Class of Failure
In Mrs. Lin's math class, there are an x number students. The following 7 true statements can be made about the number of students.
- If x is a multiple of 7, x is between 45 and 55 (inclusive).
- If x is a multiple of 5, x is between 56 and 99 (inclusive).
- If x is a multiple of 3, x is between 16 and 44 (inclusive).
- If x is even, it is strictly less than 16.
- x does not have 4 positive factors.
- x is strictly less than 100.
- There is no possible value of x that is both odd and prime.
Find the product of the possible values of \(x - 1\).