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If x is a negative number, what is the value of x?

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If x is a negative number, what is the value of x?

by gmattesttaker2 » Mon Feb 04, 2013 8:23 pm
Hello,


This is from one of the Practice tests. I was wondering if you can please assist here?


If x is a negative number, what is the value of x?

1) x^2 = 1

2) x^2 + 3x + 2 = 0

OA: A


My approach was as follows:

x^2 = 1

Sqrt (x^2 ) = 1

-x = 1

x = -1

Hence, A


x^2 + 3x + 2 = 0

x^2 + 3x = -2

x(x + 3) = -2

x = -2, -5

Hence, A


I was not sure about this approach since with 1) I am getting x = -1 whereas with 2) I am getting x = -2/-5

Thanks for your help.

Best Regards,
Sri
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by GMATGuruNY » Mon Feb 04, 2013 8:35 pm
gmattesttaker2 wrote: If x is a negative number, what is the value of x?

1) x^2 = 1

2) x^2 + 3x + 2 = 0
Statement 1: x² = 1
x² - 1 = 0
(x+1)(x-1) = 0
x=-1 or x=1.
Since x<0, we know that x=-1.
SUFFICIENT.

Statement 2: x² + 3x + 2 = 0
(x+2)(x+1) = 0.
x=-2 or x=-1.
Since x could be either value, INSUFFICIENT.

The correct answer is A.
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by Brent@GMATPrepNow » Tue Feb 05, 2013 7:16 am
gmattesttaker2 wrote: x^2 + 3x + 2 = 0
x^2 + 3x = -2
x(x + 3) = -2
x = -2, -5
The problem has to do with your last step.
If x(x + 3) = -2, we can't then conclude that x = -2 or -5

To solve a quadratic, we should set it equal to zero (x^2 + 3x + 2 = 0), and then try to factor.
We get (x+1)(x+2) = 0
This means that either (x+1)=0 or (x+2)=0, which means x = -1 or -2

Cheers,
Brent
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