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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Now,
|x-1| < |x-3|
=> |x-1|^2 < |x-3|^2
=> (x-1)^2 < (x-3)^2
=> x^2-2x+1 < x^2-6x+9
=> 4x < 8
=> x < 2

Thus, condition 1) is sufficient.

Condition 2)
Since the solution set of the question does not contain the solution set of condition 2), condition 2) is not sufficient.

In inequality questions, the law "Question is King" tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient

Therefore, A is the answer.
Answer: A