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Square root

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Square root

by pbanavara » Mon Jan 12, 2009 9:04 am
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
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by amitabhprasad » Mon Jan 12, 2009 10:12 am
I am getting "A"
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Re: Square root

by matt7898 » Mon Jan 12, 2009 10:13 am
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
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by vittalgmat » Mon Jan 12, 2009 10:19 am
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
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by amitabhprasad » Mon Jan 12, 2009 10:22 am
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
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Isn't question asked for value of (x-4) ?
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by pbanavara » Mon Jan 12, 2009 10:29 am
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
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by vittalgmat » Mon Jan 12, 2009 11:07 am
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
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by vittalgmat » Mon Jan 12, 2009 11:09 am
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.
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by amitabhprasad » Mon Jan 12, 2009 11:20 am
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
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by pbanavara » Mon Jan 12, 2009 11:44 am
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
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