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

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)

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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