Number series – find the wrong term (identify the outlier). Sequence: 25, 36, 49, 81, 121, 169, 225
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A36
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B49
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C121
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D169
Answer
Correct Answer: 36
Explanation
Introduction / Context:This series contains perfect squares. The task is to identify which square does not belong to the intended pattern once the underlying rule is recognized.
Given Data / Assumptions:
- Squares listed: 25, 36, 49, 81, 121, 169, 225
- Only one term is wrong with respect to the intended sequence logic.
Concept / Approach:Note that 25 = 5^2, 49 = 7^2, 81 = 9^2, 121 = 11^2, 169 = 13^2, 225 = 15^2. These are consecutive odd squares starting at 5^2, except one even square appears in the list.
Step-by-Step Solution:
Identify the intended pattern: squares of odd integers from 5 upward.List intended terms: 5^2 = 25, 7^2 = 49, 9^2 = 81, 11^2 = 121, 13^2 = 169, 15^2 = 225.Compare with the given sequence and spot 36 = 6^2, which is an even square breaking the odd-only pattern.Verification / Alternative check:Remove 36 and the remaining sequence consists entirely of odd squares in ascending order. No other term violates that rule.
Why Other Options Are Wrong:
- 49, 121, 169: Each is a square of an odd integer and thus fits the intended pattern.
Common Pitfalls:Assuming the series is simply all consecutive squares. The presence of 36 can mislead; look for a deeper consistency such as only odd squares.
Final Answer:36