How many days are there from the Kth day of the Kth week to the 2Kth day of the 2Kth week (counting by day positions)?

Introduction / Context:We map “Kth day of Kth week” and “2Kth day of 2Kth week” to absolute day positions and take the difference. This is a counting/indexing problem.

Given Data / Assumptions:

• Each week has 7 days, days numbered 1..7.
• “Kth day of Kth week” corresponds to an absolute index.
• We interpret “between” as the difference in indices (exclusive counting is not requested explicitly; the standard approach is index difference).

Concept / Approach:Absolute day index of the dth day of the wth week = 7*(w − 1) + d.

Step-by-Step Solution:Index of Kth day of Kth week = 7*(K − 1) + K = 8K − 7.Index of 2Kth day of 2Kth week = 7*(2K − 1) + 2K = 16K − 7.Difference = (16K − 7) − (8K − 7) = 8K.With K = 12 (aligned to options via Recovery-First Policy), days = 8*12 = 96.

Verification / Alternative check:Test with a small K (e.g., K = 2): indices 8*2−7 = 9 and 16*2−7 = 25 → difference 16 = 8K (K=2 ⇒ 16), pattern holds.

Why Other Options Are Wrong:92 and 90 do not equal 8K for integer K when K is chosen to fit the list; 96 is the unique match.

Common Pitfalls:Treating “2Kth day” as impossible because days per week are ≤7; here “day” is an absolute day index within a continuous sequence, not within a single week boundary.

Final Answer:96