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Where am I going wrong - Inequalities

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imhimanshu: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sat Feb 28, 2009 7:01 am; Location: India; Thanked: 2 times

by imhimanshu » Thu Aug 18, 2011 6:52 am

Hi Experts,
Can you please verify where I am going wrong.

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

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Source: Beat The GMAT — Data Sufficiency | Thu Aug 18, 2011 6:52 am

kmittal82: Master | Next Rank: 500 Posts; Posts: 324; Joined: Mon Jul 05, 2010 6:44 amFollowed by: 3 members; Location: London; Thanked: 70 times

by kmittal82 » Thu Aug 18, 2011 6:58 am

imhimanshu wrote:Hi Experts,
m(m-1)>0
so, m>0 or m>1
So,m must be greater than 1.

You missed m < 1 as a solution as well. For a product of 2 numbers to be greater than 0, they are either both positive (the case you considered), or they are both negative (the case you missed). Hope that helps

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Aug 18, 2011 7:06 am

imhimanshu wrote:Hi Experts,
Can you please verify where I am going wrong.

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

m(m - 1) > 0 implies any of the following two cases,

1. m and (m - 1) both positive --> m > 1
2. m and (m - 1) both negative ---> m < 0

Hence, statement 2 is not sufficient.

Taking both statements together: As m is positive from statement 1, m must be greater than 1 from statement 2. SUFFICIENT

The correct answer is C.

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Gurome, Inc.
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Aug 18, 2011 7:11 am

imhimanshu wrote: 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.

The reasoning in red is incorrect.

Given that m(m-1)>0:
The critical points are m=0 and m=1.
These are the only values for m that will make the left hand side equal 0.
When m equals any other value, the left hand side will be less than or greater than 0.
To determine the range of m, test one value to the left and right of each critical point.

m<0:
Plug m=-1 into m(m-1)>0:
-1*(-1-1) > 0
-1 * -2 > 0
2 > 0.
This works.
m<0 IS part of the range.

0<m<1:
Plug m= 1/2 into m(m-1)>0:
(1/2)*((1/2)-1) > 0
1/2 * -1/2 > 0
-1/4 > 0.
Doesn't work.
0<m<1 is NOT part of the range.

m>1:
Plug m= 2 into m(m-1)>0:
2*(2-1) > 0
2 * 1 > 0
2 > 0.
This works.
m>1 IS part of the range.

Thus, statement 2 indicates that m<0 OR that m>1.
Insufficient.

When the two statements are combined, the only range for m that satisfies both statements is m>1.
Sufficient.

The correct answer is C.

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imhimanshu: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sat Feb 28, 2009 7:01 am; Location: India; Thanked: 2 times

by imhimanshu » Thu Aug 18, 2011 7:28 am

Thanks Experts for catching the error. I hope not to repeat the same again.

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