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

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Director
Joined: 12 Feb 2015
Posts: 875
If n is an integer and square_root(n^2-6n+9)=5, which of the ...  [#permalink]

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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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Manish

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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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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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Director
Joined: 04 Sep 2015
Posts: 632
Location: India
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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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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.

Senior Manager
Joined: 12 Sep 2017
Posts: 297
If n is an integer and square_root(n^2-6n+9)=5, which of the ...  [#permalink]

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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!!!
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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