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The function F(n) is defined as the product of all the conse

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The function F(n) is defined as the product of all the conse [#permalink] New post 15 Oct 2012, 10:16
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (02:10) correct 30% (01:36) wrong based on 46 sessions
Manhattan weekly challenge problem

The function F(n) is defined as the product of all the consecutive positive integers between 1 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[Reveal] Spoiler: OA

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Re: The function F(n) is defined as the product of all the conse [#permalink] New post 15 Oct 2012, 10:29
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thevenus wrote:
Manhattan weekly challenge problem

The function F(n) is defined as the product of all the consecutive positive integers between 1 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5


The function F(n) is defined as the product of all the consecutive positive integers between 1 and n^2, inclusive, thus F(3)=1*2*3*...*9=9!.

The function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive, thus G(3)=1^2*2^2*3^2=3!*3!.

\frac{F(3)}{G(3)}=\frac{9!}{3!*3!}=\frac{4*5*6*7*8*9}{6}=2^2*5*7*2^3*9=2^5*(5*7*9).

The power of 2 is 5.

Answer: E.
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Director
Director
User avatar
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 564
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)
Followers: 11

Kudos [?]: 123 [0], given: 75

Re: The function F(n) is defined as the product of all the conse [#permalink] New post 15 Oct 2012, 10:30
F(3)/G(3)
=product(1 to 3 ^2) / 1.2^2.3^2
=1.2.3.4.5.6.7.8.9/1.4.9
=1.2.3.(2^2).5.(2.3).7.(2^3).9/1.(2^2).9
=1.(2^7).3.5.7.9/1.(2^2).9
Loof for 2^7/2^2=2^5 ----Exponent 5

Answer: E
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Kudos [?]: 22381 [0], given: 2616

Re: The function F(n) is defined as the product of all the conse [#permalink] New post 08 Sep 2013, 05:25
Expert's post
Re: The function F(n) is defined as the product of all the conse   [#permalink] 08 Sep 2013, 05:25
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