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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

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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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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?

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, 01:52

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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

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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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