Introduction / Context:
Series based on subtracting consecutive odd numbers are common. One incorrect value breaks the flow. We will verify whether each step subtracts 1, 3, 5, 7, 9, 11, etc.
Given Data / Assumptions:
- Series: 52, 51, 48, 43, 34, 27, 16
- Only one value is inconsistent.
Concept / Approach:
Check differences and compare to the intended odd sequence: 1, 3, 5, 7, 9, 11… If a difference does not match, the corresponding term is the problem.
Step-by-Step Solution:
51 − 52 = −1 (subtract 1)48 − 51 = −3 (subtract 3)43 − 48 = −5 (subtract 5)34 − 43 = −9 (should be −7 here)27 − 34 = −7 (this −7 arrives one step late)16 − 27 = −11 (correct for the sixth step if previous were in order)Therefore, the correct fifth term should be 43 − 7 = 36, not 34. So 34 is the outlier.
Verification / Alternative check:
Corrected series: 52, 51, 48, 43, 36, 27, 16 with differences −1, −3, −5, −7, −9, −11.
Why Other Options Are Wrong:
27, 43, and 48 are compatible with the proper odd-number subtraction pattern.
Common Pitfalls:
Misreading negative differences; always align the odd-number sequence to the correct step index.
Final Answer:
34
Discussion & Comments