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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

1

This post received KUDOS

Expert's post

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.

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

1

This post received KUDOS

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. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

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. _________________

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.

Answer A _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

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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