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If x^3y^4z^5<0, is xyz>0?

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If x^3y^4z^5<0, is xyz>0? [#permalink]

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New post 25 Aug 2017, 01:12
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If \(x^3y^4z^5<0\), is \(xyz>0\)?

1) \(y<0\)
2) \(x<0\)
[Reveal] Spoiler: OA

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If x^3y^4z^5<0, is xyz>0? [#permalink]

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MathRevolution wrote:
If \(x^3y^4z^5<0\), is \(xyz>0\)?

1) \(y<0\)
2) \(x<0\)



Hi..

In \(x^3y^4z^5<0\), y^4 will always be POSITIVE so y can be NEGATIVE or POSITIVE
Also one of x and z is + and other -, xz<0..
our answer will depend on y.


lets see the statements

1) y<0..
sufficient as shown above..
xz<0 and y<0 so xyz>0
sufficient

2) x<0
we just know that z>0
nothing about y..

insuff

A
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Re: If x^3y^4z^5<0, is xyz>0? [#permalink]

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New post 27 Aug 2017, 19:09
=>The original condition \(x^3y^4z^5<0\) is equivalent to xy < 0 after dividing both sides of the inequality by \(x^2y^4z^4\).
Then the question is equivalent to y>0, since xy < 0 from the equivalent condition.

Thus the condition 1) is sufficient, since the question is if y > 0.

Ans: A
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Re: If x^3y^4z^5<0, is xyz>0? [#permalink]

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New post 11 Sep 2017, 00:40
Given \(x^3\)\(y^4\)\(z^5\)<0
is xyz>0 ?

\(x^3\)\(y^4\)\(z^5\)<0 by this as total product is -ve and power of y is even => either x is -ve or z is -ve but not both. And here we don't know if y is +ve or -ve
Also as product is greater than 0, none of it is equal to 0.

so for xyz>0 the value will be dependent on y. as xz is always -ve (as 1 of it is +ve and other is -ve)
=> if y= -ve => xyz >0
=> if y= +ve => xyz <0

1) y<0
This directly tells us that y is -ve . => xyz >0 true. Sufficient

2) x<0
This just tell x=-ve and we can imply z=+ve. But we don't know anything about y.
So not sufficient.

Answer: A

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Re: If x^3y^4z^5<0, is xyz>0?   [#permalink] 11 Sep 2017, 00:40
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