This is a value kind of DS question where we need to find a unique value for x.
Performing a visual scan of the statements, it’s very clear that statement 2 alone will not help us find a unique value for x, since x>2 represents a range. Therefore, the first thing I would do on this question is I would eliminate options B and D since they cannot be the answers. At this stage, I am left with options A, C and E as my possible answers.
Whenever such an opportunity presents itself, where you think some options can be eliminated, grab it with both hands. This means that you will have more time to spend on the statements and options that matter.
Remember that |x| = √\(x^2\).
From statement 1 alone, |x+2| = 2|x-2|. The absolute value terms can be re-written based on the concept discussed above.
So, |x+2| = √\((x+2)^2\) and |x-2| = √\((x-2)^2\). Substituting this in the equation, we get,
√\((x+2)^2\)= 2√\((x-2)^2\). Squaring both sides, we have,
\((x+2)^2\) = 4\((x-2)^2\).
Expanding the expressions based on identities and solving for the values, we obtain two values for x viz x = \(\frac{2}{3}\) and x = 6. But, we need a unique value for x. Hence, statement 1 alone is insufficient.
Answer option A can be eliminated. Possible answer options are C or E.
Combining the data from statements 1 and 2, we can say that x has to be 6 since that is the only value of x that satisfies the conditions given in both the statements.
The combination of statements is sufficient. Answer option E can be eliminated.
The correct answer option is E.
In absolute value questions where you see a modulus on either side of an equation, it’s a good idea to use the |x| = √\(x^2\) concept. This will help you to reduce the equation to a quadratic which can then be solved for the values of x.
Also remember to not jump to a conclusion that a modulus will give you two values for x and hence insufficient. That is not the case in all questions. Only when you analyse will you find out.
Hope that helps!
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