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# M21-30

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Math Expert
Joined: 02 Sep 2009
Posts: 50613

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16 Sep 2014, 00:15
7
7
00:00

Difficulty:

85% (hard)

Question Stats:

26% (00:53) correct 74% (00:40) wrong based on 169 sessions

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Is $$x^2*y^3*z \gt 0$$?

(1) $$yz \gt 0$$

(2) $$xz \lt 0$$

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Math Expert
Joined: 02 Sep 2009
Posts: 50613

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16 Sep 2014, 00:15
3
2
Official Solution:

Inequality $$x^2*y^3*z \gt 0$$ to be true:

1. $$y$$ and $$z$$ must be either both positive or both negative, so they must have the same sign (in this case $$y^3*z$$ will be positive);

AND

2. $$x$$ must not be zero (in this case $$x^2$$ will be positive).

(1) $$yz \gt 0$$. From this statement it follows that $$y$$ and $$z$$ are either both positive or both negative, so the first condition is satisfied. But we don't know about $$x$$ (the second condition). Not sufficient.
(2) $$xz \lt 0$$. From this statement it follows that $$x \ne 0$$, so the second condition is satisfied. Don't know about the signs of $$y$$ and $$z$$ (the first condition). Not sufficient. (1)+(2) Both conditions are satisfied. Sufficient.

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Concentration: General Management, Operations
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12 Feb 2016, 00:34
great question
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KUDO me plenty

Manager
Joined: 27 Aug 2014
Posts: 77

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15 Mar 2016, 21:26
Bunuel wrote:
Is $$x^2*y^3*z \gt 0$$?

(1) $$yz \gt 0$$

(2) $$xz \lt 0$$

Hi

Can you pls help with testing both statements combined. I tried bringing them both down to the same inequality sign that mostly works in linear equations bur getting stuck in non-linear set up here.
yz>0 or -yz<0 1)
xz<0 2)
Tried dividing 1) and 2) but end up losing z and any clue on its sign. Pls advice on how this process can be made to work. Thanks.
Manager
Joined: 15 May 2010
Posts: 163
Location: India
Concentration: Strategy, General Management
WE: Engineering (Manufacturing)

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21 Mar 2016, 05:45
1
even if we don't know about x, in case of both positive or negative x will not affect since it is in square. So, how A is wrong?

Thanks,

Bunuel wrote:
Official Solution:

Inequality $$x^2*y^3*z \gt 0$$ to be true:

1. $$y$$ and $$z$$ must be either both positive or both negative, so they must have the same sign (in this case $$y^3*z$$ will be positive);

AND

2. $$x$$ must not be zero (in this case $$x^2$$ will be positive).

(1) $$yz \gt 0$$. From this statement it follows that $$y$$ and $$z$$ are either both positive or both negative, so the first condition is satisfied. But we don't know about $$x$$ (the second condition). Not sufficient.
(2) $$xz \lt 0$$. From this statement it follows that $$x \ne 0$$, so the second condition is satisfied. Don't know about the signs of $$y$$ and $$z$$ (the first condition). Not sufficient. (1)+(2) Both conditions are satisfied. Sufficient.

Math Expert
Joined: 02 Sep 2009
Posts: 50613

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21 Mar 2016, 05:53
sun01 wrote:
even if we don't know about x, in case of both positive or negative x will not affect since it is in square. So, how A is wrong?

Thanks,

Bunuel wrote:
Official Solution:

Inequality $$x^2*y^3*z \gt 0$$ to be true:

1. $$y$$ and $$z$$ must be either both positive or both negative, so they must have the same sign (in this case $$y^3*z$$ will be positive);

AND

2. $$x$$ must not be zero (in this case $$x^2$$ will be positive).

(1) $$yz \gt 0$$. From this statement it follows that $$y$$ and $$z$$ are either both positive or both negative, so the first condition is satisfied. But we don't know about $$x$$ (the second condition). Not sufficient.
(2) $$xz \lt 0$$. From this statement it follows that $$x \ne 0$$, so the second condition is satisfied. Don't know about the signs of $$y$$ and $$z$$ (the first condition). Not sufficient. (1)+(2) Both conditions are satisfied. Sufficient.

If x is 0, then $$x^2y^3z$$ will be 0, not more than 0.
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Status: Brushing up rusted Verbal....
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Location: India
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GMAT Date: 11-30-2014
GPA: 3.96
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07 Sep 2016, 02:08
Is x^2∗y^3∗z>0?
(1) yz>0
(2) xz<0

Question breakup/understanding:
x^2∗y^3∗z>0
it can be possible only if we know below two facts:
I) x NOT EQUAL to 0
II) y and z are of same sign.

Statement 1: yz> 0
it means both y and z can be either positive or negative.
But no info on X
Thus not sufficient.

Statement 2: xz<0
It means either x and z are of opposite sign
It also tells the x NOT EQUAL to 0.
But no info on y.
Thus not sufficient.

Combine both Statement
we get X NOT EQUAL to 0.
Y and Z of same sign.
Thus sufficient.

other way
yz>0 (Eq 1)
xz<0 (Eq 2)
yz-xz>0
z(y-x) >0
Thus
z >0 and y-x>0
this ensures z,y same sign.
Already we know x not equal to 0 received from Eq 2
Thus Sufficient.

Please correct me if i am wrong anywhere.
Ans: C
Senior Manager
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13 Dec 2017, 07:49
+1 for C. To find the answer to this question, we need to know a) if any of x,y,or z is equal to zero or not. b) yz > 0 or not. (xy)^2*(yz).
Statement 1 gives yz>0 and y,z are not equal to 0. --> Not sufficient
Statement 2 gives x and z are not equal to 0. --> Not sufficient

Both 1 and 2 ---> Sufficient. We come to know that x,y,and z are non zero and that yz>0. Hence option C.
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Intern
Joined: 11 Apr 2016
Posts: 7
WE: Information Technology (Telecommunications)

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24 Apr 2018, 19:34
1
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 03 May 2017
Posts: 3
Concentration: General Management, Technology

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25 Aug 2018, 00:55
HI Bunuel,

If X=-1/4 Y=1 Z=1
then answer will be a no.

But if X=2 Y=-2 Z=-2
then answer will be a Yes.

No where it has been said that all three are integers.

Math Expert
Joined: 02 Sep 2009
Posts: 50613

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25 Aug 2018, 02:16
Milind27 wrote:
HI Bunuel,

If X=-1/4 Y=1 Z=1
then answer will be a no.

But if X=2 Y=-2 Z=-2
then answer will be a Yes.

No where it has been said that all three are integers.

If x = -1/4, y = 1, and z = 1, then $$x^2*y^3*z = positive*positive*positive \gt 0$$. So, the answer is still YES.

(1) $$yz \gt 0$$

(2) $$xz \lt 0$$
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Re: M21-30 &nbs [#permalink] 25 Aug 2018, 02:16
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# M21-30

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