582, 294, 150, 78, 414, 24, 15

Options

A. 414
B. 582
C. 294
D. 150

Explanation

To find the odd one out in the series: 582, 294, 150, 78, 414, 24, 15, we will analyze the pattern in the series step by step.

### Step-by-Step Solution:

1. **Identify the first number**: The first number in the series is 582.

2. **Divide by 2 and add 3**:
- Calculate \( \frac{582}{2} = 291 \)
- Now add 3: \( 291 + 3 = 294 \)
- So, the next number is 294, which is correct.

3. **Continue with the next number (294)**:
- Divide 294 by 2: \( \frac{294}{2} = 147 \)
- Add 3: \( 147 + 3 = 150 \)
- The next number is 150, which is correct.

4. **Next number (150)**:
- Divide 150 by 2: \( \frac{150}{2} = 75 \)
- Add 3: \( 75 + 3 = 78 \)
- The next number is 78, which is correct.

5. **Next number (78)**:
- Divide 78 by 2: \( \frac{78}{2} = 39 \)
- Add 3: \( 39 + 3 = 42 \)
- Here, we expect the next number to be 42, but the series has 414 instead.

6. **Next number (414)**:
- If we were to follow the pattern, we should have had 42 instead of 414. Thus, 414 does not fit the pattern.

7. **Next number (24)**:
- If we continue with 42 (the correct number), divide by 2: \( \frac{42}{2} = 21 \)
- Add 3: \( 21 + 3 = 24 \)
- The next number is 24, which is correct.

8. **Final number (15)**:
- Divide 24 by 2: \( \frac{24}{2} = 12 \)
- Add 3: \( 12 + 3 = 15 \)
- The final number is 15, which is correct.

### Conclusion:
The odd one out in the series is **414** because it does not follow the established pattern of dividing the previous number by 2 and adding 3.