Odd One Out — In 117–39, 164–41, 198–66, 213–71, three have the same quotient (first ÷ second). Identify the exception and justify.

Difficulty: Easy

Correct Answer: 164-41

Explanation:


Introduction / Context:
Number-pair classification commonly uses division to reveal a hidden constant quotient. Your goal is to find the one pair that breaks the uniform quotient rule.



Given Data / Assumptions:

  • Pairs: 117–39, 164–41, 198–66, 213–71.
  • Interpret each as (a, b) and compute a / b.


Concept / Approach:
If three quotients are equal and one is not, the latter is the odd one out.



Step-by-Step Solution:
117 / 39 = 3.198 / 66 = 3.213 / 71 = 3.164 / 41 = 4.Thus, three pairs share quotient 3; one pair yields quotient 4.



Verification / Alternative check:
Confirm by multiplication: 39*3 = 117; 66*3 = 198; 71*3 = 213; 41*3 = 123 ≠ 164 (indeed 41*4 = 164). This reconfirms the outlier.



Why Other Options Are Wrong:

  • 117–39: follows quotient 3.
  • 198–66: follows quotient 3.
  • 213–71: follows quotient 3.


Common Pitfalls:
Checking differences first does not isolate a single outlier (differences vary throughout). Division reveals the clean triad.



Final Answer:
164-41

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