HarveyKlaus wrote:

If \(\vert x\vert = \vert y\vert\), is \(\frac{x}{y} = -1\)?

My method is a little verbose to write out. Could definitely be explained more succinctly as it's trivial to see.

\(\textbf{1) } x<0\)

\(y = \pm x\)

As x is negative,

if \(y = x\), then \(\frac{x}{y} = 1\)

if \(y = -x\), then \(\frac{x}{y} = -1\)

Not Sufficient\(\textbf{2) } y>0\)

\(x = \pm y\)

As y is positive,

if \(x = y\), then \(\frac{x}{y} = 1\)

if \(x = -y\), then \(\frac{x}{y} = -1\)

Not Sufficient\(\textbf{(1 + 2)}\)

\(y = \pm n\)

\(x = \pm n\)

We know from (1) that x = -n.

We know from (2) that y = n

\(\frac{x}{y} = \frac{-n}{n} = \frac{-1}{1} = -1\)

Sufficient(C) both statements taken together are sufficient to answer the question, but neither statement alone is sufficient

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