If x is an integer greater than 1 and if y = x + 1/x, which of the following must be true? I. yx II. y is an integer III. xy > x2 (A) I only (B) III only (C) I and II only (D) I and III only (E) I, II, and III

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Answer:

Choice D Level of Difficulty E M H The best way to figure this out is to examine the extremes. It says x is an integer greater than 1, so: If we let x have its smallest value of 2, y will have a value of 2.5 . If we let x approach infinity, y also approaches infinity, but is always slightly larger than x. Therefore, as x takes integer values from 2 to infinity, y takes on values from 2.5 to infinity, and is always slightly larger than x. Notice: Case I is true, since x and y will never have the same value. Case II is false since y will never be an integer. Case III is true since if y is always bigger than x, then xy will always be larger than xx.

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