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# Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0?

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Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0? [#permalink]  25 Aug 2012, 03:59
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Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?

(1) XY > Z^4
(2) X > Z
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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0? [#permalink]  25 Aug 2012, 04:19
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Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?

Notice that since z is a non-zero integer, then z^4>0, so we can reduce the given inequality by it and the question becomes: is x^3*y^5>0? or: is xy>0?

(1) XY > Z^4 --> since z^4>0, then we have that xy>z^4>0. Sufficient.
(2) X > Z. Not sufficient as we don't know anything about y.

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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0? [#permalink]  25 Aug 2012, 04:23
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vinay911 wrote:
Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?

(1) XY > Z^4
(2) X > Z

The sign of the given expression depends on the sign of the product XY because X^3Y^5Z^4=XY*X^2Y^4Z^4 and X^2Y^4Z^4 is always non-negative. The given product can be 0 as well, if at least one of the variables is 0.

(1) Not sufficient, because Z can be 0.
(2) Not sufficient, because Z can be 0.

(1) and (2): Although from (1) we can deduce that XY>0, (because Z^4\geq0) again not sufficient, the same fast reasoning, Z can still be 0.
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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0? [#permalink]  25 Aug 2012, 04:34
Expert's post
EvaJager wrote:
vinay911 wrote:
Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?

(1) XY > Z^4
(2) X > Z

The sign of the given expression depends on the sign of the product XY because X^3Y^5Z^4=XY*X^2Y^4Z^4 and X^2Y^4Z^4 is always non-negative. The given product can be 0 as well, if at least one of the variables is 0.

(1) Not sufficient, because Z can be 0.
(2) Not sufficient, because Z can be 0.

(1) and (2): Although from (1) we can deduce that XY>0, (because Z^4\geq0) again not sufficient, the same fast reasoning, Z can still be 0.

Eva, notice that we are told that X, Y, Z are non zero integers.
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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0? [#permalink]  25 Aug 2012, 04:47
Bunuel wrote:
EvaJager wrote:
vinay911 wrote:
Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?

(1) XY > Z^4
(2) X > Z

The sign of the given expression depends on the sign of the product XY because X^3Y^5Z^4=XY*X^2Y^4Z^4 and X^2Y^4Z^4 is always non-negative. The given product can be 0 as well, if at least one of the variables is 0.

(1) Not sufficient, because Z can be 0.
(2) Not sufficient, because Z can be 0.

(1) and (2): Although from (1) we can deduce that XY>0, (because Z^4\geq0) again not sufficient, the same fast reasoning, Z can still be 0.

Eva, notice that we are told that X, Y, Z are non zero integers.

Oooooops! Thanks.

So, forget about any of the variables being 0. We need to check whether XY>0.
Then the above solution changes:

(1) Sufficient, since XY>0, (because Z^4>0).
(2) Not sufficient, as we don't know anything about Y.

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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0? [#permalink]  26 Aug 2012, 09:34
Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?

(1) XY > Z^4
(2) X > Z

My approach :-

(i) XY>Z^4
RHS is always +ve , so XY both can either be +ve or -ve
a)if XY both +ve then (X^3)(Y^5)(Z^4)>0 (because Z^4 is +ve
b)if XY both -ve then (X^3)(Y^5)(Z^4)>0 (because - - + is +ve

Suffficient

(ii) no clue about Y -insufficient

(A) wins
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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0? [#permalink]  26 Aug 2012, 21:07
it is given that x, y and z are no zero integer, if so z^4 is always positive what ever the z is.

to be positive the given expression we have to determine whether x and y have the same sign or not, keeping in mind that x and y have odd power.

statement 1

xy > z^4
XY > positive that means X and Y have the same sign

so the given expression must be positive

statement 1 is sufficient

statement 2 does not tell anything about y so insufficient

please correct me if i am wrong
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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0?   [#permalink] 26 Aug 2012, 21:07
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# Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0?

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