Classification (number pairs – powers): Three pairs follow the pattern second number = first number^3; one pair violates this cube relation. Identify the odd pair.

Difficulty: Easy

Correct Answer: 4-32

Explanation:


Introduction / Context:
Numeric classification often uses exponent relations, such as squares and cubes. In this set, the intended relation is second = first^3. Identifying the pair that breaks this rule requires quick recognition of small powers and comfort with mental arithmetic under time pressure.



Given Data / Assumptions:

  • Pairs: 2-8, 3-27, 4-32, 5-125.
  • We interpret the dash as an ordered pair (a, b) and test whether b = a^3.
  • Recall cubes: 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125.


Concept / Approach:
Compute cubes of 2, 3, 4, and 5. Compare against the second number of each pair. Any mismatch identifies the odd pair. This is a straightforward recognition task that benefits from memorizing cubes up to at least 10 for speed.



Step-by-Step Solution:

2-8 → 2^3 = 8 (fits).3-27 → 3^3 = 27 (fits).4-32 → 4^3 = 64 (does not match 32; 32 equals 2^5).5-125 → 5^3 = 125 (fits).


Verification / Alternative check:
Note that 32 is a power of 2 (2^5), which can distract solvers who lean on recognition of common powers without checking the base. Confirm by direct multiplication for 4^3: 4*4*4 = 16*4 = 64.



Why Other Options Are Wrong:

2-8 follows the cube rule.3-27 follows the cube rule.5-125 follows the cube rule.


Common Pitfalls:
Confusing powers of 2 with cubes of other integers. Always compute the exact power relation defined by the pattern rather than relying on familiarity with a single number like 32.



Final Answer:
4-32

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