Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If y is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?  Choose the most appropriate option
A) 0<y<4 B) 4<y<10 C) 10<y<20 D) 20<y<30 E) y>30
x = the product of all even numbers from 2 to n, where n is any even integer value from 2 to 60 including.   If x = 2, x - 1 = 2! -1   If x = 2x4, x - 1 = 2! (2^2) - 1   If x = 2x4x6, x - 1 = 3! (2^3) - 1   If x = 2x4x6x8, x - 1 = 4! (2^4) - 1   .   .   .   .   If x = 2x4x6x.......x60, x - 1 = 30! (2^30) - 1   Lets find y, a smallest prime factor of (x-1):   If y were 2, [(30!) (2^30) -(1)] would be divisible by 2 however thats not the case.   If y were 3, [(30!) (2^30) -(1)] would be divisible by 3 however thats not the case.   If y were 5, [(30!) (2^30) -(1)] would be divisible by 5 however thats not the case.   .   .   .   .   .   If y were 29, [(30!) (2^30) -(1)] would be divisible by 29 however thats not the case.   If none of the primes under 31 is a factor of (x-1), (x-1) must have a prime factore above 30.   ANSWy&gt;30R:y&gt;30
<result>E</result>
Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If y is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?