Find the pattern: If 264 * 2 = 6 and 870 * 3 = 11, then what is 735 * 5?

Introduction / Context:
This is a rule-finding puzzle. An unusual operator “*” is defined implicitly by examples. We must infer the hidden rule from two instances and apply it to a third.

Given Data / Assumptions:

• 264 * 2 = 6.
• 870 * 3 = 11.
• We need 735 * 5 = ?.

Concept / Approach:
Try simple digit operations combined with the second operand: dividing the first number by the second and summing the digits of the quotient fits both given examples.

Step-by-Step Solution:

Verification / Alternative check:
Alternative hypotheses (sum of digits plus/minus the second operand, product of digits, etc.) fail to satisfy both given examples, whereas the “divide then digit-sum” rule works consistently.

Why Other Options Are Wrong:
05, 03, or 16 do not match the consistent rule validated by both provided instances.

Common Pitfalls:
Jumping to ad-hoc rules that fit only one of the examples. Always verify against all given calibrators before applying to the target case.

Final Answer:
12.