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Fun Inequality

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scott.yin
 Post subject: Fun Inequality
 Post Posted: Fri Aug 26, 2011 2:28 pm 
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Course Students


Posts: 4
I understand the answer to this question is C if you assume X is positive. But if you work out both cases (pos and neg), shouldnt the answer be E?

If x is an integer, what is the value of x?

(1) -5x > -3x + 10

(2) -11x – 10 < 67
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mithunsam
 Post subject: Re: Fun Inequality
 Post Posted: Fri Aug 26, 2011 3:46 pm 
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Course Students


Posts: 76
No, both statements together give x = -6. There is no +ve case for x.

Statement 1
-5x > -3x + 10 => -2x > 10 => -x > 5 => x < -5 [This is true only when x is -ve]

Statement 2
-11x – 10 < 67 => -11x < 77 => -x < 7 => x > -7 [x could be +ve or -ve]

Together we get -7 < x < -5 => x = -6
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scott.yin
 Post subject: Re: Fun Inequality
 Post Posted: Fri Aug 26, 2011 5:43 pm 
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Course Students


Posts: 4
mithunsam wrote:
-5x > -3x + 10 => -2x > 10 => -x > 5 => x < -5 [This is true only when x is -ve]


Don't you need to test both +ve and -ve cases (flip the initial inequality)?

So wouldnt you also go ahead and find -5x < -3x + 10 => -x < 5 => x >5 ??
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mithunsam
 Post subject: Re: Fun Inequality
 Post Posted: Fri Aug 26, 2011 9:48 pm 
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Course Students


Posts: 76
scott.yin wrote:
mithunsam wrote:
-5x > -3x + 10 => -2x > 10 => -x > 5 => x < -5 [This is true only when x is -ve]


Don't you need to test both +ve and -ve cases (flip the initial inequality)?

So wouldnt you also go ahead and find -5x < -3x + 10 => -x < 5 => x >5 ??

One point to note - For -ve values, we don't just flip the inequality sign alone. We also have to multiply both left and right sides of the inequality with -1. [In this case, when you do that, you will end up in the same equation].

For addition and subtraction, you don't have to do the work, which we do for squares, square roots etc... This is because addition and subtraction do not hide signs. Multiplication hide signs (-ve*-ve = +ve). Therefore, we have to consider both scenarios. (For example, x^2 will always be +ve, but x could be +ve or -ve. Therefore, we have to consider both the scenarios.)

If you still have question, substitute 0 or +ve values in the original equation.

For x=0
-5x > -3x + 10 => -5*0 > -3*0 + 10 => 0 > 10 ---> False
For x=1
-5x > -3x + 10 => -5*1 > -3*1 + 10 => -5 > 7 ---> False
For x=2
-5x > -3x + 10 => -5*2 > -3*2 + 10 => -10 > 4 ---> False

Only -ve values could satisfy this equation.
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jnelson0612
 Post subject: Re: Fun Inequality
 Post Posted: Wed Sep 28, 2011 4:54 pm 
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ManhattanGMAT Staff


Posts: 1857
Good stuff, thanks all.

_________________
Jamie Nelson
ManhattanGMAT Instructor
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