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# If x^5y^4z^2 <0 , which of the following must be true?

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
If x^5y^4z^2 <0 , which of the following must be true?  [#permalink]

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13 May 2016, 04:59
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85% (01:07) correct 15% (01:28) wrong based on 124 sessions

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If $$x^5y^4z^2 <0$$ , which of the following must be true?

I. xy <0
II. yz <0
III. xz <0

A. I
B. II
C. III
D. I and II
E. None

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Schools: ISB '17
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Re: If x^5y^4z^2 <0 , which of the following must be true?  [#permalink]

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13 May 2016, 06:44
Ans:- x^5y^4z^2 <0

x must be negative. x<0 ; y and z can be either negative or positive as even powers is always positive.

I. xy <0 :- x<0 but y can be - or + hence xy < 0 when y>0 or xy >0 when y <0. So not always true.

II. yz <0 :- As both y and z can be + or - ; yz < 0 or yz >0 are possible

II. xz <0 :- x<0 but z can be - or + hence xz < 0 when z>0 or xz >0 when z <0. So not always true.

Ans :- E
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Re: If x^5y^4z^2 <0 , which of the following must be true?  [#permalink]

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13 May 2016, 07:05
The entire expression can be evaluated as (x) ^ (40yz)
1. For the expression to be less than the evaluated expression must be negative for which :
- X must be negative
- 40yz must be odd

2. While X can be negative, a multiple of an even number 40 is always even hence the "-" sign will get cancelled out leaving a higher value than 0.

Therefore, only option is E - None.
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Re: If x^5y^4z^2 <0 , which of the following must be true?  [#permalink]

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12 Jul 2016, 08:39
Bunuel wrote:
If x^5y^4z^2 <0 , which of the following must be true?

I. xy <0
II. yz <0
III. xz <0

A. I
B. II
C. III
D. I and II
E. None

Sorry! I'm having problem to read the question. Can the question be rewritten as (x^5)(y^4)(z^2)<0? or it's like (((x^5y))^4z)^2<0?
Math Expert
Joined: 02 Sep 2009
Posts: 58464
Re: If x^5y^4z^2 <0 , which of the following must be true?  [#permalink]

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12 Jul 2016, 09:24
iqbalfiery wrote:
Bunuel wrote:
If x^5y^4z^2 <0 , which of the following must be true?

I. xy <0
II. yz <0
III. xz <0

A. I
B. II
C. III
D. I and II
E. None

Sorry! I'm having problem to read the question. Can the question be rewritten as (x^5)(y^4)(z^2)<0? or it's like (((x^5y))^4z)^2<0?

_________________
Edited. Thank you.

It's $$x^5y^4z^2 <0$$
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Re: If x^5y^4z^2 <0 , which of the following must be true?  [#permalink]

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08 Aug 2018, 04:30
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Re: If x^5y^4z^2 <0 , which of the following must be true?   [#permalink] 08 Aug 2018, 04:30
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