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x is equal to the product of all even numbers

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by uptowngirl92 » Sun Sep 13, 2009 8:56 pm
Integer x is equal to the product of all even numbers from 2 to 60.If y is the smallest prime no. that is also a factor of x-1,then which of the following expressions must be true?
y lies bet. 0 and 4
y lies bet. 4 and 10
y lies bet. 10 and 20
y lies bet. 20 and 30
y is greater than 30

Guys please help me understand the underlying principles..
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by praky_rules » Mon Sep 14, 2009 8:34 pm
x can be reduced to 2^30*30!

consider x-1, = 2^30*30! - 1. If you choose any number from 2 to 30, x-1 will be not be divisible by that number. Consider 11 say...the 2^30*30! - 1 = 2^30*30! +10 - 11. So the remainder when x-1 is divided by 11 is 10.

None of the numbers from 2 to 30 is factor of x-1. so the factor has gottu be greater than 30
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