Explanation

Since we have a question about number properties, we will be inclined to use rules that we know, but examining specific cases can jog our memory about the rules and confirm our results. Let's go to the data statements, separately first.

Statement (1) says that is not an even integer. In one case, could be an odd integer, say 7. Then k would be 14 and k would be even. Is there any other allowed case in which we get a different answer to the question? Yes, in fact, there is: could be a non-integer, say 7.5 In that case, k would be 15 and k would not be even. Statement (1), therefore, does not give us sufficient information to answer the question. This matter is a good example of evaluating by cases requires not overlooking important cases. Your best bet of hitting all the cases is to go through a list: positive numbers, negative numbers, 0, 1, and 2, fractions between 0 and 1, fractions between -1 and 0, larger fractional numbers, large positive numbers, and "large" negative numbers. Anyway, Statement (1) is insufficient.

Statement (2) says that 5 - k is an even integer. We can write this as a pseudo-equation





Subtracting an even number from 5 will always yield an odd number. That's a rule from the Math Review and we can see that 5-2=3, 5-4=1, and so on. The integer k is always odd, so we have sufficient information to answer the question definitively in the negative. Statement (2) is sufficient.

The correct answer is (B).