If xy = y, what is the value of |x| + |y|? (1) x = -1 (2) y = 0

You cannot reduce \(xy=y\) by y to get \(x=1\). That's because y can be 0, and we cannot divide by 0. By doing so, you lose a solution, namely y = 0.

What you can do is rearrange and factor out y:

\(xy=y\)
\(xy-y=0\)
\(y(x-1)=0\)
\(y=0\) or \(x=1\) (or both)

Never reduce an equation by a variable (or expression with a variable) if you are not certain that the variable (or expression containing the variable) is not equal to zero. We cannot divide by zero.

Back to the question;

If \(xy=y\), what is the value of \(|x|+|y|\)?

(1) \(x=-1\)

Since x = -1, then x is not 1, and thus y must be 0 for the equation (\(xy=y\)) to hold. Therefore, \(|x|+|y|=1+0=1\). Sufficient.

(2) \(y=0\)

When \(y=0\), then from \(xy=y\), x can be any number, therefore we cannot determine the specific value of \(|x|+|y|\). Not sufficient.

Answer: A.

Hope it's clear.