Square root

I am getting "A"

pbanavara wrote:If [sqrt(x+4)^2] = 3, which of the following could be the value of x – 4?

a. -11
b. -7
c. -4
d. -3
c. 5

The answer is A because (x+4)^2 would have to equal 9 and so x+4 would have to equal 3 or -3 x so a value of -7 is the only one that satisfies the equation. However they ask for x-4 and -7-4=-11

This problem is based on an important rule absolute.

|x| can be written as SQRT(x^2).

So here we have |x+4| = 3

So u need to consider two values for x: ie +ve x and -ve x.

1. x is positive.
then the equation reduces to
x+4=3
ie x = -1

This is not possible coz we assumed that x is +ve

2. x is -ve.
-(x+4) = 3
Solving x = -7.

So the answer is b
HT Helps

vittalgmat wrote:This problem is based on an important rule absolute.

|x| can be written as SQRT(x^2).

So here we have |x+4| = 3

So u need to consider two values for x: ie +ve x and -ve x.

1. x is positive.
then the equation reduces to
x+4=3
ie x = -1

This is not possible coz we assumed that x is +ve

2. x is -ve.
-(x+4) = 3
Solving x = -7.

So the answer is b
HT Helps

Isn't question asked for value of (x-4) ?

The OA is A

@vittal - Thanks for explaining the steps .. I guess because of oversight you missed seeing that the question asked for x-4 and not x. A classic GMAT trap.

I have one question though - is it a general rule that sqrt(x^2) = |x| ?

because sqrt(x^2) = (x^2)^1/2 = x

- pradeep

OOOPSY Daisy!!!. thanks for pointing this out.

One point in my defense is that I am browsing this forum while working!!!.
so I dont have undivided attention to solving the problem.

Moral of the story.

1. Read the question
2. Solve the problem
3. Read the question to figure out if step 2 answers step 1.

thanks

pbanavara,
Yes that is a general rule.
Actually Ian and Cramya have explained this well.
I will send u the link if I can find it.

vittalgmat wrote:pbanavara,
Yes that is a general rule.
Actually Ian and Cramya have explained this well.
I will send u the link if I can find it.

vittal,
can you paste the link here so everybody can be benefited
Thanks

vittalgmat wrote:pbanavara,
Yes that is a general rule.
Actually Ian and Cramya have explained this well.
I will send u the link if I can find it.

That'd be great - Thanks