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The answer should be C.

1) m > 0

if m is a decimal less than 1 for ex 0.1 then m^3 < m^2.
if m is 1 then m^3 = m^2
if m is greater than 1 for ex 2 then m^3>m^2

Not sufficient.

2) m < 1
if m is a decimal less than 1 for ex 0.1 then m^3 < m^2.
if m is 0 then m^3 = m^2
if m is a negative integer for ex -1 then m^3 < m^2

Not sufficient.

Combining the 2 statements i.e. 0<m<1
m^3 < m^2.

select C
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fugitive

2) m < 1
if m is a decimal less than 1 for ex 0.1 then m^3 < m^2.
if m is 0 then m^3 = m^2
if m is a negative integer for ex -1 then m^3 < m^2
select C

All your examples in second statement give the same answer No. That m^3>m^2 cannot be true.
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Zarrolou
Is \(m^3 > m^2\)?
\(m^3-m^2>0\) or \(m(m^2-m)>0\)
I)The first part (m)is +ve if m>0
II)The second part (m^2-m) is +ve if \(m^2-m>0\) or if \(m>1\) or \(m<0\)
Put together the intervals I and II and you'll find that the equation is +ve(>0) if \(m>1\)
The question asks: is \(m>1\)?

1. m > 0
Not Sufficient

2. m < 1
Sufficient

B, to answer your question: the answer is C if the question were \(m^3 \geq{} m^2\)
In this case the value m=0 would be a problem, and m<1 would not be sufficient.
For any m<1 but \(\neq{}0\) the equation is negative (so no \(\geq{0}\)), but for m=0 equals 0: \(0\geq{0}\)
Only combining 1 and 2 we would be able to answer in this case

Zarrolou - Thanks for the wonderful explanation and also for providing the situation when C would be correct.
I have a small doubt though - You mentioned
m^3-m^2>0 or m(m^2-m)>0
I)The first part (m)is +ve if m>0
II)The second part (m^2-m) is +ve if m^2-m>0 or if m>1 or m<0

shouldnt it be m > 0? If (m^2-m) > 0 that means m(m-1) > 0 implying both m and m-1 have same signs.....so m > 1 and m > 0?
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Is m^3 > m^2?
1. m > 0
2. m < 1

Simplify the question first: \(m^3-m^2>0\) or \(m^2(m-1)>0\). Since \(m^2>=0\) for every \(m\),
\(m-1>0\) or \(m>1\).

So, the question is just: \(m>1?\)
(1) insufficient. For \(m=1/2\) the answer is No, and for \(m=2\) the answer is Yes.
(2) sufficient to give the answer No.

The correct answer is B.

Hope this helps.

Smyarga - Thanks for the simple rephrasing.
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tirbah

Zarrolou - Thanks for the wonderful explanation and also for providing the situation when C would be correct.
I have a small doubt though - You mentioned
m^3-m^2>0 or m(m^2-m)>0
I)The first part (m)is +ve if m>0
II)The second part (m^2-m) is +ve if m^2-m>0 or if m>1 or m<0

shouldnt it be m > 0? If (m^2-m) > 0 that means m(m-1) > 0 implying both m and m-1 have same signs.....so m > 1 and m > 0?


Hi tirbah,

the answer to your question is no (I am afraid). I covered this topic in a thread, you may want to check it out: tips-and-tricks-inequalities-150873.html
Should remove your doubts, let me know
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Maybe I am doing this wrong but if it isn't mentioned that m is an integer, for m<1

M^3= .125 m^2 =.25

M^3= 0 m^2 = 0

M^3= -1 m^2 =1

All widely varying answers. Shouldn't the answer be e?
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Transcendentalist
Is m^3 > m^2?

(1) m > 0
(2) m < 1

Maybe I am doing this wrong but if it isn't mentioned that m is an integer, for m<1

M^3= .125 m^2 =.25

M^3= 0 m^2 = 0

M^3= -1 m^2 =1

All widely varying answers. Shouldn't the answer be e?

The question asks: is m^3 > m^2?

If m=1/2, then m^3=1/8<1/4=m^2. The answer to the question is NO.
If m=0, then m^3=0=m^2. The answer to the question is NO.
If m=-1, then m^3=-1<1=m^2. The answer to the question is NO.

The answer is the same in all cases (m^3>m^2 holds true only for m>1).
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tirbah
Is m^3 > m^2?

(1) m > 0
(2) m < 1

As m^2 is +ve, we can rephrase the question "Is m^3 > m^2?" as "Is m > 1?".

Statement 1 does not say clearly if m >1 or if 0<m<1. Insufficient.

Statement 2 says m < 1 which is clearly answering the question. Sufficient.

Answer is B.
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Hi
A lot has been discussed on solution. What i understand is that you are struggling with Inequalities, I was in the same boat. I used Karishma's Blogs on Inequalities, the links of which is mentioned below, helped me a lot. Though i have not become an authority on Inequalities, but yes i can solve challenge problems and it has become a game....

Consider kudos if my post helps!!!!!!!!!!

Archit

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/07 ... ns-part-i/

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/07 ... s-part-ii/

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/06 ... e-factors/

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/07 ... -and-sets/
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Zarrolou
tirbah

Zarrolou - Thanks for the wonderful explanation and also for providing the situation when C would be correct.
I have a small doubt though - You mentioned
m^3-m^2>0 or m(m^2-m)>0
I)The first part (m)is +ve if m>0
II)The second part (m^2-m) is +ve if m^2-m>0 or if m>1 or m<0

shouldnt it be m > 0? If (m^2-m) > 0 that means m(m-1) > 0 implying both m and m-1 have same signs.....so m > 1 and m > 0?


Hi tirbah,

the answer to your question is no (I am afraid). I covered this topic in a thread, you may want to check it out: tips-and-tricks-inequalities-150873.html
Should remove your doubts, let me know

Zarrolou - Thanks for the link. I got that. Thanks.
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smyarga
fugitive

2) m < 1
if m is a decimal less than 1 for ex 0.1 then m^3 < m^2.
if m is 0 then m^3 = m^2
if m is a negative integer for ex -1 then m^3 < m^2
select C

All your examples in second statement give the same answer No. That m^3>m^2 cannot be true.

Hey Smyarga,

For m<1, we can take 0 as well but in that case it will not give us conclusive answer. What am I missing here?
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smyarga
fugitive

2) m < 1
if m is a decimal less than 1 for ex 0.1 then m^3 < m^2.
if m is 0 then m^3 = m^2
if m is a negative integer for ex -1 then m^3 < m^2
select C

All your examples in second statement give the same answer No. That m^3>m^2 cannot be true.

Hey Smyarga,

For m<1, we can take 0 as well but in that case it will not give us conclusive answer. What am I missing here?
Haardy7007 First, note that this is a Yes/No question: "Is m^3 greater than m^2"?

What you may have missed is if m=0, then we have m^3=m^2=0, and if the values are equal, the answer to the question is still "No, m^3 is NOT greater than m^2". In all cases in which m < 1, the answer is "No", so we do have a conclusive answer.

Another way of thinking about it is the only range that gives a "Yes" answer to " Is m^3 > m^2?" is if m > 1.

You may find it helpful to make a flashcard similar to the one below:
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