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If n is an integer and square_root(n^2-6n+9)=5, which of the ...

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New post 08 Aug 2018, 09:43
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If n is an integer and \(\sqrt{(n^2-6n+9)}\)=5, which of the following could be the value of \((n + 3)^2\)?

A) –2
B) 1
C) 4
D) 11
E) 64

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New post 08 Aug 2018, 10:00
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CAMANISHPARMAR wrote:
If n is an integer and \(\sqrt{(n^2-6n+9)}\)=5, which of the following could be the value of \((n + 3)^2\)?

A) –2
B) 1
C) 4
D) 11
E) 64


\(n^2-6n+9\) can be written as \((n-3)^2\)

Given, \(\sqrt{(n^2-6n+9)}\)=5
Squaring both sides, we have

\(n^2-6n+9=5^2\)
Or, \((n-3)^2=5^2\)
Or, \(|n-3|=5\)
So, n-3=5 or, n-3=-5
So, n=8 or, -2

Now, \((n+3)^2=(-2+3)^2=1^2=1\)
Or, \((n+3)^2=(8+3)^2=11^2=121\) (not in answer options)

Ans. (B)
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Re: If n is an integer and square_root(n^2-6n+9)=5, which of the ...  [#permalink]

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New post 09 Aug 2018, 03:52
1. square both sides.
2.find x, which will be either 8 or -2.
3.substitute value, comes either 121 or 1.

4. 1 is correct answer.
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If n is an integer and square_root(n^2-6n+9)=5, which of the ...  [#permalink]

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New post 11 Feb 2019, 18:54
CAMANISHPARMAR wrote:
If n is an integer and \(\sqrt{(n^2-6n+9)}\)=5, which of the following could be the value of \((n + 3)^2\)?

A) –2
B) 1
C) 4
D) 11
E) 64


Hello everyone!

I squared it but I have some doubt, what if I wouldn't want to square it?

What is wrong with the following?

\(\sqrt{(n^2-6n+9)}\)=5

\(\sqrt{(n - 3)(n - 3)}\)=5

\(\sqrt{(n - 3)^2}\)=5


If the GMAT gives you the squared root then you just consider the +ve option.

\((n - 3)\)=5

n = 8

Thank you so much in advance!!!
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If n is an integer and square_root(n^2-6n+9)=5, which of the ...   [#permalink] 11 Feb 2019, 18:54
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