In a certain numerical code, the operation "$" between two numbers is defined so that 5$125 = 25 and 12$48 = 4. Using the same rule, what is the value of 4$24?

Introduction / Context:
This numerical coding question defines a special operation "$" between two numbers. The expressions 5$125 and 12$48 do not represent usual arithmetic symbols but instead follow a specific relationship. You must detect the rule from the examples and then apply it to compute 4$24. Such problems are popular in reasoning tests because they reward pattern recognition and logical thinking.

Given Data / Assumptions:
- 5$125 = 25.
- 12$48 = 4.
- We need to find 4$24.
- The operation "$" is assumed to be consistent across these examples.

Concept / Approach:
We look for a simple relationship involving division or multiplication, since the results 25 and 4 are smaller than the second numbers 125 and 48. A natural guess is that the result could be the second number divided by the first number, or some variant of that idea. Once a candidate rule is identified, it must be checked against all given examples before using it to evaluate the new expression.

Step-by-Step Solution:
Step 1: For 5$125 = 25, notice that 125 ÷ 5 = 25, which matches the result. Step 2: For 12$48, compute 48 ÷ 12 = 4, which also matches the given result. Step 3: This suggests that a$b = b ÷ a for the "$" operation. Step 4: Apply this rule to 4$24. Here, a = 4 and b = 24. Step 5: Compute 24 ÷ 4 = 6.

Verification / Alternative check:
We can quickly check if any other simple rule might also work, such as a * b or b - a, but these do not produce 25 from 5 and 125 or 4 from 12 and 48. The division based rule b ÷ a is the only obvious and consistent one that fits both examples. Therefore we confidently apply it to 4 and 24 to get 6.

Why Other Options Are Wrong:
- Option 34 and option 35 are much larger than 24 and cannot be produced by dividing 24 by 4.
- Option 5 might be guessed by mistake using 24 ÷ 4 plus or minus 1, but such an adjustment would break the consistency with the original examples.

Common Pitfalls:
A common error is to try to use both numbers symmetrically, for example averaging them or multiplying them in some fashion, even though the smaller result strongly suggests division of the larger by the smaller. Another mistake is to test a rule on only one of the two examples and not on both, which can lead to an incorrect final answer.

Final Answer:
Using the rule a$b = b ÷ a, we obtain 4$24 = 24 ÷ 4 = 6.