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Is (x^7)(y^2)(z^3)>0? [#permalink]
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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 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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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. 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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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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30 Sep 2010, 06:33



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Re: Inequality sign [#permalink]
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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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Re: Inequality sign [#permalink]
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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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Re: Inequality sign [#permalink]
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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. 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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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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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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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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30 Sep 2010, 23:40



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Re: Inequality sign [#permalink]
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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 & zve 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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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 & zve 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 nonnegative > \(y^2\geq{0}\). 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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01 Oct 2010, 07:54
thanks for ur reply



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Re: Inequality sign [#permalink]
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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




Re: is a^7 * b^2 * c^3 > 0 ?
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