Data Sufficiency

nidhis.1408 wrote:If x > 1, what is the value of integer x?

(1) There are x unique factors of x.
(2) The sum of x and any prime number larger than x is odd.

Minimum possible value of x is 2.

Statement 1: Checking with first few integers greater than 1 will tell that 2 is the only integer which has exactly 2 unique factors, 1 and 2. (See note for proof)

Sufficient

Statement 2: (x + p) is odd, where p is a prime number such that p > 2
All prime numbers greater than p are odd. Hence, x must be even.

Now x can have any even value. For example,

• x = 2, p = 5
  x = 4, p = 5

Not sufficient

The correct answer is A.

Note : For x to have x unique factors, x must be divisible by all the integers starting from 1 to x. But for any x greater than 2, x and (x - 1) will be coprime integers. Hence, for any x > 2, it is not possible that (x - 1) will be a factor of x. Only possible value of x is 2.