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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.
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Since we have 1 variable (x) and 0 equations, D is most likely the answer. So, we should consider each condition on its own first.

Let’s look at the condition 1). It tells us that the average of 1 and 3 is 2. If x is between 1 and 3 inclusive, then the standard deviation of 1, 3, and x is less than that of 1 and 2.

The answer is not unique, and the condition is not sufficient, according to Common Mistake Type 2, which states that the number of answers must be only one.

Condition 2) is not sufficient, obviously.

When we consider both conditions 1) & 2) together, 1, 2, and 3 are possible values of x.

The answer is not unique, and both conditions are not sufficient, according to Common Mistake Type 2, which states that the number of answers must be only one.

Both conditions 1) and 2) together are not sufficient

Therefore, E is the answer.
Answer: E

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations,” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C, or E.