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# What is the value of integer n?

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Joined: 02 Dec 2012
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What is the value of integer n?  [#permalink]

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03 Dec 2012, 02:22
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What is the value of integer n?

(1) n(n+1) =6
(2) 2^(2n) = 16
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Joined: 02 Sep 2009
Posts: 64138
Re: What is the value of integer n?  [#permalink]

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03 Dec 2012, 02:23
What is the value of integer n?

(1) n(n+1) =6 --> $$n^2+n-6=0$$ --> $$(n+3)(n-2)=0$$ --> $$n=-3$$ or $$n=2$$. Not sufficient.
(2) 2^(2n) = 16 --> $$2^{2n}=2^4$$ --> $$2n=4$$ --> $$n=2$$. Sufficient.

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What is the value of integer n?  [#permalink]

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Updated on: 04 Feb 2019, 06:02
1
What is the value of integer n?

(1) n(n+1) =6

n & (n+1) means is TWO Consecutive integers.

Therefore, either 6 = 2 * 3 or 6 = -2 * -3 (do not forget negative values)

n =2 or -3

Insufficient

(2) 2^(2n) = 16

2^(2n) = 4 ^n = 16 = 4^2.......n =2

Sufficient

Originally posted by Mo2men on 22 Aug 2017, 04:57.
Last edited by Mo2men on 04 Feb 2019, 06:02, edited 1 time in total.
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Re: What is the value of integer n?  [#permalink]

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13 Dec 2017, 21:02
Hi All,

We're told that N is an integer. We are asked for the value of N.

1) (N)(N+1) = 6

Here, we can do a bit of algebra to create a Quadratic...

N^2 + N = 6
N^2 + N - 6 = 0
(N+3)(N-2) = 0
N = -3 or +2
With two different solutions...
Fact 1 is INSUFFICIENT

2) 2^(2N) = 16

The ONLY exponent that will fit here is 4.... 2^4 = 16.
2N = 4
N =2
Fact 2 is SUFFICIENT

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Re: What is the value of integer n?  [#permalink]

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28 Mar 2020, 10:18
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Re: What is the value of integer n?   [#permalink] 28 Mar 2020, 10:18