A special symbol operation is defined using the following examples: 45 % 11 = 7 and 59 % 34 = 7. Based on the same pattern (using digit sums), what is the value of 55 % 4 = ?

Introduction / Context:This question tests pattern recognition in a custom operator. The symbol % here does not mean the usual remainder. Instead, it follows a rule that can be inferred from the given examples, typically involving digit sums or simple number properties.

Given Data / Assumptions:

• 45 % 11 = 7
• 59 % 34 = 7
• Find 55 % 4 using the same rule.
• Assume the rule is consistent across examples.

Concept / Approach:A common coding-decoding approach is to compare the inputs with the output and test simple operations like digit-sum difference. We verify the rule on both examples before applying it to the new case.

Step-by-Step Solution: Check 45 % 11 = 7. Digit sum of 45 = 4 + 5 = 9. Digit sum of 11 = 1 + 1 = 2. Difference = 9 - 2 = 7. Matches the result. Now verify with 59 % 34 = 7. Digit sum of 59 = 5 + 9 = 14. Digit sum of 34 = 3 + 4 = 7. Difference = 14 - 7 = 7. Matches again. So the rule is: a % b = (sum of digits of a) - (sum of digits of b). Now compute 55 % 4: Digit sum of 55 = 5 + 5 = 10. Digit sum of 4 = 4. Result = 10 - 4 = 6.

Verification / Alternative check:The rule is validated by both examples, so applying it to 55 and 4 is logically consistent. The computed result 6 fits the same operation pattern.

Why Other Options Are Wrong: 7: would imply no subtraction of digit sum for 4. 5: could come from taking 10 - 5 by mistake. 10: ignoring the second number completely. 4: using digit sum of only the first number incorrectly.

Common Pitfalls:Using the normal modulo meaning, subtracting the numbers directly (55 - 4), or taking digit product instead of digit sum are frequent errors.

Final Answer:6