In a number code, the expression 9 x 3 is equal to 3, 15 x 3 is equal to 5 and 60 x 5 is equal to 12. Using the same coding rule, what is the value of 27 x 3?

Introduction / Context:
This coding and decoding question involves a simple relationship between two numbers. The expressions 9 x 3, 15 x 3 and 60 x 5 do not mean ordinary multiplication. Instead, each expression is converted to a smaller number according to a straightforward pattern. We must detect that pattern and apply it to compute the value of 27 x 3.

Given Data / Assumptions:

• 9 x 3 is coded as 3.
• 15 x 3 is coded as 5.
• 60 x 5 is coded as 12.
• We must find the coded value of 27 x 3.
• The symbol x denotes a special operation defined by the pattern, not standard multiplication.

Concept / Approach:
Given that the coded results are smaller and that each pair involves a larger first number and a smaller second number, division is a natural operation to test. We check whether the result corresponds to the first number divided by the second number for all examples. If it does, we then apply this rule to the new pair 27 and 3.

Step-by-Step Solution:
Step 1: Consider 9 x 3 = 3. If we treat x as division, 9 ÷ 3 = 3, which matches the coded result.Step 2: Check the second example with the same rule. For 15 x 3, compute 15 ÷ 3 = 5. This matches the coded value 5.Step 3: Check the third example. For 60 x 5, compute 60 ÷ 5 = 12. This matches the coded value 12.Step 4: Since all three given equations fit the rule result = first number divided by second number, we can accept this as the coding pattern.Step 5: Apply the rule to 27 x 3. Compute 27 ÷ 3.Step 6: The division 27 ÷ 3 = 9.Step 7: Therefore, the coded value of 27 x 3 is 9.

Verification / Alternative check:
To verify, note that any alternative pattern that does not rely on simple division would struggle to fit all three given examples simultaneously. Recomputing each division confirms that 9 ÷ 3 is 3, 15 ÷ 3 is 5 and 60 ÷ 5 is 12, making division the natural and consistent rule. Applying it to 27 and 3 again gives 9, confirming the answer.

Why Other Options Are Wrong:
The option 30 might arise if someone multiplies instead of divides, computing 9 × 3 or 15 × 3. The options 3 and 6 represent incorrect divisions or partial reasoning applied inconsistently. The option 12 is the result for 60 x 5 in the pattern, not for 27 x 3. None of these values are equal to 27 ÷ 3, so they do not satisfy the discovered rule.

Common Pitfalls:
Some students try to invent a more complicated relationship involving both numbers when a simple division pattern already explains all examples. Others may mistakenly invert the division or confuse which number should be the numerator. Always start by testing the simplest operations like addition, subtraction, multiplication and division before assuming a more complex rule.

Final Answer:
According to the discovered coding rule, the value of 27 x 3 is 9.