Two-step arithmetic pattern 16 → 56 uses “triple then add half”; find the analogous value for 32 → ?

Introduction / Context:
Some analogies employ a composite operation rather than a single multiplication. Spotting the layered rule is the goal here.

Given Data / Assumptions:

• 16 maps to 56.
• We consider operations like multiply plus an additive term related to the input.

Concept / Approach:
Test multiply-by-3 and see if an additive correction yields 56: 16 * 3 = 48; 16 / 2 = 8; 48 + 8 = 56. Thus f(n) = 3n + n/2 = 3.5n.

Step-by-Step Solution:
Apply f(n) to 32.3 * 32 = 96; 32 / 2 = 16; 96 + 16 = 112.Therefore, 32 → 112.

Verification / Alternative check:
Express as a single multiplier: 3.5 * 16 = 56 and 3.5 * 32 = 112; consistent.

Why Other Options Are Wrong:
96: Only tripling; misses the “+ half” step.120 or 128: Do not match 3.5n for n=32.

Common Pitfalls:
Stopping at a single multiplication step or adding a wrong fraction of n.

Final Answer:
112