\(\text{What is the value of } x^2 – y^2?\)
\(\textbf{(1) } \vert x\vert = \vert y\vert\)
\(\sqrt{x^2} = \pm x = \vert x \vert\)
\(\vert x\vert = \vert y\vert \implies x^2 = y^2\)
\(x^2 - x^2 = 0\)
Sufficient. Answer = 0
\(\textbf{(2) } x^2 + y^2 = 0\)
The minimum value of squaring a number is 0.
Therefore, to obtain the answer of 0, \(x^2\) and \(y^2\) must both produce 0.
0 is the single single input which produces 0 as output. Therefore \(x = y = 0\)
As we know \(x\) and \(y\), we can obtain \(x^2 - y^2\)
Sufficient. Answer = 0
Note that (1) provides the answer, whereas (2) provides both the answer and the value of x and y.
(D) each statement alone is sufficient
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