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# What is the value of the integer n? (1) n(n + 2) = 15 (2)

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Manager
Joined: 22 Feb 2006
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What is the value of the integer n? (1) n(n + 2) = 15 (2) [#permalink]

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22 Aug 2009, 11:03
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Please, explain your answer. Thank you,
-------------------------------------
Q13:
What is the value of the integer n?
(1) n(n + 2) = 15
(2) (n + 2)^n = 125

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
SVP
Joined: 05 Jul 2006
Posts: 1747
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Re: DS: exponent [#permalink]

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22 Aug 2009, 13:25
[quote="TriColor"]Please, explain your answer. Thank you,
-------------------------------------
Q13:
What is the value of the integer n?
(1) n(n + 2) = 15
(2) (n + 2)^n = 125

FROM 1
N^2+2N-15 = 0 IE: (N+5)(N-3) = 0 THUS N IS EITHER -5 OR 3...INSUFF

FROM 2

(n+2)^n = 5^3

thus n = 3...........suff

B
Manager
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Re: DS: exponent [#permalink]

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22 Aug 2009, 16:19
Yezz...

Yes, 3 is the answer. But how do you "prove" that there is no other integer that satisfies the equation?? Can you come out with some "LOG" manupulation that shows that "3" is the only answer?
Manager
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Re: DS: exponent [#permalink]

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22 Aug 2009, 19:53
TriColor wrote:
Yezz...

Yes, 3 is the answer. But how do you "prove" that there is no other integer that satisfies the equation?? Can you come out with some "LOG" manupulation that shows that "3" is the only answer?

"Log" is unnecessary here.
because n is integer
and (n+2)^n=125,

therefore
n>=0, (if n<0, then (n+2)^n<=1)
(n+2) is an integer, there is no other integers' any exponent equal to 125, only 5. n+2=5 => n=3
_________________

Kudos me if my reply helps!

Re: DS: exponent   [#permalink] 22 Aug 2009, 19:53
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# What is the value of the integer n? (1) n(n + 2) = 15 (2)

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