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

Correct Option (1)

The operation '$ \oplus $' represents a two-step mathematical process. First, the sum of the three given numbers is calculated. Second, the digits of this sum are added together to yield the final result.

Applying this pattern to the provided examples:

• For $ 7 \oplus 9 \oplus 10 = 8 $: The sum is $ 7 + 9 + 10 = 26 $. The sum of its digits is $ 2 + 6 = 8 $.
• For $ 9 \oplus 11 \oplus 30 = 5 $: The sum is $ 9 + 11 + 30 = 50 $. The sum of its digits is $ 5 + 0 = 5 $.
• For $ 11 \oplus 17 \oplus 21 = 13 $: The sum is $ 11 + 17 + 21 = 49 $. The sum of its digits is $ 4 + 9 = 13 $.

Following this established pattern for $ 23 \oplus 4 \oplus 15 $:

1. Calculate the sum: $ 23 + 4 + 15 = 42 $.
2. Sum the digits of the result: $ 4 + 2 = 6 $.

Thus, the value of $ 23 \oplus 4 \oplus 15 $ is $ 6 $.

Incorrect Options:

Options 2 (8), 3 (13), and 4 (15) are incorrect. These values do not align with the consistent logical pattern derived from the given examples, which involves summing the numbers and then summing the digits of that total. The application of this pattern unequivocally leads to the value 6.