# Class of Failure

Number Theory Level pending

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 $$x - 1$$.

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