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# If z is positive, is | x − y| > 0? (1) xy + 2z = z (2) x^2 − 2x = 0

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If z is positive, is | x − y| > 0? (1) xy + 2z = z (2) x^2 − 2x = 0  [#permalink]

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09 Oct 2018, 02:01
00:00

Difficulty:

65% (hard)

Question Stats:

48% (01:44) correct 52% (02:02) wrong based on 69 sessions

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If z is positive, is | x − y| > 0?

(1) xy + 2z = z

(2) x^2 − 2x = 0

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examPAL Representative
Joined: 07 Dec 2017
Posts: 890
Re: If z is positive, is |  [#permalink]

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09 Oct 2018, 02:26
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Let's start by looking at the question. an absolute value will almost always provide a positive a number, meaning the answer is almost certainly yes. the only case in which it could be "no" is if the expression in the absolute value equals exactly zero - that is, x-y=o ==> x=y. So, with that in mind, let's take a look at the statements:

1) simplifying, this gives us xy = -z. since z is positive, -z is definite negative. therefore, xy<0. this means one of x,y is negative, the other positive: what is definite, then, is that x and y are not equal! sufficient! we'll eliminate B, C & E
2) simplifying, this gives us x(x-2)=0 ==> x=0, x=2. But this tells us nothing about y (maybe y=2? maybe not?) and is thus clearly insufficient - eliminate B.

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Re: If z is positive, is |   [#permalink] 09 Oct 2018, 02:26
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