For those of you who get confused with the theoretical way of solving this question, plugging in simple values is the best way to solve this question.
Let’s take two cases:
Case 1: x = 2 and y = 2. IS x = y? YES
Case 2: x = 2 and y = -2, IS x = y? NO.
From statement I alone, |x| = |y|.
Do the values in case 1 satisfy the equation above? Yes, they do.
Do the values in case 2 satisfy the equation above? Yes, they do.
This means that using statement I alone, we obtain a YES and a NO. Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone,\( x^2\) = \(y^2\).
Do the values in case 1 satisfy the equation above? Yes, they do.
Do the values in case 2 satisfy the equation above? Yes, they do.
This means that using statement II alone, we obtain a YES and a NO. Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.
Even when we combine the two statements, both cases 1 and 2 will satisfy both equations but won’t give us a YES or a NO.
The combination of statements is insufficient. Answer option C can be eliminated.
The correct answer option is E.
Hope that helps!
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