Given : X is Integer
(1) x is even.
(x2 - 1)(x - 3) an even number
Square of any even number is even and when we subtract any odd from even you get odd.
So, (x2 - 1) is odd
(x - 3) is also odd as Even-Odd =Even
As both the numbers are odd.Therefore their product will always be Odd.
Sufficient
(2) Each prime factor of (x2 + 1) is greater than 3.
In other words X is even same as above.
How??? let us see
Given : Each prime factor of (x2 + 1) is greater than 3
Means 2 can not be prime factors or in other words (x2 + 1) has to be odd.
and this is possible only when x is even as we know square of odd is odd and adding 1 to it makes (x2 + 1)even.
Therefore x has to be even.
Example:
plug 2 in x2 + 1 = 5 Correct
plug 4 in x2 + 1 = 17 Correct
Plug 3 in x2 + 1 = 10 Incorrect as 2 is prime factor of 10.
As x is even in this case also.As shown above this is sufficient too!!
Correct answer D
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