What will come in place of question mark (?) in the given number series?
316 307 282 233 152 ?

Options

A. 35
B. 25
C. 31
D. 41

Answer

To solve the number series: 316, 307, 282, 233, 152, ?, we will analyze the pattern in the differences between the consecutive numbers.

### Step-by-Step Solution:

1. **Identify the first number and the next number in the series:**
- The first number is 316, and the second number is 307.

2. **Calculate the difference between the first two numbers:**
- 316 - 307 = 9

3. **Identify the second and third numbers in the series:**
- The second number is 307, and the third number is 282.

4. **Calculate the difference between the second and third numbers:**
- 307 - 282 = 25

5. **Identify the third and fourth numbers in the series:**
- The third number is 282, and the fourth number is 233.

6. **Calculate the difference between the third and fourth numbers:**
- 282 - 233 = 49

7. **Identify the fourth and fifth numbers in the series:**
- The fourth number is 233, and the fifth number is 152.

8. **Calculate the difference between the fourth and fifth numbers:**
- 233 - 152 = 81

9. **List the differences we have calculated:**
- The differences are: 9, 25, 49, 81.

10. **Observe the pattern in the differences:**
- The differences are:
- 9 = 3²
- 25 = 5²
- 49 = 7²
- 81 = 9²
- The pattern shows that we are subtracting the squares of consecutive odd numbers: 3, 5, 7, 9.

11. **Determine the next odd number after 9:**
- The next odd number is 11.

12. **Calculate the square of 11:**
- 11² = 121.

13. **Subtract this value from the last number in the series:**
- 152 - 121 = 31.

14. **Conclusion:**
- The number that will come in place of the question mark (?) is **31**.

### Final Answer:
31