What will come in place of question mark (?) in the following series questions?
31,33,36,?,48,59

Options

A. A)38
B. B)37
C. C)48
D. D)41

Answer

To solve the series: 31, 33, 36, ?, 48, 59, we need to identify the pattern in the differences between the numbers.

### Step-by-Step Solution:

1. **Identify the terms in the series:**
- The series is: 31, 33, 36, ?, 48, 59.

2. **Calculate the differences between consecutive terms:**
- From 31 to 33:
\[ 33 - 31 = 2 \]
- From 33 to 36:
\[ 36 - 33 = 3 \]
- From 36 to ?:
\[ ? - 36 = x \quad (\text{we will find } x) \]
- From ? to 48:
\[ 48 - ? = y \quad (\text{we will find } y) \]
- From 48 to 59:
\[ 59 - 48 = 11 \]

3. **List the differences we know:**
- The differences we have so far are: 2, 3, x, y, 11.

4. **Look for a pattern in the differences:**
- The first two differences are 2 and 3.
- The next difference (x) could be a prime number.
- The difference from 48 to 59 is 11, which is also a prime number.

5. **Assuming the differences are prime numbers:**
- The prime numbers in order are: 2, 3, 5, 7, 11.
- We have already used 2 and 3, so the next prime number after 3 is 5.

6. **Calculate the missing term using the difference of 5:**
- If we add 5 to 36:
\[ 36 + 5 = 41 \]
- Thus, the missing term (?) is 41.

7. **Verify the next difference:**
- Now, we check the difference from 41 to 48:
\[ 48 - 41 = 7 \]
- 7 is also a prime number, which fits our pattern.

8. **Final confirmation:**
- The complete differences are: 2, 3, 5, 7, 11, which are all prime numbers.

Thus, the missing term in the series is **41**.