Arithmetic progression of subtractions — detect the misfit Find the odd one out: 105, 85, 60, 30, 0, -45, -90.

Introduction / Context:
Here, the numbers are decreasing by successively larger amounts. When such a pattern is regular, any single deviation indicates the odd term. We will reconstruct the intended subtraction pattern and identify which listed number violates it.

Given Data / Assumptions:

• List: 105, 85, 60, 30, 0, -45, -90.
• We suspect a steadily increasing subtraction (by fixed steps).

Concept / Approach:
Compute consecutive differences to see if they follow a simple sequence such as −20, −25, −30, −35, −40, −45. If the given list fails one of these expected transitions, the result at that point is the misfit.

Step-by-Step Solution:
105 → 85: −20.85 → 60: −25.60 → 30: −30.Expect next: 30 − 35 = −5 (if continuing −35), but the list shows 0.Continuing the expected pattern: −5 − 40 = −45; then −45 − 45 = −90.Thus the only inconsistent value is 0; it should have been −5 for a smooth −20, −25, −30, −35, −40, −45 scheme.

Verification / Alternative check:
Look at the tail end: from −45 to −90 is a −45 step, consistent with the intended increment in subtractions. The discrepancy occurs solely at the 30 → 0 transition where −35 is expected.

Why Other Options Are Wrong:
85, 60, 30, and −45 each aligns with the expected stepped subtractions around them; only the zero breaks the run.

Common Pitfalls:
Assuming all differences must be equal; here they grow by 5 each time. Missing that nuance can hide the odd term in plain sight.

Final Answer:
0