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Math Expert V
Joined: 02 Sep 2009
Posts: 56366
If xy < 0, is x/y > z ? (1) xyz < 0 (2) x > yz  [#permalink]

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1
6 00:00

Difficulty:   65% (hard)

Question Stats: 59% (01:55) correct 41% (01:56) wrong based on 239 sessions

### HideShow timer Statistics If xy < 0, is x/y > z ?

(1) xyz < 0
(2) x > yz

Kudos for a correct solution.

_________________
Senior Manager  B
Joined: 28 Feb 2014
Posts: 294
Location: United States
Concentration: Strategy, General Management
Re: If xy < 0, is x/y > z ? (1) xyz < 0 (2) x > yz  [#permalink]

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1
1
If xy < 0, is x/y > z ?
2 scenarios
x is neg and y is pos
x is pos and y is neg

(1) xyz < 0
x is neg, y pos, z pos
x is pos, y neg, z pos
Both scenarios make z larger than x/y
Sufficient

(2) x > yz
x is neg, y pos, z neg
X is pos, y negative, z pos
If z is neg the question is yes
If z is positive question is no
Insufficient

Manager  Joined: 29 Jul 2015
Posts: 156
Re: If xy < 0, is x/y > z ? (1) xyz < 0 (2) x > yz  [#permalink]

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Bunuel wrote:
If xy < 0, is x/y > z ?

(1) xyz < 0
(2) x > yz

Kudos for a correct solution.

Since xy<0, x and y have opposite signs. And hence x/y is negative.

Statement 1:-
xyz<0
This is possible only when xy and z have opposite sign. We are already given that xy is negative.
So, z must be positive. and hence our question is answered.(x/y is not greater than z)
SUFFICIENT

Statement 2:-
Doesn't provide any information about sign of z.
INSUFFICIENT

SVP  V
Joined: 26 Mar 2013
Posts: 2284
Re: If xy < 0, is x/y > z ? (1) xyz < 0 (2) x > yz  [#permalink]

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If xy < 0, is x/y > z ?

From the prompt,

x & y have different signs

(1) xyz < 0

xy is negative ....so z must be positive..... answer to question is NO (negative value can't be greater than positive one).

Sufficient

(2) x > yz

Let x =negative value then y is positive value. So z is negative.

Divide by y

x/y>z

Let x =positive value then y is negative value. So z is either positive or negative.

Divide by y then flip sign

x/y<z

Insufficient

VP  V
Joined: 23 Feb 2015
Posts: 1128
Re: If xy < 0, is x/y > z ? (1) xyz < 0 (2) x > yz  [#permalink]

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peachfuzz wrote:
If xy < 0, is x/y > z ?
2 scenarios
x is neg and y is pos
x is pos and y is neg

(1) xyz < 0
x is neg, y pos, z pos
x is pos, y neg, z pos
Both scenarios make z larger than x/y
Sufficient

(2) x > yz
x is neg, y pos, z neg
X is pos, y negative, z pos
If z is neg the question is yes
If z is positive question is no
Insufficient

I'm just talking about the red part..
In the question stem: if xy<0, then
x-->(+)
y-->(-)

or,
x-->(-)
y-->(+)
If z is negative, the answer can't be YES always.
Here is test cases:
suppose,
x=-10
y=5
and z=-6
then, x/y>z?
-->-10/5>-6?
-->-2>-6?
--> YES
But, if
x=-10
y=5
and z=-1,
then, x/y>z?
-->-10/5>-1?
-->-2>-1?
-->NO....
Am I right Bunuel?
Thank you brother...
_________________
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Manager  G
Joined: 29 Oct 2016
Posts: 209
Concentration: Finance, Economics
GMAT 1: 620 Q50 V24 GRE 1: Q167 V147 If xy < 0, is x/y > z ? (1) xyz < 0 (2) x > yz  [#permalink]

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If xy < 0, is x/y > z ?

(1) xyz < 0
(2) x > yz

From stmt (1) and xy < 0,we can conclude that z > 0.
Since x and y must have the opposite sign,x/y <0.Thus,x/y < z.SUFFICIENT

From stmt (2)
x > yz.It could be transform to x/y > z ONLY if y > 0.We don't know for sure that y must be > 0.INSUFFICIENT

Ans A
Intern  B
Joined: 14 Feb 2018
Posts: 18
Re: If xy < 0, is x/y > z ? (1) xyz < 0 (2) x > yz  [#permalink]

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Are there any links anyone can provide that can help me with a strategy to solve these type of questions?
Math Expert V
Joined: 02 Sep 2009
Posts: 56366
Re: If xy < 0, is x/y > z ? (1) xyz < 0 (2) x > yz  [#permalink]

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1 Re: If xy < 0, is x/y > z ? (1) xyz < 0 (2) x > yz   [#permalink] 02 Sep 2018, 21:23
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