amitjash wrote:

If xy + z = z, is |x - y| > 0?

(1) x ≠ 0

(2) y = 0

We can start by simplifying the given equation:

xy + z = z

xy = 0

We see that either x or y or both x and y must be zero.

We also see that the question is asking whether the absolute value of x - y is greater than zero. Since the absolute value of any quantity will be positive except when the quantity is 0, the only way in which absolute value of x - y won’t be greater than zero is if it’s equal to zero, and that will only occur if x = y. Let’s keep this in mind as we analyze our statements.

Statement One Alone:

x ≠ 0

Since xy = 0, if x does not equal zero, then y MUST equal zero. Thus, since x cannot equal y, the absolute value of x - y will always be greater than zero. Statement one alone is sufficient to answer question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

y = 0

Since y = 0, x could or could not equal zero, and thus we do not have enough information to answer the question. For instance, if y = 0 and x = 1, then |x - y| is greater than zero; however, if y = 0 and x = 0, then |x - y| is not greater than zero.

Answer: A

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