If x is an integer between 27 and 54, what is the value of x?

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 to be the answer. So, we should consider each condition on its own first.

Condition 1)
The possible values of x are 30, 37, 44 and 51.
Since condition 1) does not yield a unique solution, it is not suffiecient.

Condition 2)
The possible values of x are 29, 32, 35, 38, 41, 44, 47, 50 and 53.
Since condition 2) does not yield a unique solution, it is not suffiecient.

Conditions 1) & 2)
When we conisder both conditions together, the only possible value of x is 44.

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.

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.