If x is an integer and x ≠ 31, is (31 - x)/x an integer?

(31-x)/x can be written as 31/x - 1. Here -1 is already an integer, so 31/x - 1 will be an integer only when 31/x is an integer. This will be true only if x takes the following values: 1, 31, -1, -31 (its easy to see which values will satisfy because 31 is a prime number and thus has only 2 factors - 1 and 31. But the negative values of these will also result in integer). But we are already given that x is NOT equal to 31. So the only possible integer values of x which will result in 31/x being an integer are: 1, -1, -31.

(1) x > 1
This means there is simply no value x can take which will make 31/x an integer (because 1, -1, -31 are not possible here given that x > 1). So this can never be an integer. This gives us an answer as NO to the question. Sufficient.

(2) x is an even number.
Since 31 is odd, it can never be divisible by any even number. So 31/x cannot be an integer. This gives us an answer as NO to the question. Sufficient.

Hence D answer