Where am I going wrong - Inequalities

[imhimanshujaggi]

Hi Experts,
Can you please verify where I am going wrong.Its a MGMAT question

If m <> 0, is m^3> m^2

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

my approach -

Since it is given that m^3 > m^2

and m^2 > 0 (always). So, it is safe to divide by m^2
Hence, the question becomes is m>1

1. Insufficient as m can lie b/w 0-1
2. Here I am going wrong.

Given - m^2>m
My take -
m^2-m > 0
m(m-1)>0
so, m>0 or m>1
So,m must be greater than 1.
But as per solution, It is incorrect. I know, this can be solved by plugging the values. However, I usually avoid them because I usually miss one or the other scenario. I would appreciate if someone can help me in catching the error.

Thanks

[mithunsam]

There are two issues.

For statement 1 -> you assumed "Since it is given that m^3 > m^2". The question didn't state that. The question is asking whether m^3 is > m^2. Therefore, the only information you have when looking at statement 1 are m>0 and m<> 0 (m<>0 is from question, but it is irrelevent now as Statement 1 states m>0)

Statement 1 is insufficient as m could be >1 or it could be between 0&1.

For statement 2 -> You considered only the +ve case. m could be either +ve or -ve. Question states that m<>0, but nothing more. (Remember, as I mentioned in statement 1, you cannot assume that m^3 is > m^2).

Therfore, solution for statement 2 goes as below...

If m +ve
m^2 > m
m^2-m > 0
m(m-1) >0
m>0 or m>1 => m>1

If m -ve
m^2 < m
m^2-m<0
m(m-1)<0
m<0 or m<1 => m<1

So, from statement 2, m is either >1 or <1
Insufficient

Together they are sufficient, as statment 1 removes m<0 condition and statement 2 removes 0<m<1 condition. That leaves us with m>1.

ANSWER C

[jnelson0612]

mithunsam, excellent!