A number D236DO can be divided by 36 if D is :

Options

A. a. 8
B. b. 6
C. c. 1
D. d. more than one values are possible

Answer

To determine the value of D in the number D236D such that it is divisible by 36, we need to check the divisibility rules for both 4 and 9, since 36 = 4 × 9.

### Step 1: Check divisibility by 4
A number is divisible by 4 if the last two digits form a number that is divisible by 4. In our case, the last two digits are "6D".

- The possible values for D are from 0 to 9. We will check each case:
- If D = 0, then 60 is divisible by 4.
- If D = 1, then 61 is not divisible by 4.
- If D = 2, then 62 is not divisible by 4.
- If D = 3, then 63 is not divisible by 4.
- If D = 4, then 64 is divisible by 4.
- If D = 5, then 65 is not divisible by 4.
- If D = 6, then 66 is not divisible by 4.
- If D = 7, then 67 is not divisible by 4.
- If D = 8, then 68 is divisible by 4.
- If D = 9, then 69 is not divisible by 4.

Thus, the possible values of D for divisibility by 4 are D = 0, 4, or 8.

### Step 2: Check divisibility by 9
A number is divisible by 9 if the sum of its digits is divisible by 9. The digits of the number D236D are D, 2, 3, 6, and D. Therefore, the sum of the digits is:

\[ D + 2 + 3 + 6 + D = 2D + 11 \]

Now we need to check the values of D that we found in Step 1 (0, 4, 8) to see which makes \( 2D + 11 \) divisible by 9.

- For D = 0:
\[ 2(0) + 11 = 11 \] (not divisible by 9)

- For D = 4:
\[ 2(4) + 11 = 8 + 11 = 19 \] (not divisible by 9)

- For D = 8:
\[ 2(8) + 11 = 16 + 11 = 27 \] (divisible by 9)

### Conclusion
The only value of D that satisfies both conditions (divisible by 4 and 9) is D = 8.

Thus, the answer is:
**D = 8**