Solving questions like this one algebraically can get complicated, but it's worth understanding the intricacies rather than spending several minutes picking numbers.

Statement (1) is sufficient. To simplify the inequality, we can divide both sides by x. However, since we are dividing by a variable that could be positive or negative, we need to consider both possibilities.
If x is positive, then we can divide both sides by x without any ramifications:
2 > x
In other words, if x is positive, x is less than 2. Or: 0 < x < 2.
If x is negative, we can divide both sides by x, but we must change the direction of the inequality sign:
2 < x
In other words, if x is negative, x is greater than 2. That's impossible -- if x is greater than 2, it must be positive. Since this generates a contradiction, we know that x cannot be negative. The only acceptable range for x is between 0 and 2. Thus, the answer to the question is "no."

Statement (2) is insufficient. If x is less than 1, it could be negative or it could be positive (between 0 and 1). Choice (A) is correct.