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# If x^4*y < 0 and x*y^4 > 0 which of the following must be true?

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Intern
Joined: 21 Jun 2010
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If x^4*y < 0 and x*y^4 > 0 which of the following must be true? [#permalink]

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Updated on: 28 Sep 2015, 02:46
5
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5% (low)

Question Stats:

76% (00:55) correct 24% (01:00) wrong based on 260 sessions

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If x^4*y < 0 and x*y^4 > 0 which of the following must be true?

A) x > y
B) y > x
C) x = y
D) x < 0
E) y > 0

Originally posted by shamikba on 02 Jul 2010, 23:42.
Last edited by Bunuel on 28 Sep 2015, 02:46, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x^4*y < 0 and x*y^4 > 0 which of the following must be true? [#permalink]

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02 Jul 2010, 23:58
2
The first idea which comes up in mind is that $$x>0$$ & $$y<0$$. As $$x^4$$ cant be negative & if $$x^4 * y <0$$ then it implies that $$y<0$$, similarly the second inequality shows that $$x>0$$. But both these inequalities ($$x>0 & y<0$$) are not mentioned in the options, hence the only option then left is $$x>y$$ as $$x$$ is positive & $$y$$ is negative. So option "A" is correct.
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Re: If x^4*y < 0 and x*y^4 > 0 which of the following must be true? [#permalink]

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03 Jul 2010, 01:13
If x^4.y < 0 and x.y^4 > 0 which of the following must be true?

Start x^4.y < 0
x^4 >0 always so to satisfy above y<0

x.y^4 > 0
since y^4 > 0 x will be greater than zero. so x>0

hence x>0 & y<0

so ans is A
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Re: If x^4*y < 0 and x*y^4 > 0 which of the following must be true? [#permalink]

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28 May 2016, 08:41
Hi, l understand above solutions. But l tried solving the problem using another approach where l got stuck:

Given that, x^4 * y < 0 and y^4 * x > 0.
Hence, xy (y^3 - x^3) > 0 (As we can subtract inequalities with opposite direction)
So, xy (y-x)(y^2+xy+b^2)>0
From there we can say: y>x. Answer (B)
l know A is the correct choice here. Could someone help?

Regards.
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Re: If x^4*y < 0 and x*y^4 > 0 which of the following must be true? [#permalink]

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28 May 2016, 10:38
1
Hi, l understand above solutions. But l tried solving the problem using another approach where l got stuck:

Given that, x^4 * y < 0 and y^4 * x > 0.
Hence, xy (y^3 - x^3) > 0 (As we can subtract inequalities with opposite direction)
So, xy (y-x)(y^2+xy+b^2)>0
From there we can say: y>x. Answer (B)
l know A is the correct choice here. Could someone help?

Regards.

Hi,

$$xy (y-x)(y^2+xy+b^2)>0$$ can give you following cases...
1) all three xy, (y-x), and (y^2+xy+b^2) are >0...
2) Any two are '-' and the remaining third is '+'..

you have taken a case where all three are '+' ......
But xy<0 as x>0 and y<0..
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Re: If x^4*y < 0 and x*y^4 > 0 which of the following must be true? [#permalink]

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26 Sep 2017, 02:31
shamikba wrote:
If x^4*y < 0 and x*y^4 > 0 which of the following must be true?

A) x > y
B) y > x
C) x = y
D) x < 0
E) y > 0

shamikba please use brackets or gmatclub maths function to make the question clear . Is x^4*y = (x^4)*y or x^(4*y)
(x^4)*y < 0
Since x^4 >0 So, y<0

Also x*y^4 > 0
Since y^4 > 0. So, x>0

Hence y<0<x
So, x>y
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Re: If x^4*y < 0 and x*y^4 > 0 which of the following must be true? [#permalink]

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01 Oct 2017, 09:50
Hello experts,
What is the difference between must be true and could be true question? What particular we have to look for in both type of question?
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Re: If x^4*y < 0 and x*y^4 > 0 which of the following must be true? [#permalink]

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01 Oct 2017, 10:32
1
For must be true questions, all you have to do is work through options and try to find one case for which that option is not true. Then eliminate that option. Work through Process of elimination.
For could be true questions. all you have to do is work through the options and try to find one case for which any of the options is true. If you find even one case for which any one of the option is true. Pick that option.
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If x^4*y < 0 and x*y^4 > 0 which of the following must be true? [#permalink]

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01 Oct 2017, 12:52
shamikba wrote:
If $$(x^4)(y) < 0$$ and $$(x)(y^4) > 0$$ which of the following must be true?

A) x > y
B) y > x
C) x = y
D) x < 0
E) y > 0

$$(x^4)(y) < 0$$, is negative.

The term $$x^4$$, because raised to an even power, is positive.

So for the result to be negative, $$y$$ MUST be negative.

That is, we have
$$(x^4) (y) < 0$$ ----->
$$(+ term) (-) < 0$$ (result is negative)

Next: $$(x) (y^4) > 0$$ is positive.

Now the term $$y^4$$ is positive (raised to an even power). For the result to be positive, $$x$$ MUST be positive.

We have

$$(x) (y^4) > 0$$ ------>
$$(+)(+ term) > 0$$ (result is positive)

If x must be positive and y must be negative, x > y

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If x^4*y < 0 and x*y^4 > 0 which of the following must be true?   [#permalink] 01 Oct 2017, 12:52
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