What will come in place of question mark(?) in given number series.
600 599 591 564 ? 375

Options

A. 500
B. 496
C. 490
D. 504

Answer

To solve the problem of finding the missing number in the series: 600, 599, 591, 564, ?, 375, we will analyze the differences between the numbers step by step.

### Step-by-Step Solution:

1. **Identify the Series**: The given series is 600, 599, 591, 564, ?, 375.

2. **Calculate the Differences**:
- From 600 to 599:
\[ 600 - 599 = 1 \]
- From 599 to 591:
\[ 599 - 591 = 8 \]
- From 591 to 564:
\[ 591 - 564 = 27 \]

3. **Observe the Pattern in Differences**:
- The differences we calculated are: 1, 8, and 27.
- Notice that these differences can be expressed as cubes:
- \(1 = 1^3\)
- \(8 = 2^3\)
- \(27 = 3^3\)

4. **Predict the Next Difference**:
- Following the pattern, the next difference should be \(4^3\):
\[ 4^3 = 64 \]

5. **Calculate the Missing Number**:
- Now, we subtract this difference from the last known number in the series (564):
\[ 564 - 64 = 500 \]

6. **Final Step**:
- The missing number in the series is 500.

7. **Check the Next Difference**:
- To ensure the pattern continues, we can check the next number:
- From 500 to 375:
\[ 500 - 375 = 125 \]
- \(125 = 5^3\), which confirms the pattern.

### Conclusion:
The missing number in the series is **500**.