Vincen wrote:If \(x > 1\), what is the value of \(x\)?

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

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT

Let's take each statement one by one.

(1) There are \(x\) unique factors of \(x\).

The only possible value of x could be 2. For x = 2, the factors are 1 and 2. There are two factors.

If we take x = 3, its factors are 1 and 3; there are two factors ≠ x = 3.

Similarly, if we take x = 4, its factors are 1, 2 and 4; there are three factors ≠ x = 4.

There is no need to check further. Sufficient.

(2) The sum of \(x\) and any prime number larger than \(x\) is odd.

Case 1: Say x = 2, and a prime no. greater than x = 3; thus, 2 + 3 = 5. We have x = 2.
Case 2: Say x = 4, and a prime no. greater than x = 7; thus, 4 + 7 = 11. We have x = 11.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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