What is the sum of all unique solutions for

Expert replies

M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Sat Mar 31, 2018 8:00 am

What is the sum of all unique solutions for x^2+6x+9=|x+3| ?

A. -12
B. -9
C. -7
D. -5
E. 0

The OA is B.

When I solved this problem I got 0. Why is B the correct answer? <i class="em em-confused"></i>

Like this post

Source: Beat The GMAT — Problem Solving | Sat Mar 31, 2018 8:00 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Sat Mar 31, 2018 8:31 am

Hi.

This is the way I'd solve it:

$$x^2+6x+9=|x+3|\ $$ $$\Rightarrow\ \ x^2+6x+9=x+3\ \ or\ \ \ x^2+6x+9=-\left(x+3\right)$$ Now, solving the first equation we get: $$x^2+5x+6=0$$ $$\Rightarrow\ \ \left(x+3\right)\left(x+2\right)=0$$ $$\Rightarrow\ x_1=-3\ ,\ \ \ x_2=-2\ \ .$$ Solving the second equation we get: $$x^2+6x+9=-\left(x+3\right)$$ $$\Rightarrow\ \ x^2+7x+12=0$$ $$\Rightarrow\ \ \left(x+4\right)\left(x+3\right)=0$$ $$\Rightarrow\ \ x_3=-4\ ,\ \ x_4=-3.$$ Now, the unique solutions are x_1=-3, x_2=-2, x_3=-4.

Therefore, $$x_1+x_2+x_3=-3-2-4=-9.$$ Hence, the correct answer is the option B.

I hope it helps you.

Like this post

GMAT/MBA Expert

ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

by ErikaPrepScholar » Sat Mar 31, 2018 11:48 am

$$x^2+6x+9=\left|x+3\right|$$ The absolute value gives us two options: $$x^2+6x+9=x+3$$ or $$x^2+6x+9=-\left(x+3\right)$$ $$x^2+6x+9=-x-3$$ Solving each individually:
$$x^2+6x+9=x+3$$ $$x^2+5x+6=0$$ $$\left(x+2\right)\left(x+3\right)=0$$ $$x=-2\ and\ x=-3$$
and $$x^2+6x+9=-x-3$$ $$x^2+7x+12=0$$ $$\left(x+3\right)\left(x+4\right)=0$$ $$x=-3\ and\ x=-4$$
Notice that x=-3 is a solution for both equations. We are looking for total *unique* solutions, so we'll only include it once.
So our unique solutions are -2, -3, and -4. To find the sum, we'll add them together: $$-2\ +\left(-3\right)+\left(-4\right)=-2-3-4=-9$$ This gives B as the correct answer.

Erika John - Content Manager/Lead Instructor
https://gmat.prepscholar.com/gmat/s/

Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/

Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial

Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review