### Instruction: Bob's favorite number is between $50$ and $100$.  It is a multiple of $11$, but not a multiple of $2$.  The sum of its digits is a multiple of $3$.  What is Bob's favorite number?### Response: To start, I will list the multiples of $11$ that are between $50$ and $100$.
They are $55, 66, 77, 88, 99$.
Next, I will eliminate any that are multiples of $2$, since that would violate the second condition.
That means I can cross out $66$ and $88$.
That leaves $55, 77, 99$ as possible candidates.
Now, I will check the sum of the digits of each number and see if they are multiples of $3$.
For $55$, the sum of the digits is $5 + 5 = 10$, which is not a multiple of $3$.
For $77$, the sum of the digits is $7 + 7 = 14$, which is also not a multiple of $3$.
For $99$, the sum of the digits is $9 + 9 = 18$, which is a multiple of $3$.
Therefore, the only number that satisfies all the conditions is $99$.