Classification (number pairs – linear rule): In three pairs the second value follows y = 4x + 2; one pair violates this rule. Identify the odd pair.

Difficulty: Easy

Correct Answer: 9 : 40

Explanation:


Introduction / Context:
Classification problems with ordered pairs frequently hide a simple arithmetic mapping between the first and second numbers. Recognizing a linear relation saves time. In this set, most pairs satisfy the function y = 4x + 2. Your task is to identify the pair that does not satisfy this mapping, indicating a deliberate distractor placed to test attention to detail rather than computational complexity.



Given Data / Assumptions:

  • Pairs to test: (6, 26), (11, 46), (9, 40), (16, 66).
  • Candidate rule: y = 4x + 2.
  • Compute for each x and compare to the listed y.


Concept / Approach:
Apply the same function to every first element. If three pairs match exactly and one does not, the non-matching pair is the odd one out. Linear rules are common because they are easy to compute mentally yet still discriminate careful solvers.



Step-by-Step Solution:

For x = 6: y = 4*6 + 2 = 24 + 2 = 26 → matches (6, 26).For x = 11: y = 4*11 + 2 = 44 + 2 = 46 → matches (11, 46).For x = 16: y = 4*16 + 2 = 64 + 2 = 66 → matches (16, 66).For x = 9: y should be 4*9 + 2 = 36 + 2 = 38, but the given pair states 40. This pair breaks the rule.


Verification / Alternative check:
Check for off-by-two or typographical error possibilities. Even if 40 appears close to 38, classification requires exact adherence; therefore the pair remains the outlier.



Why Other Options Are Wrong:

(6, 26), (11, 46), and (16, 66) satisfy y = 4x + 2 precisely.


Common Pitfalls:
Assuming a different pattern (for example, 5x - something). Test the simplest consistent rule first; if it fits three of four perfectly, it is almost certainly the intended mapping.



Final Answer:
9 : 40

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