In the series 28, 30, 36, 48, ?, 98, 140, which number should replace the question mark to continue the pattern?

Introduction / Context:This number series grows in a way that suggests increasing differences rather than constant steps or simple multiplication. The question tests your ability to detect a pattern in the differences and how those differences change from one step to the next, which is a common reasoning skill in aptitude exams.

Given Data / Assumptions:- The series is: 28, 30, 36, 48, ?, 98, 140.- All terms are positive integers.- The differences between consecutive terms seem to grow according to a secondary pattern.

Concept / Approach:We start by computing the first-level differences between consecutive terms. Then, we examine how these differences themselves change. If these second-level changes follow a predictable structure, such as consecutive even numbers, we can extend the pattern to determine the missing first-level difference and hence the missing term in the series.

Step-by-Step Solution:- Compute consecutive differences: 30 - 28 = 2 36 - 30 = 6 48 - 36 = 12 ? - 48 = ? 98 - ? = ? 140 - 98 = 42- We know the first known differences are 2, 6, 12 and the last known is 42.- Observe that 2, 6, 12 can be seen as 2, 2 + 4, 2 + 4 + 6.- The sequence of differences between these differences is: 6 - 2 = 4, 12 - 6 = 6.- This suggests that the increments between differences are 4, 6, 8, 10, 12, etc.- So the next difference should be 12 + 8 = 20, then 20 + 10 = 30, and finally 30 + 12 = 42 matches the last gap.- Therefore the missing differences are 20 between 48 and the next term, and 30 between that term and 98.- Compute the missing term: 48 + 20 = 68, and 68 + 30 = 98 which matches the given series.

Verification / Alternative check:- The complete difference sequence becomes 2, 6, 12, 20, 30, 42.- Differences between these are 4, 6, 8, 10, 12: a neat pattern of consecutive even numbers.- Rebuilding the series using these differences gives exactly 28, 30, 36, 48, 68, 98, 140.

Why Other Options Are Wrong:- 65, 67, and 72 do not allow the differences to follow the 2, 6, 12, 20, 30, 42 pattern with second-level differences of 4, 6, 8, 10, 12.- Substituting any of these alternatives breaks the smooth progression in the differences and makes the later terms inconsistent.- Only 68 preserves the elegant double-layered pattern in the series.

Common Pitfalls:Some candidates stop after noticing that the differences are 2, 6, 12 and assume some arbitrary continuation like 18 or 24 without checking second-level differences. Others miscalculate one of the intermediate differences and miss the simple even-number progression. Always go one layer deeper if the first level differences themselves are not constant.

Final Answer:The number that should replace the question mark in the series is 68, so the correct option is 68.