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

Question

GMAT CLUB TESTS' FRESH QUESTION

If  z ≠ 0 , is  x = y  ?

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

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

rahulkashyap · Answer

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

chetan2u · Answer

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
eq{y} 
Sufficient

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

D

Bunuel · Answer

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

Archit3110 · Answer

#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

Ypsychotic · Answer

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.

LoneSurvivor · Answer

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

Bunuel · Answer

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 eq 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 eq y . Sufficient. Answer: D

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

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