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

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.

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?

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

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