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

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

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New post 13 Apr 2018, 02:02
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A
B
C
D
E

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(N/A)

Question Stats:

80% (01:19) correct 20% (00:02) wrong based on 4 sessions

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

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New post 13 Apr 2018, 03:14
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
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If xyz ≠ 0, is xyz > 0? (1) xz < 0 (2) x + y + z = 0 [#permalink]

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New post Updated on: 13 Apr 2018, 03:47
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, 03:36.
Last edited by selim on 13 Apr 2018, 03:47, edited 1 time in total.
If xyz ≠ 0, is xyz > 0? (1) xz < 0 (2) x + y + z = 0   [#permalink] 13 Apr 2018, 03:36
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