In a certain coding rule, an expression of the form a % b is evaluated by using the digits of the numbers a and b. For example, 35 % 31 = 12 and 92 % 30 = 14. Using the same pattern, what is the value of 15 % 24 ?

Introduction / Context:
This problem uses a coding rule based on the digits of two numbers. The symbol % here does not represent the usual remainder operation; instead it stands for a special function defined by the examples. We are given two equations that show how 35 % 31 and 92 % 30 are evaluated and asked to apply the same pattern to 15 % 24. This type of question is common in logical reasoning sections and focuses on recognising patterns in digits rather than in the whole numbers themselves.

Given Data / Assumptions:

• 35 % 31 is equal to 12.
• 92 % 30 is equal to 14.
• The same coding rule is used in both examples.
• We are required to evaluate 15 % 24 according to that rule.
• Only the digits of the numbers, not their usual arithmetic relationship, are used to construct the result.

Concept / Approach:
When two digit numbers are involved, a common trick is to use the sum of digits, the difference of digits or some combination of these to produce a small result. Here, 35 % 31 gives 12, which is significantly smaller than either 35 or 31. We can check whether 12 arises from adding the sum of the digits of 35 to the sum of the digits of 31. Similarly, we can test the second example and see if the same rule holds. If it does, we can safely apply that digit sum rule to the new pair 15 and 24.

Step-by-Step Solution:
Step 1: For 35 % 31, compute the sum of digits of 35: 3 + 5 = 8. Step 2: Compute the sum of digits of 31: 3 + 1 = 4. Step 3: Add these two sums: 8 + 4 = 12, which matches the given result 35 % 31 = 12. Step 4: Now check the second example 92 % 30. Sum of digits of 92 is 9 + 2 = 11, and of 30 is 3 + 0 = 3. Step 5: Add these sums: 11 + 3 = 14, which exactly matches 92 % 30 = 14. Step 6: The pattern is therefore clear: a % b equals the sum of the digits of a plus the sum of the digits of b. Step 7: Apply this rule to 15 % 24. Sum of digits of 15 is 1 + 5 = 6. Step 8: Sum of digits of 24 is 2 + 4 = 6. Adding these sums gives 6 + 6 = 12.

Verification / Alternative check:
The discovered rule works perfectly for both examples and leads to a unique, simple value for the new expression. As an alternative check, we can briefly consider other possible rules, such as differences of digits or products, and see that they do not consistently produce 12 and 14 for the original pairs. Since the digit sum plus digit sum pattern is both simple and fully consistent, it is almost certainly the intended coding rule.

Why Other Options Are Wrong:
Option 25 could arise by adding 15 and 10, but there is no basis for that in the digit sums. Option 33 would require 15 and 18 as intermediate sums, which is not correct. Option 28 and option 18 similarly fail to match the rule where we simply add the sums of the digits. Each of these options is designed to attract test takers who either guess or apply an inconsistent pattern. Only 12 is fully justified by the given examples.

Common Pitfalls:
A typical mistake is to use the standard meaning of the symbol % and look for a remainder, which is not relevant here. Another error is to focus on operations such as 35 minus 31 or 92 minus 30 and then try to manipulate those differences to get the results, which does not yield a stable rule. Some students also miss that the pattern might involve separate sums of digits rather than the whole numbers. Always pay attention to how small the coded result is compared to the originals, as this often signals a digit based operation.

Final Answer:
Using the rule that a % b equals the sum of the digits of a plus the sum of the digits of b, the value of 15 % 24 is 12.