GRE algebra question, evaluate the expression

Question

Given x,y<0,

What is the value of

$$\frac{\sqrt{x^2}}{x} - \sqrt{\frac{-y}{\left\lvert y \right\rvert}}$$

Since $x$ and $y$ are negative that means the first term should reduce to

$$\frac{\left\lvert x \right\rvert}{x}$$

and the second term reduces to

$$\sqrt{\frac{\left\lvert y \right\rvert}{\left\lvert y \right\rvert}}$$

So the answer is $-1-1=-2$ ..... or so I thought.

The answer key says the answer is $y-1$ which I don't follow at all. The site has goofed some answers already so is the goof on their part or mine?

You are if $a \ne 0$ then $|a|/a$ is simply 1 or -1 depending on whether or not a is positive or negative. As $x,y < 0$ this is $(-1) - \sqrt{-(-1)}$ which is $-2$. — fleablood, Dec 18 '16 at 21:53

score 3 · Accepted Answer · answered Dec 18 '16 at 21:49

3

You're correct.

$$\text{sgn}(x) - \sqrt{-\text{sgn}(y)} = -1 -\sqrt{+1} = -2$$

answered Dec 18 '16 at 21:49

zahbaz

2

Perhaps the book thought the problem was $-y\frac{\sqrt{x^2}}{x} - \sqrt{\frac{-y}{\left\lvert y \right\rvert}}$ ? – zahbaz Dec 18 '16 at 21:52

1 Answers1