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

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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 ?
[Reveal] Spoiler: OA

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30 Sep 2010, 06:23
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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.

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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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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30 Sep 2010, 06:33
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 $$x*z>0$$.
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30 Sep 2010, 06:34
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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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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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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.

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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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.

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.

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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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.

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.

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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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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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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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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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

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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01 Oct 2010, 07:54

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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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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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19 Apr 2013, 12:32
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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
C
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Re: is a^7 * b^2 * c^3 > 0 ? [#permalink]

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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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20 Apr 2013, 04:54
yezz wrote:
is a^7 * b^2 * c^3 >0

a) bc<0
b) ac>0

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