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

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

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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Source: Beat The GMAT — Data Sufficiency | Mon Feb 04, 2013 8:23 pm

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 » 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: xÂ² = 1
xÂ² - 1 = 0
(x+1)(x-1) = 0
x=-1 or x=1.
Since x<0, we know that x=-1.
SUFFICIENT.

Statement 2: xÂ² + 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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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