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Inequalities involving powers - Not able to solve

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gmatrant: Master | Next Rank: 500 Posts; Posts: 416; Joined: Wed Oct 03, 2007 9:08 amFollowed by: 1 member; Thanked: 10 times

by gmatrant » Fri May 24, 2013 9:08 pm

Consider the equation x^2 > x , simplifying it as below
=> x^2-x>0
=> x(x-1)>0
so x>0 or x>1.

Just curious values for x<0 is also valid for the above equation but when I solve mathematically I don't seem to get this as an option
Can you plase let me know where I am going wrong.

Thanks
gmatrant

A kudos or thanks would do great if my answer has helped you

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Source: Beat The GMAT — Problem Solving | Fri May 24, 2013 9:08 pm

Atekihcan: Master | Next Rank: 500 Posts; Posts: 149; Joined: Wed May 01, 2013 10:37 pmFollowed by: 9 members; Thanked: 54 times

by Atekihcan » Sat May 25, 2013 1:40 am

gmatrant wrote:... x(x-1)>0
so x>0 or x>1.

x(x - 1) > 0 means the product of x and (x - 1) is positive.
So, either both x and (x - 1) are positive or both x and (x - 1) are negative
So, either x > 0 and (x - 1) > 0 or x < 0 and (x - 1) < 0
So, either x > 0 and x > 1 or x < 0 and x < 1
So, either x > 1 or x < 0

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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 » Sat May 25, 2013 1:42 am

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deepsea13: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sun Jun 12, 2011 7:47 amFollowed by: 1 member

by deepsea13 » Tue May 28, 2013 3:08 am

gmatrant wrote:Consider the equation x^2 > x , simplifying it as below
=> x^2-x>0
=> x(x-1)>0
so x>0 or x>1.

Just curious values for x<0 is also valid for the above equation but when I solve mathematically I don't seem to get this as an option
Can you plase let me know where I am going wrong.

Thanks
gmatrant

ON simplifying we get x(x-1)> 0

Two possible cases x and (x-1) are both positive or they're both negative.
If both are positive, then x>0 and x>1
If both are negative, then x<0 x<1

Now from the above two, we can conclude that x<0 and x>1.

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