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# What is the value of (n + 1)^2?

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Math Expert
Joined: 02 Sep 2009
Posts: 55804
What is the value of (n + 1)^2?  [#permalink]

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01 Jun 2016, 04:30
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Difficulty:

25% (medium)

Question Stats:

74% (01:35) correct 26% (01:43) wrong based on 203 sessions

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What is the value of (n + 1)^2?

(1) n^2 - 6n = -9
(2) (n-1)^2 = n^2 - 5

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Re: What is the value of (n + 1)^2?  [#permalink]

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01 Jun 2016, 05:06
1. n(n-6)=-9 --> n=3 or n=1 two distinct values ...insufficient !!
2. n2+1-2n-n2+5=0 2n-6=0 , n=3 sufficient !!

B
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Posts: 7765
Re: What is the value of (n + 1)^2?  [#permalink]

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01 Jun 2016, 05:22
2
1
CounterSniper wrote:
1. n(n-6)=-9 --> n=3 or n=1 two distinct values ...insufficient !!
2. n2+1-2n-n2+5=0 2n-6=0 , n=3 sufficient !!

B

Hi,

n(n-6)=-9 means n= 3..... not n=1..

(1) $$n^2 - 6n = -9$$
$$n^2-6n=-9.............n^2-6n+9=0.............(n-3)^2 = 0................n=3$$

Statement 1 is suff...

(2) $$(n-1)^2 = n^2 - 5$$
$$n^2-2n+1 =n^2-5................-2n+1=-5...............2n=5+1=6...............n=3$$

again suff

D
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Re: What is the value of (n + 1)^2?  [#permalink]

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15 Jun 2016, 15:45
Top Contributor
Bunuel wrote:
What is the value of (n + 1)²?

(1) n² - 6n = -9
(2) (n - 1)² = n² - 5

Target question: What is the value of (n + 1)²?

Statement 1: n² - 6n = -9
This is a quadratic equation, so let's set it equal to zero: n² - 6n + 9= 0
Factor to get: (n - 3)(n - 3) = 0
So, n = 3
Since we know that n has only one value (n= 3), we can easily determine the value of (n + 1)²
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (n - 1)² = n² - 5
Expand left side: n² - 2n + 1 = n² - 5
Subtract n² from both sides: -2n + 1 = -5
Subtract 1 from both sides: -2n = - 6
Solve: n = 3
Since we know that n has only one value (n= 3), we can easily determine the value of (n + 1)²
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Some useful videos for solving this question:

Cheers,
Brent
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Re: What is the value of (n + 1)^2?  [#permalink]

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21 Dec 2017, 19:13
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Re: What is the value of (n + 1)^2?   [#permalink] 21 Dec 2017, 19:13
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