I'm thinking of a number.

• if it is not a multiple of 4, then it is between 60 and 69
• if it is a multiple of 3 it is between 50 and 59
• if it is not a multiple of 6 it is between 70 and 79.

What is the number?

If the number is not a multiple of 4, then it is between 60 and 69. Then, it is not a multiple of 3, but it is a multiple of 6. That is impossible. Therefore, the number is a multiple of 4. If it is a multiple of 3, then it is between 50 and 59. Also, it is a multiple of 12. There are no multiples of 12 between 50 and 59, so the number is not a multiple of 3. Therefore, it cannot be a multiple of 6. Then, it is between 70 and 79. Since the number is divisible by 4, it is either 72 or 76. Since it is not divisible by 6, it must be 76. Therefore, the number is 76.

Posted by Math Man on 2017-06-04 21:17:34