Find the Missing Digits in 3?8?: Divisible by 9 Challenge

Complete the number so that it is divisible by 9 without a remainder:

$3?8?$

To determine the digits needed in the number $3?8?$ so that it is divisible by 9, follow these steps:

• Step 1: According to the divisibility rule for 9, the sum of the digits in the number must be divisible by 9.
• Step 2: Compute the sum of known digits: $3 + 8 = 11$.
• Step 3: Let the unknown digits be represented by $x$ and $y$. The sum of all digits will be $11 + x + y$.
• Step 4: For the number to be divisible by 9, $11 + x + y$ must be a multiple of 9.
• Step 5: Determine possible values for $x$ and $y$ so that the sum is as follows: 11 + x + y = 18 (next multiple of 9 after 11).
• Step 6: Doing the arithmetic, we require $x + y = 7$.
• Step 7: Examine the possible digit combinations for $x$ and $y$ that sum to 7:
  - $(x, y) = (0, 7), (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1), (7, 0)$.
• Step 8: Check given answer choices for these pairs and notice none match exactly.

Upon verifying these computations against the choices available, we conclude that the correct answer is None of the above.