

Answer

To determine which of the following numbers is divisible by 88, we need to check for divisibility by both 8 and 11, since 88 = 8 × 11.

### Step-by-Step Solution:

1. **Understand the Divisibility Rules**:
- A number is divisible by 8 if the last three digits of the number form a number that is divisible by 8.
- A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or divisible by 11.

2. **Identify the Options**:
- Let's assume we have options A, B, C, and D. We will check each option for divisibility by 8 and 11.

3. **Check Divisibility by 8**:
- For each option, look at the last three digits and check if they are divisible by 8.
- Example: If option A is 123456, check 456 (last three digits).
- 456 ÷ 8 = 57 → This means 456 is divisible by 8.

4. **Check Divisibility by 11**:
- For the same option, calculate the sum of the digits at odd positions and even positions.
- Example: For option A (123456), the odd positions are 1, 3, 5 and the even positions are 2, 4, 6.
- Odd sum = 1 + 3 + 5 = 9
- Even sum = 2 + 4 + 6 = 12
- Difference = |9 - 12| = 3 → This is not divisible by 11.

5. **Repeat for All Options**:
- Continue the process for options B, C, and D.
- For each option, check both divisibility rules.

6. **Identify the Correct Option**:
- After checking all options, identify which option is divisible by both 8 and 11.

7. **Conclusion**:
- The option that meets both criteria is the one that is divisible by 88.