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# If z ≠ 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
If z ≠ 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2  [#permalink]

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18 Jul 2018, 02:37
1
10
00:00

Difficulty:

65% (hard)

Question Stats:

57% (01:48) correct 43% (01:57) wrong based on 183 sessions

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GMAT CLUB TESTS' FRESH QUESTION

If $$z ≠ 0$$, is $$x = y$$ ?

(1) $$xy + \frac{1}{|z|} = 0$$

(2) $$\frac{x}{y} + z^2 = 0$$

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Re: If z ≠ 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2  [#permalink]

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18 Jul 2018, 03:56
from a we know that xy = negative number, as 1/|x| is 1/ positive. Therefore, x and y are of the opposite signs.

same applies for statement b, as x^2 is always positive
Math Expert
Joined: 02 Aug 2009
Posts: 7991
If z ≠ 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2  [#permalink]

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18 Jul 2018, 04:05
If $$z ≠ 0$$, is $$x = y$$ ?

(1) $$xy + \frac{1}{|z|} = 0$$..
$$xy=-\frac{1}{|z|}$$, so xy is a NEGATIVE number and thus $$x\neq{y}$$
Sufficient

(2) $$\frac{x}{y} + z^2 = 0$$..
$$\frac{x}{y}=-z^2$$, so xy is NEGATIVE
Same as A
Sufficient

D
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Re: If z ≠ 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2  [#permalink]

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24 Dec 2018, 01:40
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION

If $$z ≠ 0$$, is $$x = y$$ ?

(1) $$xy + \frac{1}{|z|} = 0$$

(2) $$\frac{x}{y} + z^2 = 0$$

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Re: If z ≠ 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2  [#permalink]

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24 Dec 2018, 03:02
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION

If $$z ≠ 0$$, is $$x = y$$ ?

(1) $$xy + \frac{1}{|z|} = 0$$

(2) $$\frac{x}{y} + z^2 = 0$$

#1:
lzlxy=0
so x y have to be of opposite signs , sufficient

#2:
x/y+ z2= 0

again x& y have to be of opposite signs, sufficient

IMO D
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Re: If z ≠ 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2  [#permalink]

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26 Dec 2018, 00:34
1
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION

If $$z ≠ 0$$, is $$x = y$$ ?

(1) $$xy + \frac{1}{|z|} = 0$$

(2) $$\frac{x}{y} + z^2 = 0$$

Statement 1) |z| is always positive. SO, xy=-1/|z|, xy is always negative. But, x =y, xy=x^2, which is always positive. So, x is not equal to y. Sufficient.

Statement 2) z^2 is always positive. So, x/y is always negative, which means either x is positive and y is negative or vice versa. In either case, x is not equal to y. Sufficient.

Hence, Option D is correct.
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Joined: 23 Nov 2016
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Re: If z ≠ 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2  [#permalink]

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31 Mar 2019, 05:56
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION

If $$z ≠ 0$$, is $$x = y$$ ?

(1) $$xy + \frac{1}{|z|} = 0$$

(2) $$\frac{x}{y} + z^2 = 0$$

S1: XY=-1/|Z|
This means X and Y are different sign so x=Not Y
S1: Sufficient

S2: X/Y=-Z^2
So x and y are different sign . so x=not y
S2 : Sufficient

+1 for D

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Re: If z ≠ 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2   [#permalink] 31 Mar 2019, 05:56
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