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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.
Condition 1)
Since we have 2 < \(\sqrt{|x-2|}\) < 4, we have 4 < | x – 2 | < 16, by squaring everything.
Two Cases
First Case – positive value
(x – 2) = 4
x = 6
(x – 2) = 16
x = 18
Then we have 6 < x < 18
Second Case – negative value
-(x – 2) = 4
-x + 2 = 4
-x = 2
x = -2
-(x - 2) = 16
-x + 2 = 16
-x = 14
x = -18
Then we have -14 < x < -2
It means we have -14 < x < -2 or 6 < x < 18.
However, we don’t have either a maximum value of x or a minimum value of x.
Since we can’t specify a unique solution, it is not sufficient.
Condition 2)
Since condition 2) does not yield a unique solution, it is not sufficient.
Conditions 1) & 2)
Using our solutions from earlier, namely -14 < x < -2 or 6 < x < 18, we know that the possible values of x satisfying both conditions are -13, -12, … , -3 and 7, 8, … , 17.
The maximum value of x is 17 and the minimum value of x is -13.
The difference between the maximum and the minimum value of x is 17 – (-13) = 30.
Therefore, C is the answer.
Answer: C
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.
