In a certain numerical code, the symbol "%" represents a special operation between two numbers. It is given that 3 % 2 = 50 and 2 % 4 = 60. Using the same rule, what is the value of 5 % 4?

Introduction:
This question defines a custom operation using the "%" symbol, distinct from its usual use in percentages. Two sample equations involving small integers are provided, and we must deduce the common rule that produces results 50 and 60. After discovering this rule, we apply it to the new pair 5 and 4 to find the value of 5 % 4. It is a simple arithmetic pattern recognition exercise.

Given Data / Assumptions:
The code gives the following:
1) 3 % 2 = 50
2) 2 % 4 = 60
We need to determine 5 % 4. We assume:
1) The same operation % is applied consistently in all three cases.
2) The outputs are closely related to basic combinations of the two input numbers, probably through sums or products scaled by a constant.

Concept / Approach:
Since the answer values 50 and 60 end in zero, it is natural to suspect that the underlying operation involves multiplication by 10. We test whether taking the sum of the two numbers and multiplying by 10 matches the results in both examples. If this rule fits all given cases, we then use it directly to compute the new value.

Step-by-Step Solution:
Step 1: For 3 % 2, test the sum based rule: compute (3 + 2) * 10.Step 2: The sum 3 + 2 is 5, and 5 * 10 = 50, which matches the given value exactly.Step 3: For 2 % 4, compute (2 + 4) * 10.Step 4: The sum 2 + 4 is 6, and 6 * 10 = 60, again matching the given value.Step 5: Since the formula (a + b) * 10 explains both examples, we adopt it as the definition of a % b.Step 6: Apply this formula to 5 % 4: compute (5 + 4) * 10.Step 7: The sum 5 + 4 is 9, and 9 * 10 = 90.Step 8: Therefore, the value of 5 % 4 is 90.

Verification / Alternative check:
Check that no simpler common rule fits both examples. The plain sum gives 5 and 6, not 50 and 60. The product, 3 * 2 = 6 and 2 * 4 = 8, also does not match. Only the scaled sum formula (a + b) * 10 explains both given equations. Hence, the derived rule is consistent and appropriate.

Why Other Options Are Wrong:
The values 16, 9, 20, and 45 appear unrelated to the pattern used in the examples. They might arise by squaring, simple addition, or partial multiplication, but none of those schemes produce both 50 and 60 from the first two pairs. Therefore, they cannot be correct if we insist on a single consistent operation definition.

Common Pitfalls:
Students may focus on more complicated operations such as squares or cubes without first trying simple linear relationships involving sums and constants. Another common mistake is to find a rule that works for one example but fails to validate against the second. Always ensure that all given samples fit the same formula before answering.

Final Answer:
According to the pattern, the value of 5 % 4 is 90.