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If m not equal to zero is m^3 > m^2 ?

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If m not equal to zero is m^3 > m^2 ? [#permalink]

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If m not equal to zero is m^3 > m^2 ?

(1) m > 0

(2) m^2 > m
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Sep 2012, 01:37, edited 1 time in total.
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Re: Is m ≠ 0, is m^3 > m^2? [#permalink]

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sasha40612 wrote:
7. Is m ≠ 0, is m^3 > m^2?
(1) m > 0
(2) m^2 > m



(1) m > 0

If m is between 0 and 1, \(m^3\) will be less than \(m^2\) e.g. \((1/2)^3 = 1/8\) while \((1/2)^2 = 1/4\).
If m is greater than 1, \(m^3\) will be greater than \(m^2\).
Not sufficient.

(2) \(m^2 > m\)
\(m^2 - m > 0\)
\(m(m - 1) > 0\)
So either m < 0 or m > 1
If m is negative, \(m^3\) is less than \(m^2\)
If m > 1, \(m^3\) is greater than \(m^2\)
Not sufficient.

Using both, we know that m>1. In this case \(m^3\) will be greater than \(m^2\). Sufficient.

Answer (C)
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Re: if m not equal to zero is m^3 > m^2 ? [#permalink]

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harikris wrote:

if m not equal to zero is m^3 > m^2 ?

1) m>0

2) m^2 > m


The question asks if m^3 > m^2. We can safely divide by m^2 on both sides without worrying about whether to reverse the inequality, because m^2 can never be negative. So the question is just asking "Is m > 1?"

Statement 1 is now clearly not sufficient. Statement 2 is true for every negative number, but is also true when m > 1, so is not sufficient. When we combine the statements, we know m is positive from Statement 1, so we can safely divide both sides by m in Statement 2, and we find m > 1, which is what we wanted to prove. So the answer is C.
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If m not equal to zero is m^3 > m^2 ?

Since \(m\neq{0}\), then \(m^2>0\) and we can safely divide \(m^3 > m^2\) by it. Thus, the question becomes: is \(m>1\)?

(1) m > 0. Not sufficient.

(2) m^2 > m --> \(m(m-1)>0\) --> \(m<0\) or \(m>1\). Not sufficient.

(1)+(2) Intersection of the ranges from (1) and (2) is \(m>1\). Sufficient.

Answer: C.
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Re: Is m ≠ 0, is m^3 > m^2? [#permalink]

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in order to determine whether m^3 > m^2

we need two information i) m is an integer and i) m is positive .


statement (1) just says it is positive . so not sufficient . statements (2) says it is integer . not sufficient .

now both statements together we know two information ! it is sufficient .

hints : to determine the nature of an unknown variable in any given equation , we need to know two properties of the given variable from the five properties , i) positive ii) negative iii) integer vi) fraction and v) zero . so at first , determine which two properties an unknow variable has ! one property in case of zero . Unfortunately we natural think that unknow variable such as "M " here is always positive integer .

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Is m ≠ 0, is m^3 > m^2? [#permalink]

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Is m ≠ 0, is m^3 > m^2?

(1) m > 0
(2) m^2 > m

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Re: If m not equal to zero is m^3 > m^2 ? [#permalink]

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Re: Is m ≠ 0, is m^3 > m^2? [#permalink]

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New post 22 Feb 2017, 19:35
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Re: Is m ≠ 0, is m^3 > m^2?   [#permalink] 22 Feb 2017, 19:35
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