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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
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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, 03:32
1
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:08) correct 33% (01:23) wrong based on 24 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: 7107
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, 23:26
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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A function f(n) is defined as 2^{n-2} when n is odd and 3^{n/2} &nbs [#permalink] 25 Sep 2018, 23:26
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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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