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# M25-34

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Math Expert
Joined: 02 Sep 2009
Posts: 48041

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16 Sep 2014, 01:24
3
19
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Difficulty:

95% (hard)

Question Stats:

28% (01:01) correct 72% (00:54) wrong based on 460 sessions

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Is $$(x^7)(y^2)(z^3) \gt 0$$ ?

(1) $$yz \lt 0$$

(2) $$xz \gt 0$$

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Math Expert
Joined: 02 Sep 2009
Posts: 48041

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16 Sep 2014, 01:24
4
9
Official Solution:

Inequality $$x^7*y^2*z^3 \gt 0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (in order $$x^7*z^3$$ to be positive) AND $$y$$ must not be zero (in order $$x^7*y^2*z^3$$ not to equal to zero).

(1) $$yz \lt 0$$. This statement implies that $$y \neq 0$$. Don't know about $$x$$ and $$z$$. Not sufficient.

(2) $$xz \gt 0$$. This statement implies that $$x$$ and $$z$$ are either both positive or both negative. Don't know about $$y$$: if $$y=0$$, then the expression is not positive it's equal 0 . Not sufficient.

Notice that if 

(1)+(2) Sufficient.

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Joined: 23 Oct 2014
Posts: 4

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17 Nov 2014, 04:54
1
Bunuel wrote:
Official Solution:

Inequality $$x^7*y^2*z^3 \gt 0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (in order $$x^7*z^3$$ to be positive) AND $$y$$ must not be zero (in order $$x^7*y^2*z^3$$ not to equal to zero).

(1) $$yz \lt 0$$. This statement implies that $$y \neq 0$$. Don't know about $$x$$ and $$z$$. Not sufficient.

(2) $$xz \gt 0$$. This statement implies that $$x$$ and $$z$$ are either both positive or both negative. Don't know about $$y$$. Not sufficient.

(1)+(2) Sufficient.

Hi Bunuel, for (2) don't we know that y is always positive given it's raised to the power of 2 (and there's no imaginery numbers on the GMAT)?

Therefore, if y is always positive, then (2) is sufficient?
Intern
Joined: 25 Dec 2012
Posts: 17

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17 Nov 2014, 06:19
1
illusion10 wrote:
Bunuel wrote:
Official Solution:

Inequality $$x^7*y^2*z^3 \gt 0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (in order $$x^7*z^3$$ to be positive) AND $$y$$ must not be zero (in order $$x^7*y^2*z^3$$ not to equal to zero).

(1) $$yz \lt 0$$. This statement implies that $$y \neq 0$$. Don't know about $$x$$ and $$z$$. Not sufficient.

(2) $$xz \gt 0$$. This statement implies that $$x$$ and $$z$$ are either both positive or both negative. Don't know about $$y$$. Not sufficient.

(1)+(2) Sufficient.

Hi Bunuel, for (2) don't we know that y is always positive given it's raised to the power of 2 (and there's no imaginery numbers on the GMAT)?

Therefore, if y is always positive, then (2) is sufficient?

Yes I agree, I think the answer must be B, because with the information given the answer is always > 0
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Joined: 17 Oct 2012
Posts: 68
Location: India
Concentration: Strategy, Finance
WE: Information Technology (Computer Software)

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17 Nov 2014, 06:32
illusion10 wrote:
Bunuel wrote:
Official Solution:

Inequality $$x^7*y^2*z^3 \gt 0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (in order $$x^7*z^3$$ to be positive) AND $$y$$ must not be zero (in order $$x^7*y^2*z^3$$ not to equal to zero).

(1) $$yz \lt 0$$. This statement implies that $$y \neq 0$$. Don't know about $$x$$ and $$z$$. Not sufficient.

(2) $$xz \gt 0$$. This statement implies that $$x$$ and $$z$$ are either both positive or both negative. Don't know about $$y$$. Not sufficient.

(1)+(2) Sufficient.

Hi Bunuel, for (2) don't we know that y is always positive given it's raised to the power of 2 (and there's no imaginery numbers on the GMAT)?

Therefore, if y is always positive, then (2) is sufficient?

For statement (2), Y could be zero also, in that case $$x^7*y^2*z^3 \gt 0$$ will not hold true.
Intern
Joined: 25 Dec 2012
Posts: 17

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17 Nov 2014, 06:35
gbascurs wrote:
illusion10 wrote:
Bunuel wrote:
Official Solution:

Inequality $$x^7*y^2*z^3 \gt 0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (in order $$x^7*z^3$$ to be positive) AND $$y$$ must not be zero (in order $$x^7*y^2*z^3$$ not to equal to zero).

(1) $$yz \lt 0$$. This statement implies that $$y \neq 0$$. Don't know about $$x$$ and $$z$$. Not sufficient.

(2) $$xz \gt 0$$. This statement implies that $$x$$ and $$z$$ are either both positive or both negative. Don't know about $$y$$. Not sufficient.

(1)+(2) Sufficient.

Hi Bunuel, for (2) don't we know that y is always positive given it's raised to the power of 2 (and there's no imaginery numbers on the GMAT)?

Therefore, if y is always positive, then (2) is sufficient?

Yes I agree, I think the answer must be B, because with the information given the answer is always > 0

I saw what is the problem with B, Y can be 0 or not.....
Intern
Joined: 23 Oct 2014
Posts: 4

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19 Nov 2014, 03:51
1
chetan86 wrote:
illusion10 wrote:
Bunuel wrote:
Official Solution:

Inequality $$x^7*y^2*z^3 \gt 0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (in order $$x^7*z^3$$ to be positive) AND $$y$$ must not be zero (in order $$x^7*y^2*z^3$$ not to equal to zero).

(1) $$yz \lt 0$$. This statement implies that $$y \neq 0$$. Don't know about $$x$$ and $$z$$. Not sufficient.

(2) $$xz \gt 0$$. This statement implies that $$x$$ and $$z$$ are either both positive or both negative. Don't know about $$y$$. Not sufficient.

(1)+(2) Sufficient.

Hi Bunuel, for (2) don't we know that y is always positive given it's raised to the power of 2 (and there's no imaginery numbers on the GMAT)?

Therefore, if y is always positive, then (2) is sufficient?

For statement (2), Y could be zero also, in that case $$x^7*y^2*z^3 \gt 0$$ will not hold true.

Thanks, definitely got caught out on that trap!
Intern
Joined: 12 Oct 2014
Posts: 1

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31 Dec 2014, 02:47
I think the answer should be B. Given that Y is squared, it can be inferred that the middle Y term is POSITIVE. If both X and Z are negative, it yields a final positive number. Likewise, if both X and Z are positive, it yields a final positive number as well.
Math Expert
Joined: 02 Sep 2009
Posts: 48041

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31 Dec 2014, 04:54
meisin123 wrote:
I think the answer should be B. Given that Y is squared, it can be inferred that the middle Y term is POSITIVE. If both X and Z are negative, it yields a final positive number. Likewise, if both X and Z are positive, it yields a final positive number as well.

y^2 is not positive, it's non-negative, so it CAN be 0.
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Joined: 03 Aug 2011
Posts: 289
Concentration: Strategy, Finance
GMAT 1: 640 Q44 V34
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15 Feb 2015, 05:08
2
I just love this kind of GMAT questions. They know after reading (A) you will assume you know what "y" is. Genious!
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Thank you very much for reading this post till the end! Kudos?

Intern
Joined: 15 Aug 2014
Posts: 7
GMAT 1: 640 Q47 V31

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09 Apr 2015, 07:26
I got this question in the GMATClub test and picked B as the answer. Should have considered y could also be zero.

Really nice question, thank you!
Manager
Joined: 28 Dec 2013
Posts: 68

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04 Nov 2015, 16:28
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. There's not a clear explanation why c is sufficient can you please show with numbers ?
Senior Manager
Joined: 31 Mar 2016
Posts: 400
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

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22 Aug 2016, 04:30
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 12 Jan 2017
Posts: 16

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13 Jul 2018, 07:09
Bunuel wrote:
Official Solution:

Inequality $$x^7*y^2*z^3 \gt 0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (in order $$x^7*z^3$$ to be positive) AND $$y$$ must not be zero (in order $$x^7*y^2*z^3$$ not to equal to zero).

(1) $$yz \lt 0$$. This statement implies that $$y \neq 0$$. Don't know about $$x$$ and $$z$$. Not sufficient.

(2) $$xz \gt 0$$. This statement implies that $$x$$ and $$z$$ are either both positive or both negative. Don't know about $$y$$: if $$y=0$$, then the expression is not positive it's equal 0 . Not sufficient.

Notice that if 

(1)+(2) Sufficient.

This is a super sneaky one because generally I think you'll see xyz =/= 0, whereas here it's not present and the test-taker will still assume it.
Re: M25-34 &nbs [#permalink] 13 Jul 2018, 07:09
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# M25-34

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