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

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Bunuel
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If z 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2 [#permalink] New post   18 Jul 2018, 02:37
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Question Stats:

64% (01:41) correct 36% (01:57) wrong based on 376 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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D
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Bunuel
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Re: If z 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2 [#permalink] New post   08 Nov 2021, 10:22
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Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION



If \(z ≠ 0\), is \(x = y\) ?


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

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


Official Solution:


If \(z ≠ 0\), is \(x = y\) ?

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

Re-arrange: \(\frac{1}{|z|}=-xy\)

Now, the left hand side is an absolute value, which is positive, so \(-xy\) must also be positive.

\(-xy > 0\);

\(xy < 0\). \(x\) and \(y\) have the opposite signs, so \(x \neq y\). Sufficient.

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

Re-arrange: \(z^2=-\frac{x}{y}\)

Now, the left hand side is the square of an integer, which is positive, so \(-\frac{x}{y}\) must also be positive.

\(-\frac{x}{y} > 0\);

\(\frac{x}{y} < 0\). \(x\) and \(y\) have the opposite signs, so \(x \neq y\). Sufficient.


Answer: D
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rahulkashyap
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Re: If z 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2 [#permalink] New post   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
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Re: If z 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2 [#permalink] New post   18 Jul 2018, 04:05
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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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Bunuel
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Re: If z 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2 [#permalink] New post   24 Dec 2018, 01:40
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Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION



If \(z ≠ 0\), is \(x = y\) ?


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

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


Par of GMAT CLUB'S New Year's Quantitative Challenge Set

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Re: If z 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2 [#permalink] New post   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] New post   26 Dec 2018, 00:34
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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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Re: If z 0, is x = y ? (1) xy = -1/|z| (2) x/y = -z^2 [#permalink] New post   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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