If *x* is an integer greater than 1 and if *y* = *x* + 1/*x*, which of the following must be true?

I. *y* ≠ *x*

II. *y* is an integer

III. *x**y* > *x*^{2}

(A) I only

(B) III only

(C) I and II only

(D) I and III only

(E) I, II, and III

Level of Difficulty E

The best way to figure this out is to examine the extremes. It says

If we let

If we let

Therefore, as

Notice:

Case I is true, since

Case II is false since

Case III is true since if

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