If 7 ⊕ 9 ⊕ 10 = 8 , 9 ⊕ 11 ⊕ 30 = 5 , 11 ⊕ 17 ⊕ 21 = 13 , what is the value of 23 ⊕ 4 ⊕ 15 ?

The problem defines a new operation 'oplus'. We need to find the rule for this operation based on the given examples. Let's analyze the given statements: 1. 7 oplus 9 oplus 10 = 8 2. 9 oplus 11 oplus 30 = 5 3. 11 oplus 17 oplus 21 = 13 Let's test the rule: The result of 'oplus' operation is the sum of the digits of the sum of the numbers. Let S(N) denote the sum of digits of N. So, a oplus b oplus c = S(a + b + c). Let's verify this rule with the given examples: 1. 7 oplus 9 oplus 10: Sum of numbers = 7 + 9 + 10 = 26. Sum of digits of the sum = S(26) = 2 + 6 = 8. (Matches the given result) 2. 9 oplus 11 oplus 30: Sum of numbers = 9 + 11 + 30 = 50. Sum of digits of the sum = S(50) = 5 + 0 = 5. (Matches the given result) 3. 11 oplus 17 oplus 21: Sum of numbers = 11 + 17 + 21 = 49. Sum of digits of the sum = S(49) = 4 + 9 = 13. (Matches the given result) The rule is consistent across all three examples. Now, apply this rule to find the value of 23 oplus 4 oplus 15: 1. Sum of numbers = 23 + 4 + 15 = 42. 2. Sum of digits of the sum = S(42) = 4 + 2 = 6. Therefore, 23 oplus 4 oplus 15 = 6. Comparing this with the given options: A) 6 - This matches our calculated value. B) 8 - Incorrect. C) 13 - Incorrect. D) 15 - Incorrect. The final answer is A. The final answer is $\boxed{\text{6}}$