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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: 49273
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
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Difficulty:

75% (hard)

Question Stats:

50% (01:46) correct 50% (01:39) wrong based on 58 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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Joined: 09 Oct 2015
Posts: 222
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: 6792
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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If z ≠ 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2 &nbs [#permalink] 18 Jul 2018, 04:05
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