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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: 11 Feb 2015
Posts: 608
If n is an integer and square_root(n^2-6n+9)=5, which of the ...  [#permalink]

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08 Aug 2018, 08:43
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:40) correct 35% (01:27) wrong based on 54 sessions

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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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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
If n is an integer and square_root(n^2-6n+9)=5, which of the ...  [#permalink]

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08 Aug 2018, 09:00
1
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: 520
Location: India
WE: Information Technology (Computer Software)
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, 02:52
1. square both sides.
2.find x, which will be either 8 or -2.
3.substitute value, comes either 121 or 1.

Re: If n is an integer and square_root(n^2-6n+9)=5, which of the ... &nbs [#permalink] 09 Aug 2018, 02:52
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