Find the odd number out in the pattern: 582, 605, 588, 611, 634, 617, 600.

Introduction / Context:
Many numeric sequences alternate between two fixed increments. Testing a simple +a, −b pattern often resolves such sets. Here, adding 23 and subtracting 17 alternately fits all but one term.

Given Data / Assumptions:

• Start at 582
• Hypothesis: +23, −17, +23, −17, …

Concept / Approach:
Apply the alternating operations consecutively and compare the expected list with the given list. The mismatch pinpoints the odd term.

Step-by-Step Solution:
582 + 23 = 605 ✔605 − 17 = 588 ✔588 + 23 = 611 ✔611 − 17 = 594 (but the list shows 634) ✖Continuing the pattern from the correct 594: +23 ⇒ 617 ✔; −17 ⇒ 600 ✔

Verification / Alternative check:
Reconstructing the intended sequence yields: 582, 605, 588, 611, 594, 617, 600. Only 634 breaks the pattern, while all other terms align neatly when 594 is used in its place.

Why Other Options Are Wrong:
611/605/600 conform to the alternating +23/−17 rule; 634 does not and is therefore the odd entry.

Common Pitfalls:
Trying non-alternating progressions or varying step sizes, which complicates rather than clarifies the structure; overlooking that two neighbors can validate the intended steps.

Final Answer:
634