Which of the following is not divisible by 11?

Options

A. 1331
B. 3333
C. 1111
D. 1010

Answer

To determine which of the given numbers is not divisible by 11, we will apply the divisibility rule for 11. The rule states that we need to find the difference between the sum of the digits at odd positions and the sum of the digits at even positions. If this difference is 0 or divisible by 11, then the number is divisible by 11.

Let's analyze each option step by step:

### Step 1: Check 1331
- **Odd positions:** 1 (1st position) + 3 (3rd position) = 1 + 3 = 4
- **Even positions:** 3 (2nd position) + 1 (4th position) = 3 + 1 = 4
- **Difference:** 4 - 4 = 0
- Since 0 is divisible by 11, **1331 is divisible by 11**.

### Step 2: Check 33313
- **Odd positions:** 3 (1st) + 3 (3rd) + 3 (5th) = 3 + 3 + 3 = 9
- **Even positions:** 3 (2nd) + 1 (4th) = 3 + 1 = 4
- **Difference:** 9 - 4 = 5
- Since 5 is not divisible by 11, **33313 is not divisible by 11**.

### Step 3: Check 1111
- **Odd positions:** 1 (1st) + 1 (3rd) = 1 + 1 = 2
- **Even positions:** 1 (2nd) + 1 (4th) = 1 + 1 = 2
- **Difference:** 2 - 2 = 0
- Since 0 is divisible by 11, **1111 is divisible by 11**.

### Step 4: Check 1010
- **Odd positions:** 1 (1st) + 1 (3rd) = 1 + 1 = 2
- **Even positions:** 0 (2nd) + 0 (4th) = 0 + 0 = 0
- **Difference:** 2 - 0 = 2
- Since 2 is not divisible by 11, **1010 is not divisible by 11**.

### Conclusion
From our analysis, the numbers that are not divisible by 11 are **33313** and **1010**. However, since the question asks for one option, we can conclude that **33313 is the first number that is not divisible by 11**.

### Final Answer
**33313 is not divisible by 11.**

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