Seven number set: The sum of seven numbers is 235. The average of the first three is 23 and that of the last three is 42. Find the fourth number.

Introduction / Context:
This is a partition of totals problem where we remove the known blocks to get the central term.

Given Data / Assumptions:

• Total of seven = 235
• First three average = 23
• Last three average = 42

Concept / Approach:
Compute sums of the first and last triplets, subtract from the grand total to obtain the middle (fourth) element.

Step-by-Step Solution:

Verification / Alternative check:
Recompose totals to confirm the grand total remains 235.

Why Other Options Are Wrong:

• 126 and 195 are component sums, not the standalone fourth value.
• 69 is the first triplet sum, not the fourth element.

Common Pitfalls:
Mixing sums with single values or forgetting there are seven numbers in total.

Final Answer: