If $*$ means adding $6$ times the second number to the first number, then $(1 * 2) * 3$ equals

### Concept & Formula This question tests logical operators, where an arbitrary symbol is defined as a specific mathematical sequence. You must strictly follow the order of operations (BODMAS), computing inner brackets first. ### Step-by-Step Solution * **Given:** * The operator rule: $x * y = x + 6y$ * The expression to evaluate: $(1 * 2) * 3$ * **Calculation / Deduction:** 1. Evaluate the expression inside the parentheses first: $(1 * 2)$. Here, first number $= 1$, second number $= 2$. $$1 * 2 = 1 + 6(2) = 1 + 12 = 13$$ 2. Substitute the result back into the original expression: $(1 * 2) * 3$ becomes $13 * 3$. 3. Apply the operator rule again to $13 * 3$. Here, first number $= 13$, second number $= 3$. $$13 * 3 = 13 + 6(3) = 13 + 18 = 31$$ ### Exam Strategy & Shortcut Simply write the operations explicitly as algebraic substitutions: $(1 + 6 \times 2) + 6 \times 3 = 13 + 18 = 31$. It is a straightforward calculation that requires no special tricks, just careful attention to not mix up the "first" and "second" numbers. ### Common Pitfall A frequent mistake is ignoring the parentheses and attempting to evaluate $2 * 3$ first, or misapplying the rule by adding $6$ times the *first* number to the second, which would completely change the outcome. ### Final Answer Therefore, the correct answer is 31.