If x > 1, what is the value of x?

So as per statement, is x=2?

Yes, as the statement1.

1. Sufficient

as 2 is >1 and has 2 unique factors 1 and 2.

every other x >1 does not have x unique factors.

2. Not sufficient

x + prime greater than 1 is odd

as x >1

x ( x + odd = odd => x must be even)
2 + 3 is odd
4 + 5 is odd


Answer is A.

If x>1, what is the value of integer x?

(1) There are x unique factors of x --> x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x, inclusive but x can not be divisible by x-1 unless x=2, for example 3 is not divisible by 2, 4 is not divisible by 3, etc, but 2 is divisible by 1 (other value of x which has x distinct positive factors (1) is excluded by the stem as x>1). So this statement implies that x=2. Sufficient.

(2) The sum of x and any prime number larger than x is odd --> x+prime=odd, now as x itself is more than 1 then prime more than x cannot be 2 thus it's odd and we have x+odd prime=odd --> x=even, so x could be ANY even number. Not sufficient.

Answer: A.

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