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Is (x^7)(y^2)(z^3)>0?

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Is (x^7)(y^2)(z^3)>0? [#permalink]

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New post 30 Sep 2010, 06:09
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Is (x^7)(y^2)(z^3)>0?

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

[Reveal] Spoiler:
From GMAT Club Test - m25 - Q34

The OA is C but I think it's E
Statement (1) : clearly insufficient since we don't have the sign of Z (since it has an odd exponent)
Statement (2) : clearly insufficient since Y can be 0
Both (1) and (2) : well yes Y can't be 0 but we still can't tell the sign of Z ! Consider this example : X=4 , Y= -1, Z= -1 ; we will have both statements right but the original expression will be negative

Am I wrong ?
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Re: Inequality sign [#permalink]

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Barkatis wrote:
From GMAT Club Test - m25 - Q34

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

1. \(yz \lt 0\)
2. \(xz \gt 0\)




The OA is C but I think it's E
Statement (1) : clearly insufficient since we don't have the sign of Z (since it has an odd exponent)
Statement (2) : clearly insufficient since Y can be 0
Both (1) and (2) : well yes Y can't be 0 but we still can't tell the sign of Z ! Consider this example : X=4 , Y= -1, Z= -1 ; we will have both statements right but the original expression will be negative

Am I wrong ?


Inequality \(x^7*y^2*z^3>0\) to be true:
I. \(x\) and \(z\) must be either both positive or both negative, AND II. \(y\) must not be zero.

(1) \(yz<0\) --> \(y\neq{0}\) (II is satisfied). Don't know about \(x\) and \(z\). Not sufficient.

(2) \(xz>0\) --> \(x\) and \(z\) are either both positive or both negative (I is satisfied). Don't know about \(y\). Not sufficient.

(1)+(2) Both conditions are satisfied. Sufficient.

Answer: C.

As for your doubt: we are not interested in the sign of \(z\), we need \(x\) and \(z\) to be be either both positive or both negative. Next, your example is not valid: x=4, y=-1, z=-1 --> yz=4>0 and xz=-4<0 and we are given that \(yz<0\) and \(xz>0\).

Hope it helps.
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Re: Inequality sign [#permalink]

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New post 30 Sep 2010, 06:28
Am sorry, in the question is it x exponent z or the product between x and z ??

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Re: Inequality sign [#permalink]

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Re: Inequality sign [#permalink]

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Barkatis wrote:
Am sorry, in the question is it x exponent z or the product between x and z ??


It is the product.

Is \((x^7)(y^2)(z^3) \gt 0\) ? reduced to is Is \((x)(y^2)(z) \gt 0\) ? -> I have removed the squared values as they do not play any role in changing the sign, but I kept \(y^2\) to consider the y=0 condition.
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Re: Inequality sign [#permalink]

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New post 30 Sep 2010, 06:53
Bunuel wrote:
Barkatis wrote:
Am sorry, in the question is it x exponent z or the product between x and z ??


It's product: \(y*z<0\) and \(x*z>0\).


Ah oki ! Thanks I didn't pay attention to that

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Re: Inequality sign [#permalink]

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New post 30 Sep 2010, 15:30
Bunuel wrote:
From GMAT Club Test - m25 - Q34

Inequality \(x^7*y^2*z^3>0\) to be true:
I. \(x\) and \(z\) must be either both positive or both negative, AND II. \(y\) must not be zero.

(1) \(yz<0\) --> \(y\neq{0}\) (II is satisfied). Don't know about \(x\) and \(z\). Not sufficient.

(2) \(xz>0\) --> \(x\) and \(z\) are either both positive or both negative (I is satisfied). Don't know about \(y\). Not sufficient.

(1)+(2) Both conditions are satisfied. Sufficient.

Answer: C.

As for your doubt: we are not interested in the sign of \(z\), we need \(x\) and \(z\) to be be either both positive or both negative. Next, your example is not valid: x=4, y=-1, z=-1 --> yz=4>0 and xz=-4<0 and we are given that \(yz<0\) and \(xz>0\).

Hope it helps.



I have a doubt; Why can't B only be true because we care for x and z signs and from II either they both are +ive or -ive and this will provide us the result.
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Re: Inequality sign [#permalink]

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New post 30 Sep 2010, 15:36
onedayill wrote:
Bunuel wrote:
From GMAT Club Test - m25 - Q34

Inequality \(x^7*y^2*z^3>0\) to be true:
I. \(x\) and \(z\) must be either both positive or both negative, AND II. \(y\) must not be zero.

(1) \(yz<0\) --> \(y\neq{0}\) (II is satisfied). Don't know about \(x\) and \(z\). Not sufficient.

(2) \(xz>0\) --> \(x\) and \(z\) are either both positive or both negative (I is satisfied). Don't know about \(y\). Not sufficient.

(1)+(2) Both conditions are satisfied. Sufficient.

Answer: C.

As for your doubt: we are not interested in the sign of \(z\), we need \(x\) and \(z\) to be be either both positive or both negative. Next, your example is not valid: x=4, y=-1, z=-1 --> yz=4>0 and xz=-4<0 and we are given that \(yz<0\) and \(xz>0\).

Hope it helps.



I have a doubt; Why can't B only be true because we care for x and z signs and from II either they both are +ive or -ive and this will provide us the result.


Please read the solution carefully.

Inequality \(x^7*y^2*z^3>0\) to be true:
I. \(x\) and \(z\) must be either both positive or both negative, AND II. \(y\) must not be zero.

So for (2): we know that \(x\) and \(z\) are either both positive or both negative, BUT we don't know whether \(y\) equals to zero, because if it is then \(x^7*y^2*z^3=0\) and not more than zero.

Hope it's clear.
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Re: Inequality sign [#permalink]

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New post 30 Sep 2010, 17:16
Bunuel wrote:
onedayill wrote:
Bunuel wrote:
From GMAT Club Test - m25 - Q34

Inequality \(x^7*y^2*z^3>0\) to be true:
I. \(x\) and \(z\) must be either both positive or both negative, AND II. \(y\) must not be zero.

(1) \(yz<0\) --> \(y\neq{0}\) (II is satisfied). Don't know about \(x\) and \(z\). Not sufficient.

(2) \(xz>0\) --> \(x\) and \(z\) are either both positive or both negative (I is satisfied). Don't know about \(y\). Not sufficient.

(1)+(2) Both conditions are satisfied. Sufficient.

Answer: C.

As for your doubt: we are not interested in the sign of \(z\), we need \(x\) and \(z\) to be be either both positive or both negative. Next, your example is not valid: x=4, y=-1, z=-1 --> yz=4>0 and xz=-4<0 and we are given that \(yz<0\) and \(xz>0\).

Hope it helps.



I have a doubt; Why can't B only be true because we care for x and z signs and from II either they both are +ive or -ive and this will provide us the result.


Please read the solution carefully.

Inequality \(x^7*y^2*z^3>0\) to be true:
I. \(x\) and \(z\) must be either both positive or both negative, AND II. \(y\) must not be zero.

So for (2): we know that \(x\) and \(z\) are either both positive or both negative, BUT we don't know whether \(y\) equals to zero, because if it is then \(x^7*y^2*z^3=0\) and not more than zero.

Hope it's clear.


Sorry to say but still I didn't get this...

Why are we checking Y must not be zero?
Why can;t its be X or Z not to be zero
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Re: Inequality sign [#permalink]

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New post 30 Sep 2010, 21:46
@onedayill

we need not consider if x or z is equal to zero ...

BECAUSE if you are considering only stm2 seperately then it itself says that x*z>0 that means that none of them is zero atleast.

Hope this clarifies...

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Re: Inequality sign [#permalink]

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New post 30 Sep 2010, 23:40
onedayill wrote:
Sorry to say but still I didn't get this...

Why are we checking Y must not be zero?
Why can;t its be X or Z not to be zero


Statement (2) says \(xz>0\), so neither \(x\) nor \(z\) equals to zero.

Check similar problems for practice:
qs-98341.html?hilit=satisfied
m21-q30-96613.html?hilit=inequality%20true%20must

Hope it helps.
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Re: Inequality sign [#permalink]

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New post 01 Oct 2010, 04:40
from statement 1:
it depends on the value of x , x can be either positive or negative
so statement 1 not sufficient

from statement 2:
xz>0
case1: x +ve & z +ve
case 2: x -ve & z-ve
we know that y2 is +ve
so from case 1:x7y2z3= (+)(+)(+)= +
so from case 2:x7y2z3= (-)(+)(-)= +
so B alone sufficient

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Re: Inequality sign [#permalink]

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New post 01 Oct 2010, 05:29
anilnandyala wrote:
from statement 1:
it depends on the value of x , x can be either positive or negative
so statement 1 not sufficient

from statement 2:
xz>0
case1: x +ve & z +ve
case 2: x -ve & z-ve
we know that y2 is +ve
so from case 1:x7y2z3= (+)(+)(+)= +
so from case 2:x7y2z3= (-)(+)(-)= +
so B alone sufficient


And again: please read the solution above.

The red part is the reason of many mistakes on GMAT.

Square of a number is not positive, it's non-negative --> \(y^2\geq{0}\). So for (2): we know that \(x\) and \(z\) are either both positive or both negative, BUT we don't know whether \(y\) equals to zero, because if it is, then \(x^7*y^2*z^3=0\) and not more than zero.

Hope it's clear.
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Re: Inequality sign [#permalink]

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New post 01 Oct 2010, 07:54
thanks for ur reply

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Re: Inequality sign [#permalink]

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New post 01 Oct 2010, 09:53
Here the important thing is to remember that y can not be 0 if the statement is true. Therefore also statement A is needed.

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is a^7 * b^2 * c^3 > 0 ? [#permalink]

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New post 19 Apr 2013, 12:26
is a^7 * b^2 * c^3 >0

a) bc<0
b) ac>0

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Re: is a^7 * b^2 * c^3 > 0 ? [#permalink]

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Is \(a^7 * b^2 * c^3 >0\)

1) bc<0
2 options : +,- and -,+ but no info about a. Not sufficient

2) ac>0
2 options : +,+ and -,- but no info about b (That could equal 0 here's the trick in my opinion). Not sufficient

1+2) with 1 we know that \(b\neq{0}\)
with 2 in both cases a^8*c*3 is > 0
\(+^7*+*3>0\)
\(-^7*-^3>0\) as well
We are not able to say so by just looking at statement 2 because \(b\) could be \(0\), using both statement we can discard that possibility. Sufficient
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Re: is a^7 * b^2 * c^3 > 0 ? [#permalink]

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New post 19 Apr 2013, 12:35
Zarrolou wrote:
Is \(a^7 * b^2 * c^3 >0\)

1) bc<0
2 options : +,- and -,+ but no info about a. Not sufficient

2) ac>0
2 options : +,+ and -,- but no info about b (That could equal 0 here's the trick in my opinion)

1+2) with 1 we know that \(b\neq{0}\)
with 2 in both cases a^8*c*3 is > 0
\(+^7*+*3>0\)
\(-^7*-^3>0\) as well
We are not able to say so by just looking at statement 2 because \(b\) could be \(0\), using both statement we can discard that possibility
C


perfect , thanks man :)

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Re: is a^7 * b^2 * c^3 > 0 ? [#permalink]

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Re: is a^7 * b^2 * c^3 > 0 ?   [#permalink] 20 Apr 2013, 04:54
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