Find the odd set: In each triple (a, b, c), the largest number should equal the sum of the other two (largest = sum of smaller two). Identify the set that does NOT follow this rule.
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A2, 15, 13
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B7, 12, 4
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C4, 15, 11
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D6, 18, 12
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ENone of these
Answer
Correct Answer: 7, 12, 4
Explanation
Introduction / Context:This classification problem uses an additive relation inside triples. The rule: in each triple, the largest member must equal the sum of the other two. One triple fails to meet this requirement; that is the odd set you must identify.
Given Data / Assumptions:
- Triples: (2, 15, 13), (7, 12, 4), (4, 15, 11), (6, 18, 12).
- Assume standard integer arithmetic.
Concept / Approach:For each triple, sort or mentally identify the largest value, then verify largest = sum of the other two. If equality fails, that triple is the odd one out.
Step-by-Step Solution:
(2, 15, 13): largest 15; 2 + 13 = 15 → fits.(7, 12, 4): largest 12; 7 + 4 = 11 ≠ 12 → fails.(4, 15, 11): largest 15; 4 + 11 = 15 → fits.(6, 18, 12): largest 18; 6 + 12 = 18 → fits.Verification / Alternative check:Re-express as largest − (sum of others) should equal 0. Only the second triple yields 12 − (7 + 4) = 1 ≠ 0, confirming the violation.
Why Other Options Are Wrong:They satisfied the additive identity exactly and thus are not the odd item.
Common Pitfalls:Picking the wrong largest element or mis-adding small numbers under time pressure. Always identify the maximum first, then add carefully.
Final Answer:7, 12, 4 is the odd set.