Introduction / Context:
Number series and odd-one-out reasoning problems test your ability to detect hidden arithmetic patterns. In this sequence, exactly one term is inconsistent with a simple rule. The task is to find and justify which number violates the rule.
Given Data / Assumptions:
- Series shown: 582, 605, 588, 611, 634, 617, 600
- Exactly one term is incorrect (odd one out).
- Options to choose from: 634, 611, 605, 600
Concept / Approach:
Check first-order differences to uncover a repeating increment/decrement pattern. Many series use alternating additions and subtractions with fixed steps. If a single term breaks that pattern, it is the outlier.
Step-by-Step Solution:
Compute consecutive differences:605 − 582 = +23588 − 605 = −17611 − 588 = +23634 − 611 = +23617 − 634 = −17600 − 617 = −17A clean alternating pattern would be: +23, −17, +23, −17, +23, −17.Up to the fourth step the result should be: 582 → 605 (+23), 605 → 588 (−17), 588 → 611 (+23), 611 → 594 (−17 expected), then 594 → 617 (+23), 617 → 600 (−17).But the given fourth term is 634 instead of the expected 594. This breaks the alternating pattern.
Verification / Alternative check:
Reconstruct the intended series using +23/−17 alternation: 582, 605, 588, 611, 594, 617, 600.Only 634 fails to fit this corrected list.
Why Other Options Are Wrong:
611: Fits as 588 + 23.605: Fits as 582 + 23.600: Fits as 617 − 17.
Common Pitfalls:
Stopping after inspecting only a few differences, or assuming constant differences rather than an alternating pattern.
Final Answer:
634
Discussion & Comments