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If xy > 0, is xyz < 0?

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
If xy > 0, is xyz < 0?  [#permalink]

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22 Apr 2016, 04:32
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:32) correct 35% (01:14) wrong based on 123 sessions

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If xy > 0, is xyz < 0?

(1) xz > 0
(2) yz > 0

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Joined: 13 Apr 2015
Posts: 1683
Location: India
Re: If xy > 0, is xyz < 0?  [#permalink]

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22 Apr 2016, 12:02
1
xy > 0 --> x and y have the same signs
Is xyz < 0?

St1: xz > 0 --> x and z have the same signs
Suppose x = +ve --> y = +ve and z = +ve --> Is xyz < 0? No
Suppose x = -ve --> y = -ve and z = -ve --> Is xyz < 0? Yes
Not Sufficient

St2: yz > 0 --> y and z have the same signs
Suppose y = +ve --> x = +ve and z = +ve --> Is xyz < 0? No
Suppose y = -ve --> x = -ve and z = -ve --> Is xyz < 0? Yes
Not Sufficient

Combining St1 and St2: xy > 0; xz > 0; yz > 0
x = +ve --> y = +ve and z = +ve
x = -ve --> y = -ve and z = -ve
Still not sufficient

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If xy > 0, is xyz < 0?  [#permalink]

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30 Aug 2018, 06:24
niks18 VeritasKarishma chetan2u pushpitkc

Quote:
If xy > 0, is xyz < 0?

(1) xz > 0
(2) yz > 0

Is it appropriate to combine two statements
as:
xy $$z^2$$ > 0

I incorrectly chose (C) here
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Joined: 25 Feb 2013
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GPA: 3.82
Re: If xy > 0, is xyz < 0?  [#permalink]

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30 Aug 2018, 06:31
1
niks18 VeritasKarishma chetan2u pushpitkc

Quote:
If xy > 0, is xyz < 0?

(1) xz > 0
(2) yz > 0

Is it appropriate to combine two statements
as:
xy $$z^2$$ > 0

I incorrectly chose (C) here

Even if you combine the two statements you cannot arrive at xyz<0.

It is given that xy>0, so you simply need to know whether z<0 and on combining you will not get this information

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Math Expert
Joined: 02 Aug 2009
Posts: 8006
Re: If xy > 0, is xyz < 0?  [#permalink]

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30 Aug 2018, 06:49
1
niks18 VeritasKarishma chetan2u pushpitkc

Quote:
If xy > 0, is xyz < 0?

(1) xz > 0
(2) yz > 0

Is it appropriate to combine two statements
as:
xy $$z^2$$ > 0

I incorrectly chose (C) here

So when you get xyz^2>0, it just tells you xy>0..
But if all three are negative..xyz^2 will be >0 but xyz<0..
However if all three are positive..xyz^2 will be >0 and xyz>0
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Re: If xy > 0, is xyz < 0?  [#permalink]

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30 Aug 2018, 07:05
Bunuel wrote:
If xy > 0, is xyz < 0?

(1) xz > 0
(2) yz > 0

xy > 0 -> x and y have same signs

(1) xz > 0 -> x and z have same signs -> x, y, z have same signs. If all 3 variables are negative -> Yes. If all 3 variables are positive -> No. --> Not sufficient.
(2) yz > 0 -> y and z have same signs -> x, y, z have same signs. If all 3 variables are negative -> Yes. If all 3 variables are positive -> No. --> Not sufficient.
(1)+(2) x, y, z have same signs -> Not sufficient.

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Re: If xy > 0, is xyz < 0?  [#permalink]

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10 Sep 2019, 22:37
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Re: If xy > 0, is xyz < 0?   [#permalink] 10 Sep 2019, 22:37
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