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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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27 Sep 2018, 05:57
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82% (00:52) correct 18% (01:32) wrong based on 66 sessions

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

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

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

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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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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.

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

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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

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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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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.

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