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

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Intern
Joined: 12 Jul 2012
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If m not equal to zero is m^3 > m^2 ?  [#permalink]

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Updated on: 25 Sep 2012, 01:37
2
00:00

Difficulty:

35% (medium)

Question Stats:

60% (00:57) correct 40% (00:45) wrong based on 122 sessions

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

(1) m > 0

(2) m^2 > m

Originally posted by harikris on 24 Sep 2012, 23:12.
Last edited by Bunuel on 25 Sep 2012, 01:37, edited 1 time in total.
Edited the question.
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Posts: 1345
Re: if m not equal to zero is m^3 > m^2 ?  [#permalink]

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25 Sep 2012, 00:15
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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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Re: If m not equal to zero is m^3 > m^2 ?  [#permalink]

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25 Sep 2012, 01:42
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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.

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Is m ≠ 0, is m^3 > m^2?  [#permalink]

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02 Sep 2014, 22:42
Is m ≠ 0, is m^3 > m^2?

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

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02 Sep 2014, 23:01
3
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.

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Joined: 03 Jul 2013
Posts: 32
Re: Is m ≠ 0, is m^3 > m^2?  [#permalink]

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03 Sep 2014, 02:17
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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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Re: If m not equal to zero is m^3 > m^2 ?  [#permalink]

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16 Mar 2018, 19:23
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