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

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Manager
Joined: 06 Oct 2009
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Location: Mexico
Concentration: Entrepreneurship, Finance
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WE: Sales (Commercial Banking)
If p is an integer and m= -p + (-2)^p, is m^3 >= -1 [#permalink]

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06 Jul 2010, 20:14
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Question Stats:

32% (00:51) correct 68% (01:58) wrong based on 31 sessions

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

(1) p is even

(2) $$p^3 \leq -1$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Jul 2016, 10:38, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Manager
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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
1
KUDOS
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
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.

Hope the above was useful.

regards,
Jack

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

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08 Jul 2010, 09:52
1
KUDOS
St-1 : P is even
M= -p+ (-2)^p
If P is positive, (-2)^p will be positive and greater than P,
So M will be positive and m^3 >= -1

If P is negative, -p will be positive and (-2)^p will be 1/(-2)^-p which is less than 1
So M will be positive and m^3 >=1, SUFFICIENT

St-2 : P^3 <= -1
Which implies P <= -1
So –P is positive.
(-2)^p will be less than 1

So M will be positive and m^3 >= 1, SUFFICIENT

SO Ans-D
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+1 kudos me if this is of any help...

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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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Manager
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Location: Mexico
Concentration: Entrepreneurship, Finance
GPA: 3.85
WE: Sales (Commercial Banking)
Re: If p is an integer and m= -p + (-2)^p, is m^3 >= -1 [#permalink]

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09 Jul 2010, 20:17
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!!

As always my friends, you made a great job... Correct answer D

Thanks pals..

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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
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If p is an integer and m= -p + (-2)^p, is m^3 >= -1   [#permalink] 20 Sep 2017, 05:16
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