MathRevolution wrote:

[GMAT math practice question]

If \(x<-1\), is \(\sqrt{(-x)|x|}\)\(/y=1\)?

1) \(y=|x|\)

2) \(y=-x\)

\(\sqrt{(-x)|x|}\)\(/y=1\). Square both sides to get

\((-x)|x|=y^2\). Now as \(x<-1\) i.e negative so \(|x|=-x\)

therefore, the question stem Is \((-x)(-x)=y^2 => x^2=y^2\) ?

Statement 1: \(y=|x|\), square both sides to get \(y^2=x^2\).

SufficientStatement 2: \(y=-x\), square both sides to get \(y^2=x^2\).

SufficientOption

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Alternatively, assume some values for x and test the stem

Statement 1: let \(x=-2\) so \(y=|-2|=2\)

Question stem \(\sqrt{-(-2)|-2|}=y=>\sqrt{4}=y =>y=2\) . Sufficient

Statement 2: let \(x=-2\) so \(y=-(-2)=2\). Same as statement 1. Sufficient