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

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

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 15 Jun 2016, 15:45.
Last edited by BrentGMATPrepNow on 25 May 2020, 12:55, edited 1 time in total.
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Re: What is the value of (n + 1)^2? [#permalink]
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Re: What is the value of (n + 1)^2? [#permalink]
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