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Math Expert V
Joined: 02 Sep 2009
Posts: 56304

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28 00:00

Difficulty:   95% (hard)

Question Stats: 27% (01:26) correct 73% (01:11) wrong based on 375 sessions

### HideShow timer Statistics Is $$(x^7)(y^2)(z^3) \gt 0$$ ?

(1) $$yz \lt 0$$

(2) $$xz \gt 0$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 56304

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10
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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Intern  Joined: 23 Oct 2014
Posts: 4

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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: 16

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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
Manager  Joined: 17 Oct 2012
Posts: 61
Location: India
Concentration: Strategy, Finance
WE: Information Technology (Computer Software)

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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: 16

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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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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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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 V
Joined: 02 Sep 2009
Posts: 56304

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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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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 ### Show Tags

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
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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
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I think this is a high-quality question and I agree with explanation.
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Joined: 12 Jan 2017
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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.
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Joined: 16 Jun 2018
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I don't agree with the explanation. I think the answer should be B, because if at we consider the value of any of the variables x / y/ z as 0, then the question in itself will not hold true.
Math Expert V
Joined: 02 Sep 2009
Posts: 56304

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Sheetal15 wrote:
I don't agree with the explanation. I think the answer should be B, because if at we consider the value of any of the variables x / y/ z as 0, then the question in itself will not hold true.

The correct answer is C. For (2) if y = 0, (which does NOT contradict the second statement) then the expression (x^7∗y^2∗z^3) will not positive it will be 0. This is explained couple of times above.
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Its easy to see that if we know the signs of x and z we can determine whether the question is > 0, PROVIDED Y =/= 0

Y= 0 must be tested here.

Statement 1 indicates that Y cannot equal 0, but doesn't indicate the signs of x, therefore Insufficient

Statement 2 indicates that xz> 0, but we don't know if y=0.

If y=0 then (positive)*0^even exponent is not greater than 0
If y is not equal to zero than (positive)*(y)^even exponent > 0
I tripped on this mistake myself. Making a note for retention.
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+1 Kudos if you like my post pls! Re: M25-34   [#permalink] 13 Jul 2019, 21:31
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# M25-34

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