If a binary operation * is defined by x * y = x + 2y, find 2 * (3 * 4)

Analysis

To solve this problem, we need to apply the rules of binary operations. A binary operation is simply a rule that tells you how to combine two numbers. Here, the rule is $x * y = x + 2y$. This means you take the first number ($x$) and add it to twice the second number ($y$).

Concept

When you see an expression with brackets like $2 * (3 * 4)$, you must follow the BODMAS rule. You must solve the operation inside the parentheses (brackets) first before proceeding to the outer operation.

Step-by-Step Solution

Step 1: Solve the operation inside the brackets $(3 * 4)$ Using the rule $x * y = x + 2y$:

• Here, $x = 3$ and $y = 4$.
• $3 * 4 = 3 + 2(4)$
• $3 * 4 = 3 + 8$
• $3 * 4 = 11$

Step 2: Substitute the result back into the original expression Now the expression $2 * (3 * 4)$ becomes $2 * 11$.

Step 3: Solve the final operation $2 * 11$ Using the same rule $x * y = x + 2y$:

• Here, $x = 2$ and $y = 11$.
• $2 * 11 = 2 + 2(11)$
• $2 * 11 = 2 + 22$
• $2 * 11 = 24$

Conclusion

Following the order of operations, we calculated the value inside the bracket first, then combined it with the remaining number to arrive at 24.

The correct option is A.

Exam Tip

In binary operation questions, always pay close attention to the order of the variables. If the formula was $x * y = 2x + y$, the answer would be different! Always write down your $x$ and $y$ values clearly before substituting them into the formula to avoid "sign" or "position" errors.