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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] New post 30 Sep 2010, 05:09
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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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Re: Inequality sign [#permalink] New post 30 Sep 2010, 05:23
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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.

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] New post 30 Sep 2010, 05:28
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] New post 30 Sep 2010, 05:33
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Re: Inequality sign [#permalink] New post 30 Sep 2010, 05:34
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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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Re: Inequality sign [#permalink] New post 30 Sep 2010, 05:53
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] New post 30 Sep 2010, 14:30
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] New post 30 Sep 2010, 14:36
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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] New post 30 Sep 2010, 16:16
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] New post 30 Sep 2010, 20:46
@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] New post 30 Sep 2010, 22:40
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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] New post 01 Oct 2010, 03:40
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] New post 01 Oct 2010, 04:29
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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] New post 01 Oct 2010, 06:54
thanks for ur reply
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Re: Inequality sign [#permalink] New post 01 Oct 2010, 08:53
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] New post 19 Apr 2013, 11:26
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] New post 19 Apr 2013, 11:32
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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
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Re: is a^7 * b^2 * c^3 > 0 ? [#permalink] New post 19 Apr 2013, 11:35
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] New post 20 Apr 2013, 03:54
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Re: is a^7 * b^2 * c^3 > 0 ?   [#permalink] 20 Apr 2013, 03:54
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