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

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

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New post 21 Dec 2018, 04:24
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Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?

(1) XY>Z^4

(2) X > Z
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Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?  [#permalink]

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New post 21 Dec 2018, 10:12
Question, whether \(X^3Y^5Z^4 > 0\)

From statement 1:

\(XY > Z^4\)
Since Z^4 is always positive.
Either X and Y are both negative or X and Y are both positive.
Hence, \(X^3Y^5Z^4\) will always be greater than 0.
Sufficient.

From statement 2:

\(X > Z\)
If X = -2 and Z = -3.
-2 > -3
But, \(X^3Y^5Z^4 < 0\)
If x = 2 and Z = 1.
Then \(X^3Y^5Z^4 > 0\)
Hence, Insufficient.

A is the answer.
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Re: Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?  [#permalink]

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New post 08 Jan 2019, 18:33
We need to see whether both x and y are positive or not for the inequality to be true.

1. product of xy is greater than z^4. We already know that z^4 will be positive so xy is positive. Hence Sufficient

2. we cannot conclude the value of y (+ve or -ve). Insufficient.

Hence A is the answer
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Re: Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?  [#permalink]

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New post 09 Jan 2019, 06:29
To prove: X^3*Y^5*Z^4>0
For this statement to be true, following cases must be satisfied:
Case 1: All terms: x^(3), y^(5) and z^(4) are positive
so possible values :X,Y should be positive, Z can be positive or negative
Case 2: z^(4) is positive, y^(5)*x^(3) is negative
Possible values:Z is positive/negative, y is positive, x is negative...xy is negative
Z is positive/negative, x is positive, y is negative.....xy is negative

Statement 1: XY>Z^4
z^(4) is always positive. so XY is also positive. so from above, case 1 is satisfied. Statement is sufficient

Statement 2: X>Z
Insufficient

Answer A
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Re: Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?  [#permalink]

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New post 09 Jan 2019, 09:54
chand567 wrote:
Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?

(1) XY>Z^4

(2) X > Z



(1) XY> Z^4. Since X>4 must >0, this means XY>0. This is good because we can factor out XY without changing the sign of our expression

XY(x^2Y^4Z^4) >0 Now, since xy>0, x^2,y^2, z^4 must >0 then the entire expression must >0 Suff

(2) X> Z Suppose x=-2 z=-1 y=1 our expression becomes (-2)^3(1)^5(1)^4<0 giving us a NO. Now suppose x=1, y=1 Z=1, our expression becomes 1>0 giving us a yes. Since we get a Yes and a No by testing different appropriate values (2) is NS

Answer is A
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Re: Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ? &nbs [#permalink] 09 Jan 2019, 09:54
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Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?

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