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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: 58435
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, 03:01
00:00

Difficulty:

55% (hard)

Question Stats:

53% (01:46) correct 47% (01:58) wrong based on 122 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: 1150
Re: If z is positive, is |  [#permalink]

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09 Oct 2018, 03:26
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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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CrackVerbal Quant Expert
Joined: 23 Apr 2019
Posts: 38
Re: If z is positive, is | x − y| > 0? (1) xy + 2z = z (2) x^2 − 2x = 0  [#permalink]

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23 Jul 2019, 03:52
Hi,

Absolute value questions are a treat to work out, as they always test your reasoning ability on quant. The complex the question looks, the more easy it is to solve.

The big point to understand while solving these kinds of questions is that very simple pieces of information are provided in very complex forms. so you just need to look through the fluff to figure out what the question is actually asking. It becomes imperative to always break down the question stem.

Given z is positive, Is |x - y| > 0. Now the big takeaway here is to understand that |something| will always be 0 or positive and not only positive. So the question basically asks us to prove if x = y or not, since for all other values of x and y, x - y will always be positive.

So the question now is, Is x = y?

Statement 1: xy + 2z = z

xy = -z

Since z is positive, -z will always be negative ----> xy = negative ----> x and y can never be equal. Sufficient.

Statement 2: x^2 - 2x = 0

Taking x common -----> x(x - 2) = 0 -----> x = 0 or x = 2.

This does not give us any info about y, so x can/cannot be equal to y. Insufficient.

Takeaway : On inequalities and absolute value questions, try to break down the question stem

CrackVerbal Quant Expert
Re: If z is positive, is | x − y| > 0? (1) xy + 2z = z (2) x^2 − 2x = 0   [#permalink] 23 Jul 2019, 03:52
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