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

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Re: If xy + z = z, is |x - y| > 0? [#permalink]

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07 Feb 2014, 20:08
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If xy + z = z, is |x - y| > 0? or given xy = 0 (either x or y or both 0), is |x-y|> 0? Squaring, is x^2 + y^2 -2xy > 0 ?

(1) x # 0 (Not equal to): x^2 is +ve. y = 0. So, x^2 + y^2 -2xy > 0
(2) y = 0: if x = 0, NO. If x = 1, x^2 + y^2 -2xy > 0. YES.

A.

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Re: If xy + z = z, is |x - y| > 0? [#permalink]

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24 Sep 2015, 05:04
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Re: If xy + z = z, is |x - y| > 0? [#permalink]

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08 Nov 2016, 15:42
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Re: If xy + z = z, is |x - y| > 0? [#permalink]

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11 Nov 2016, 08:14
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.

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Re: If xy + z = z, is |x - y| > 0?   [#permalink] 11 Nov 2016, 08:14

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