Classification – Odd one out (ratio pairs): Choose the pair that breaks the constant division rule: 704, 11 • 256, 4 • 832, 13 • 310, 5.

Difficulty: Easy

Correct Answer: 310, 5

Explanation:


Introduction / Context:
Ordered-number pairs often encode a constant ratio: first divided by second equals a fixed constant across most options. Identifying that constant immediately exposes the lone mismatched pair.


Given Data / Assumptions:

  • Pairs: (704, 11), (256, 4), (832, 13), (310, 5).
  • Try exact integer ratios first; avoid rounding.


Concept / Approach:
Compute first/second for each pair. If three ratios match exactly at the same value and one does not, the nonmatching pair is the odd one out.


Step-by-Step Solution:
704 / 11 = 64 (exact since 64 * 11 = 704).256 / 4 = 64 (since 64 * 4 = 256).832 / 13 = 64 (since 64 * 13 = 832).310 / 5 = 62 (since 62 * 5 = 310), not 64.


Verification / Alternative check:
Express each first value as 64 * second value; the first three satisfy this identity, whereas 310 = 62 * 5 fails. No other simple common ratio fits all four simultaneously.


Why Other Options Are Wrong:

  • (704, 11), (256, 4), (832, 13) maintain the invariant first = 64 * second.


Common Pitfalls:
Rounding 310/5 up to 64 is incorrect; classification problems expect exact relationships, not approximations.


Final Answer:
310, 5

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