(32, 24, 8) — Select the optioned triple that follows the same structural rule as the given triple.

Introduction / Context:
Number-triple analogies frequently encode a structural relation among the three numbers. For (32, 24, 8), observe that 8 is the greatest common divisor (gcd) of 32 and 24. The task is to find the optioned triple where the third number equals gcd(first, second).

Given Data / Assumptions:

• gcd(32, 24) = 8 matches the third element.
• We seek the option whose third element equals the gcd of the first two.

Concept / Approach:
Test each candidate quickly: gcd(26, 32) = 2 (≠ 42); gcd(34, 24) = 2 (≠ 14); gcd(24, 16) = 8 (matches 8); gcd(42, 34) = 2 (≠ 16). Only option (24, 16, 8) preserves the same structural rule.

Step-by-Step Solution:
1) Hypothesize the rule “third = gcd(first, second).”2) Compute gcd for each option.3) Select the triple where the equality holds: (24, 16, 8).

Verification / Alternative check:
Alternative simple rules (e.g., arithmetic differences) do not align across all options; the gcd pattern uniquely identifies the correct triple.

Why Other Options Are Wrong:

• (26, 32, 42), (34, 24, 14), (42, 34, 16): their third terms do not equal the gcd of the first two numbers.

Common Pitfalls:
Testing only arithmetic differences and overlooking gcd/lcm structural relations.

Final Answer:
(24, 16, 8 )