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exoticanb4u: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Tue Aug 18, 2009 8:52 pm

by exoticanb4u » Sun Oct 11, 2009 6:28 pm

Can someone please solve this question?

I am getting -16 as answer, but the OA says -8

What is the sum of all roots of the equation
|x + 4|^2 - 10|x + 4| = 24?

BTW the source is magoosh

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Source: Beat The GMAT — Problem Solving | Sun Oct 11, 2009 6:28 pm

cooline: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Tue Jan 09, 2007 10:12 pm

by cooline » Mon Oct 12, 2009 5:32 am

I am getting 4 for an answer, can you please give the explanation.

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mp2437: Master | Next Rank: 500 Posts; Posts: 177; Joined: Thu Aug 14, 2008 11:59 am; Thanked: 25 times

by mp2437 » Mon Oct 12, 2009 6:54 am

I get an answer of 8.

Distribute:
|x + 4|^2 - 10|x + 4| = (x^2 + 8x + 16) - 10x - 40 = 24
x^2 - 2x - 48 = 0. Factors are (x - 8)(x+6) = 0, so you get roots x = +8, x = -6.

To check: plug in each root and see if it works. x = -6 doesn't, so the only root that fits the bill is x = 8.

I did the same thing taking the negative part of the absolute value, but the check did not work when I plugged in the values.

Not sure where -8 comes into play. Can someone clarify.

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