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# A function f(n) is defined as 2^{n-2} when n is odd and 3^{n/2}

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Joined: 26 Feb 2016
Posts: 3359
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A function f(n) is defined as 2^{n-2} when n is odd and 3^{n/2}  [#permalink]

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25 Sep 2018, 04:32
1
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Difficulty:

35% (medium)

Question Stats:

74% (01:30) correct 26% (01:28) wrong based on 30 sessions

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A function f(n) is defined as $$2^{n-2}$$ when n is odd and $$3^{\frac{n}{2}}$$ when n is even. What is the value of f(f(f(f(f(f(f(3))))))))?

A. 1
B. 2
C. 3
D. 9
E. 81

Source: Experts Global

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Joined: 02 Aug 2009
Posts: 7764
A function f(n) is defined as 2^{n-2} when n is odd and 3^{n/2}  [#permalink]

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26 Sep 2018, 00:26
1
pushpitkc wrote:
A function f(n) is defined as $$2^{n-2}$$ when n is odd and $$3^{\frac{n}{2}}$$ when n is even. What is the value of f(f(f(f(f(f(f(3))))))))?

A. 1
B. 2
C. 3
D. 9
E. 81

Source: Experts Global

2 ways..

1)..
$$2^{n-2}$$ when n is odd means $$2^{n-2}$$ will be EVEN and next function becomes..
$$3^{\frac{n}{2}}$$ when n is even, $$3^{\frac{n}{2}}$$ will be ODD
so if the initial number is ODD as in this case, the function will result in E,O,E,O....
there are total 7 functions in f(f(f(f(f(f(f(3)))))))), so 7th wil be EVEN
ONLY B has a even value

B

2) solve
$$2^{n-2}$$ when n is odd... when n=3,.... $$2^{n-2}=2^{3-2}=2$$ ..
$$3^{\frac{n}{2}}$$ when n is even,.....when n=2,... $$3^{\frac{n}{2}}=3^{\frac{2}{2}}=3$$ when n is even
so the values are 2,3,2,3..
we are looking for 7th , so 2

B
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A function f(n) is defined as 2^{n-2} when n is odd and 3^{n/2}   [#permalink] 26 Sep 2018, 00:26
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