What should come in place of question mark (?) in the following number series.
32 ? 52 88 152 252

Options

A. 36
B. 30
C. 35
D. 32

Answer

To solve the number series: 32, ?, 52, 88, 152, 252, we need to identify the pattern in the differences between the numbers.

### Step-by-Step Solution:

1. **Identify the Known Values**:
The series is: 32, ?, 52, 88, 152, 252.

2. **Calculate the Differences**:
We will find the differences between the consecutive numbers in the series:
- Difference between 52 and 88: \( 88 - 52 = 36 \)
- Difference between 88 and 152: \( 152 - 88 = 64 \)
- Difference between 152 and 252: \( 252 - 152 = 100 \)

Now we have the differences:
- \( ? - 32 \)
- \( 52 - ? \)
- 36, 64, 100

3. **Analyze the Differences**:
The differences we found are:
- 36 (which is \( 6^2 \))
- 64 (which is \( 8^2 \))
- 100 (which is \( 10^2 \))

The differences appear to be the squares of even numbers:
- \( 6^2 = 36 \)
- \( 8^2 = 64 \)
- \( 10^2 = 100 \)

The pattern suggests that the difference before 36 should be \( 4^2 = 16 \).

4. **Calculate the Missing Value**:
Now we can find the missing number:
- From the first difference: \( ? - 32 = 16 \)
- Therefore, \( ? = 32 + 16 = 48 \)

5. **Verify with the Next Difference**:
To confirm, we can check the next difference:
- From the second difference: \( 52 - ? = 36 \)
- Thus, \( 52 - 48 = 4 \) (which is \( 4^2 \)).

This confirms our calculations.

### Final Answer:
The value that should come in place of the question mark (?) is **48**.