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If none of x, y, & z equals to 0, is x^4y^5z^6 > 0?

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If none of x, y, & z equals to 0, is x^4y^5z^6 > 0?  [#permalink]

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New post 27 Sep 2018, 05:57
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86% (00:45) correct 14% (01:38) wrong based on 57 sessions

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Re: If none of x, y, & z equals to 0, is x^4y^5z^6 > 0?  [#permalink]

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New post 27 Sep 2018, 06:17
Bunuel wrote:
If none of x, y, & z equals to 0, is \(x^4y^5z^6 > 0\)?


(1) \(y > x^4\)

(2) \(y > z^5\)


Statement (1) tells us that y >0 because x^4 must be positive.

This is sufficient. If neither x, y, or z = 0 and y is positive, then we know that \(x^4y^5z^6 > 0\) = positive


Statement (2) does not tell us that y is positive or negative. z could be negative which would make \(z^5\) negative.

Not Sufficient.


Answer = A
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Re: If none of x, y, & z equals to 0, is x^4y^5z^6 > 0?  [#permalink]

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New post 27 Sep 2018, 06:33
x and z will always be positive, despite the +- nature of x,z as they have even powers.
We have to detect weather y is + or -

1. y is greater than positive \(x^4\). y is positive. suff.
2. as we dont know the +- nature of z, we cant say for sure y is positive or not. not suff

IMO
Ans: A
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If none of x, y, & z equals to 0, is x^4y^5z^6 > 0?  [#permalink]

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New post Updated on: 29 Sep 2018, 07:40
Bunuel wrote:
If none of x, y, & z equals to 0, is \(x^4y^5z^6 > 0\)?


(1) \(y > x^4\)

(2) \(y > z^5\)


For \(x^4y^5z^6 > 0\) to be true, \(x^4\), \(y^5\) and \(z^6\) have to be all positive numbers.

x and z could be negative numbers themselves but their positive even powers will turn them into positive numbers.

The real question here is if y is a positive number or negative.

(1) \(y > x^4\)

\(x^4\) we know is an even number because of the positive even power of x and if y is greater than that, it means y is a positive number.

Thus, Positive x Positive x Positive > 0

SUFFICIENT


(2) \(y > z^5\)

If z is positive, \(z^5\) will be positive and a y greater than that will be positive too. That will result in Even x Even x Even > 0

However, if z is negative, \(z^5\) will be negative as well and a y greater than that could either be negative or positive.

Thus, Positive x Negative x Positive < 0

INSUFFICIENT

The answer is A.
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Originally posted by MsInvBanker on 27 Sep 2018, 09:55.
Last edited by MsInvBanker on 29 Sep 2018, 07:40, edited 1 time in total.
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Re: If none of x, y, & z equals to 0, is x^4y^5z^6 > 0?  [#permalink]

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New post 29 Sep 2018, 07:32
Bunuel wrote:
If none of x, y, & z equals to 0, is \(x^4y^5z^6 > 0\)?


(1) \(y > x^4\)

(2) \(y > z^5\)



\(x^4\) and \(z^6\)yields a positive result . thus we all about need to know whether y is positive.

Statement 1: \(y>x^4\). \(x^4\) will always be positive. thus y has to be positive. Sufficient.

Statement : \(y>z^5\). NOT clear. z= -2.\(z^5 = -32\) and y = -2. NOT sufficient.

The best answer is A.
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Re: If none of x, y, & z equals to 0, is x^4y^5z^6 > 0? &nbs [#permalink] 29 Sep 2018, 07:32
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