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What is the value of the integer n?

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

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New post 25 Oct 2010, 00:25
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What is the value of the integer n?

(1) n(n+2)=15
(2) (n+2)^n =125

[Reveal] Spoiler:
Answer is B.
But I don’t know how to finish it…
(n+2)^n=5^3
How it is n=3, here base n=2 and 5 is not same..


OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-the-integer-n-1-n-n-2-15-2-n-107149.html
[Reveal] Spoiler: OA

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Re: Value of an integer [#permalink]

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New post 25 Oct 2010, 00:34
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the first statement n(n+2)=15 would give two integer values as -3 and 5; not conclusive

The second statement (n+2)^n =125 can be written as

(n+2)^n = 5^3
=(3+2)^3 =5^3 --replacing n with 3
LHS =RHS

n =3, conclusive

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Re: What is the value of the integer n? (1) n(n+2)=15 (2) [#permalink]

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New post 29 May 2014, 08:32
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(A) Insufficient
n= -5 -5*(-5+2) = -5*(-3) = 15 OR
n= 3 3*(3+2) = 3*5 = 15

(B) Sufficient
n= 3
\((3+2)^2\) = \(5^3\)

Mods please hide the answer in the first post

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Re: What is the value of the integer n? (1) n(n+2)=15 (2) [#permalink]

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New post 29 May 2014, 08:53

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

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New post 04 Jun 2014, 04:03
Could you perhaps tell us how you came up with the numbers that you plugged in?
I lost valuable time by first trying to re-write the equations (without success).

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

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New post 04 Jun 2014, 04:10
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Expert's post
Saabs wrote:
Could you perhaps tell us how you came up with the numbers that you plugged in?
I lost valuable time by first trying to re-write the equations (without success).


What is the value of the integer n?

(1) n(n + 2) = 15 --> \(n^2+2n-15=0\) --> \((n+5)(n-3)=0\) --> \(n=-5\) or \(n=3\). Not sufficient.

(2) (n + 2)^n = 125 --> as \(n\) is an integer then \((n + 2)^n=125^1=5^3\) (125 can be written as integer^integer only in those two ways), only \(n=3\) works: \((2+3)^3=5^3=125\). Sufficient.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-the-integer-n-1-n-n-2-15-2-n-107149.html
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Re: What is the value of the integer n?   [#permalink] 04 Jun 2014, 04:10
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