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# What is the value of the integer n?

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Manager
Joined: 06 Feb 2010
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What is the value of the integer n? [#permalink]

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25 Oct 2010, 00:25
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69% (01:53) correct 31% (01:03) wrong based on 142 sessions

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What is the value of the integer n?

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

[Reveal] Spoiler:
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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25 Oct 2010, 00:34
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KUDOS
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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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
$$(3+2)^2$$ = $$5^3$$

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

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29 May 2014, 08:53
Expert's post
b2bt wrote:
(A) Insufficient
n= -5 -5*(-5+2) = -5*(-3) = 15 OR
n= 3 3*(3+2) = 3*5 = 15

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

______________
Done. Thank you.
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Re: What is the value of the integer n? [#permalink]

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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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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.

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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