If m≠0, is m^3m^2?

Question

If  m≠0 , is  m^3>m^2 ?

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

abhinav5 · Answer

m^3m^2>m --------------0------------------------1---------------- Number line m<0 01 1)Two possibilities for m>0 so insufficient 2)m(m-1)>0 m<0 or m>1 Two possibilities so insufficient. 1)+2) m>1 Sufficient C is the answer

Bunuel · Answer

If  m≠0 , is  m^3>m^2 ?

The square of a number is always non-negative, so 0 or positive (m^2 in the problem is positive only since given that m is not 0). Thus we can safely reduce  m^3>m^2  by m^2 to get the simplified question: is m > 1?

(1)  m>0 . Not sufficient.

(2)  m^2>m . This is true for all negative numbers (because in this case (m^2 = positive) > (m = negative)) as well as for numbers greater than 1. Not sufficient.

(1)+(2) Since from (1) m > 0, then by reducing (2) by m we'll get m > 1. Sufficient.

Answer: C.

Hope it's clear.

EncounterGMAT · Answer

Bunuel

2)  m^2>m . This is true for all negative numbers (because in this case (m^2 = positive) > (m = negative)) as well as for numbers greater than 1. Not sufficient .

But m^2>m will be m>1 which is equal to the question stem. So can you explain statement 2? Or else even the question can be neg^3 > neg^2?

Bunuel · Answer

As given in the solution m^2 > m is true if m < 0 AND m > 1, so from (2) we cannot be sure that m > 1. Here you cannot reduce m^2 > m by m because we don't know its sign. If m > 0, then by reducing we'd get m > 1 but if m < 0, then by reducing we'd get m < 1 (recall that we should flip the sign when reducing/multiplying by a negative value).

Aamirso · Answer

1 alone is of course not sufficient because each provides little information.
2 alone will lead to "yes" for positive values such as m=3 and no for negative values such m=-3. Hence. 2 is also insufficient.

It's between C and E.

Combining, if m is positive and m^2 > m which means that m is greater than 1. For all m>1, m^3 > m^2. Hence, yes, m^3 > m^2.

C is the answer.

ManjariMishra · Answer

chetan2u , VeritasKarishma , Bunuel , gmatbusters I am a bit confused here ..,m is not given as integer then if 0 1/2 is false from both 1 and 2 we get m>0 but it doesn't justify the m>1 m can be 0

Bunuel · Answer

It's not clear what you are trying to say. (2) says that m^2 > m. This is true if m < 0 and m > 1. (1) says that m > 0, so the first case from (2) (m < 0) is out and we are left with m > 1 only.

ARIEN3228 · Answer

Here's my approach. Please point out errors, if any.

Analysis of question Stem:

IS m^3>m^2 ?

The above inequality holds true only and only if m>0 and m is an integer,

Statement1:

m>0

M is positive. Does not provide information about nature of m. Could be an integer or a fraction.  Insufficient

Statement 2:

m^2>m

subtracting both sides of the ineqality with m

m^2-m>0

m(m-1)>0

Clear m cannot take values of 0 or 1. Implies m>0 and m>1. No unique value.

We can also infer from statement 2 that m is an integer. However m could be positive or negative.

Therefore  Insufficient

Statement 1 and Statement 2 combined.

m>0, m is always positive- Sufficient.
M is an integer.

Ans: C

chetan2u · Answer

Hi, Look at the RED portion.. If 1/4>1/2 and statement II fails, this means m cannot be 1/2 .. similarly for all values between 0 and 1... So as per you too.. Statement I says m>0 Statement II says -11

chetan2u · Answer

Making the inequality into equality is not a good way to approach such questions. 
Solve keeping the inequality intact.

bumpbot · Answer

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If m≠0, is m^3>m^2?

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