I am a two-digit number greater than 50.

The product of my digits is not 12, but 12 goes into it exactly.
The sum of my digits is odd.
The sum of my digits is less than 13
What am I?
What am I if I am less than 50?

"The product of my digits is not 12, but 12 goes into it exactly. "

I could be: 24 36 48 60 72 84 96

"I am greater than 50", leaves us with
60 72 84 96
"sum of digits is odd", leaves us with
72 96
"sum of my digits is less than 13"
I am 72

If "I am less than 50", then I am 36

To find the answer to the given problem, we need to follow a step-by-step approach and consider all the given conditions.

First, we know that the number is a two-digit number greater than 50. So, we can start by listing all the two-digit numbers greater than 50: 51, 52, 53, ..., 98, 99.

Next, we need to consider the condition that the product of the digits is not 12, but 12 goes into it exactly. This means that the two digits must have a product that is a multiple of 12.
To determine which two-digit numbers meet this condition, we can calculate the product of each number's digits and check if it is divisible by 12:
- For example, for the number 51, the product of its digits (5 * 1) is 5, which is not divisible by 12, so it does not meet the condition.
- Similarly, for the number 52, the product of its digits (5 * 2) is 10, which is also not divisible by 12.
- We can continue this process for all the two-digit numbers greater than 50 until we find a number that satisfies this condition.

Now, let's consider the condition that the sum of the digits is odd and less than 13. This means that the sum of the two digits must be an odd number less than 13.
To find the numbers that meet this condition, we can calculate the sum of each number's digits and check if it is an odd number less than 13:
- For example, for the number 51, the sum of its digits (5 + 1) is 6, which is even and not less than 13.
- For the number 52, the sum of its digits (5 + 2) is 7, which is an odd number less than 13.
- We can continue this process for all the two-digit numbers greater than 50 until we find a number that satisfies this condition.

Combining both conditions, we can look for a number that satisfies both the condition of having a product divisible by 12 and a sum of digits that is odd and less than 13.
From the analysis above, we can see that the number that meets both conditions is 63.

Therefore, if the given number is greater than 50, it is 63.

Now, let's consider the case when the number is less than 50. Following the same steps, we can check all the two-digit numbers less than 50 to find a number that meets both conditions.
- For the number 41, the product of its digits (4 * 1) is 4, which is not a multiple of 12.
- For the number 42, the product of its digits (4 * 2) is 8, which is also not a multiple of 12.
- We can continue this process until we find a number that satisfies both conditions.

Analyzing all the possibilities, we can see that there is no two-digit number less than 50 that satisfies both conditions. Therefore, the answer is - There is no number that meets both conditions and is less than 50.