In the following question, select the missing number from the given series: 57, 69, 81, 93, ?, 117

Introduction / Context:
This problem is based on a simple arithmetic series with a constant positive difference. Each term increases by the same amount. The series is 57, 69, 81, 93, ?, 117, and we are required to identify the missing number that keeps the increments uniform.

Given Data / Assumptions:
- Series: 57, 69, 81, 93, ?, 117.- The fifth term is missing.- The sequence increases steadily.- The simplest and most likely pattern is addition of a fixed number at each step.

Concept / Approach:
We calculate the differences between consecutive known terms. If the difference is the same between several pairs, we can assume an arithmetic progression and apply that difference to find the missing term. This is among the most basic types of series used in reasoning tests.

Step-by-Step Solution:
- From 57 to 69: 69 - 57 = 12.- From 69 to 81: 81 - 69 = 12.- From 81 to 93: 93 - 81 = 12.- Thus, the common difference is +12.- To find the next term after 93, add 12: 93 + 12 = 105.- Check the final term: 105 + 12 = 117, which matches the series.

Verification / Alternative check:
- With 105 added, the complete sequence is 57, 69, 81, 93, 105, 117.- Each transition adds exactly 12, confirming an arithmetic progression.- No alternative value maintains this constant difference throughout.

Why Other Options Are Wrong:
- 104, 111, 108 and 99 lead to differences that are not all equal to 12.- For example, if 108 were chosen, then 108 - 93 = 15 and 117 - 108 = 9, breaking the constant step pattern.

Common Pitfalls:
- Some candidates fail to check all steps and may select a value that fits one gap but not the entire series.- Miscalculations in adding 12 can lead to incorrect answers such as 104 or 108.- Overcomplicating an obviously linear series with higher order reasoning is unnecessary and time consuming.

Final Answer:
The series is an arithmetic progression with common difference 12, so the missing term is 105.