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# If xyz ≠ 0, is xyz > 0? (1) xz < 0 (2) x + y + z = 0

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Math Expert
Joined: 02 Sep 2009
Posts: 51218
If xyz ≠ 0, is xyz > 0? (1) xz < 0 (2) x + y + z = 0  [#permalink]

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13 Apr 2018, 01:02
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:27) correct 31% (01:43) wrong based on 48 sessions

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If xyz ≠ 0, is xyz > 0?

(1) xz < 0
(2) x + y + z = 0

_________________
Intern
Joined: 28 Apr 2014
Posts: 49
GMAT 1: 640 Q50 V25
Re: If xyz ≠ 0, is xyz > 0? (1) xz < 0 (2) x + y + z = 0  [#permalink]

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13 Apr 2018, 02:14
IMO E
ST 1
either of x or z is +ve
but we don't know about y
insufficient

St2
can't predict the signs
insufficient

combining
x=-5 y=2 z=3 xyz<0
x=3 y=-1 z=-2 xyz>0
insufficient
Director
Joined: 31 Oct 2013
Posts: 881
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If xyz ≠ 0, is xyz > 0? (1) xz < 0 (2) x + y + z = 0  [#permalink]

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Updated on: 13 Apr 2018, 02:47
Bunuel wrote:
If xyz ≠ 0, is xyz > 0?

(1) xz < 0
(2) x + y + z = 0

Important points:
1. xyz=/ 0. it means none of xyz are o.
we are looking for xyz>0.

statement 1: xz<0. we can conclude that one of z or x is negative. no information regarding y which could be negative or positive. Not sufficient.

statement 2: x+y+z=0. we know that none of the properties is 0. another point to be noted that all 3 can be negative. Thus it is a combo of both negative and positive.

case 1: x=-6
y=-6
z=12
x+y+z=0
-6-6+12=0

case 2: x=-6
y=12
z=-6
x+y+z=0
-6+12-6=0

case 3: x=12
y=-6
z=-6

x+y+z=0
12-6-6=0

try to analyze more: x=12
y=12
z=-24

12+12-24=0

so ultimately it is impossible to determine how many negative properties we have. It could be 2 or 1.

combining strategies: from 1 we can conclude that either x or z is negative. from 2 we know either any of the 2 or 1 properties has negative value. common thing in both statement is that one of the property could be negative. If only a property is negative xyz will not be greater that 0.

Thus, the best answer is C.

Originally posted by selim on 13 Apr 2018, 02:36.
Last edited by selim on 13 Apr 2018, 02:47, edited 1 time in total.
Director
Joined: 02 Oct 2017
Posts: 728
Re: If xyz ≠ 0, is xyz > 0? (1) xz < 0 (2) x + y + z = 0  [#permalink]

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28 Apr 2018, 05:16
I) xz<0
Y can be either > or < than zero
Making xyz either > or < 0
Insufficient

II)x+y+z=0
xyz not equal to zero
So it can be many cases

2,-1,-1 xyz>0
3,1,-4. Xyz<0

Combining both statements won't result anything

Posted from my mobile device
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Re: If xyz ≠ 0, is xyz > 0? (1) xz < 0 (2) x + y + z = 0 &nbs [#permalink] 28 Apr 2018, 05:16
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# If xyz ≠ 0, is xyz > 0? (1) xz < 0 (2) x + y + z = 0

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