Question

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?

Answer 1

99

Explanation:

There are 3 clues:

●between 50 and 100

●multiple of 11 AND not a multiple of 2

●divisible by 3

The clue that narrows down the choices pretty quickly is the second clue, divisible by 11 and not by 2 leaves only 55, 77, and 99 as a possible answer. Because 2 goes into all even numbers, we eliminate all even numbers.

(We are using the first clue to eliminate all the numbers less than 50)

The third clue says that the sum of the digits is a multiple of 3. That is the divisibility test for 3. It means that the number is divisible by 3.

Only 99 (out of 55, 77, 99) is divisible by 3.

Bob's favorite number is 99.