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Re: If p is an integer and m= -p + (-2)^p, is m^3 >= -1 [#permalink]

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06 Jul 2010, 23:19

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Hi,

For condition 1, lets plug answers, p=2, m= -2 + (-2)^2 = 2 p=-2, m= -(-2) + (-2)^-2 = 2 + 0.25 p=0, m= 0 +1 So condition 1 is sufficient to Answer the Q

For condition 2, P3<=-1, hence p<=-1 Lets again plug answers, p=-2, m= 2 + 0.25 p=-3, m= 3 - 0.125 p=-1, m= 1 - 0.5 So again condition 2 is sufficient to answer the question.

Re: If p is an integer and m= -p + (-2)^p, is m^3 >= -1 [#permalink]

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08 Jul 2010, 10:42

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Bull78 wrote:

I can´t really see the answer!

If p is an integer and \(m= -p + (-2)^p\), is \(m^3>= -1\)

1) p is even

2) \(p^3<= -1\)

Many thanks to all!!

Is \(m^3>= -1\) mean that is \(m= -1,0,1,2,....\). So if we can find the value of \(m\) we can answer the question.

Stmt \(1\): \(p\) is even. If \(p\) is even then there are two cases, whether \(p\) is positive or negative. If p is positive, then \(-p\) is negative. At the same time \(-2^p\) will be positive & adding \(-p\) & \(-2^p\) will always be positive. ( You can plug in the numbers & check). Second case, if \(p\) is negative, then \(-p\) will be positive & \(-2^p\) will result in a fraction. In this case again \(m\) will be greater than \(-1\) & we can say that stmt 1 is sufficient.

Stmt \(2\): \(p^3<= -1\). It shows that \(p<0\), means \(p\) is negative. If \(p\) is negative then \(-p\) will be positive & \(-2^p\) will result in a fraction. The addition of \(-p\) & \(-2^p\) will give the positive result. Hence Stmt 2 is also sufficient.

Answer "D". Kindly correct if I am wrong.
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Re: If p is an integer and m= -p + (-2)^p, is m^3 >= -1 [#permalink]

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20 Sep 2017, 05:16

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