If [(x+4)^2]^(1/2) = 3, which of the following could be...

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

If [(x+4)^2]^(1/2) = 3, which of the following could be...

by AAPL » Sun Jan 28, 2018 2:10 pm

$$If\ \sqrt{\left(x+4\right)^2}=3,\ which\ of\ the\ following\ could\ be\ the\ value\ of\ x-4?$$
A. -11
B. -7
C. -4
D. -3
E. 5

The OA is A.

Is there a strategic approach to this PS question? Can any experts help me, please? I don't have clear what can I do to solve it. I just need isolate the x? I don't understand it. Thanks for your help.

Quote

Source: Beat The GMAT — Problem Solving | Sun Jan 28, 2018 2:10 pm

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

by M7MBA » Mon Jan 29, 2018 2:08 am

Hi AAPL.

Let's take a look at your question.

Let's try option by option:

(1) x-4 = -11, this implies that x=-7. Then $$\sqrt{\left(x+4\right)^2}=\sqrt{\left(-7+4\right)^2}=\sqrt{\left(-3\right)^2}=3.\ \ \text{TRUE}$$

(2) x-4 = -7 this implies that x=-3. Then $$\sqrt{\left(x+4\right)^2}=\sqrt{\left(-3+4\right)^2}=\sqrt{\left(1\right)^2}=1\ne3.\ \ \text{FALSE}$$

(3) x-4 = -4 this implies that x=0. Then $$\sqrt{\left(x+4\right)^2}=\sqrt{\left(0+4\right)^2}=\sqrt{\left(4\right)^2}=4\ne3.\ \ \text{FALSE}$$

(4) x-4 = -3 this implies that x=1. Then $$\sqrt{\left(x+4\right)^2}=\sqrt{\left(1+4\right)^2}=\sqrt{\left(5\right)^2}=5\ne3.\ \ \text{FALSE}$$

(5) x-4 = 5 this implies that x=9. Then $$\sqrt{\left(x+4\right)^2}=\sqrt{\left(9+4\right)^2}=\sqrt{\left(13\right)^2}=13\ne3.\ \ \text{FALSE}$$

Hence, the correct answer is the option A.

I hope this answer can help you.

Feel free to ask me again if you have a doubt.

Regards.

Quote

GMAT/MBA Expert

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

by ErikaPrepScholar » Mon Jan 29, 2018 6:00 am

Hey folks,

Another option is to manipulate the original equation to solve for x -

We have:
$$\sqrt{\left(x+4\right)^2}=3$$

Squaring both sides gives:
$$\left(x+4\right)^2=9$$

Taking the square root of both sides gives:
$$x+4=3\ OR\ x+4=-3$$

Solving these equations individually gives:
$$x=-1\ OR\ x=-7$$

At this point, it's tempting to select answer choice B (-7), but remember that the question asks for the value of x - 4, not x. If x = -1, then x - 4 = -5. If x = -7, then x = -11. Of these, only -11 is an answer: A.

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

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Jan 30, 2018 10:29 am

AAPL wrote:$$If\ \sqrt{\left(x+4\right)^2}=3,\ which\ of\ the\ following\ could\ be\ the\ value\ of\ x-4?$$
A. -11
B. -7
C. -4
D. -3
E. 5

Simplifying the left hand side of the equation, we have:

|x + 4| = 3

Thus x + 4 = 3, or x + 4 = -3.

If x + 4 = 3, then x = -1, and so x - 4 = -5.

If x + 4 = -3, then x = -7, and so x - 4 = -11.

Since -5 is not one of the answer choices, the answer must be -11.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]