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

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

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Re: DS: exponent [#permalink] New post 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?
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Re: DS: exponent [#permalink] New post 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
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Re: DS: exponent   [#permalink] 22 Aug 2009, 19:53
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