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Back to the question.
Is x an integer? (1) x is evenly divisible by 1/2. (2) x is evenly divisible by 2.
This is not a good question. Definitely not a GMAT type.
On GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that: 1. \(a\) is an integer; 2. \(b\) is an integer; 3. \(\frac{a}{b}=integer\).
So the terms "divisible", "multiple", "factor" ("divisor") are used only about integers (at least on GMAT).
So, you won't see statement like "x is evenly divisible by 1/2" on GMAT.
Suppose that the intended meaning of this question was as below:
Is x an integer? (1) x divided by 1/2 is an integer --> now, if x=1 (1 divided by 1/2 equals to 2) then the answer to the question will be YES but if x=0.5 (0.5 divided by 1/2 equals to 1) then the answer to the question will be NO. Not sufficient.
(2) x is evenly divisible by 2 --> directly tells us that x is an even integer. Sufficient.