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# If the integers a and n are greater than 1 and the product

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Manager
Joined: 27 Mar 2008
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If the integers a and n are greater than 1 and the product [#permalink]  09 Aug 2008, 18:03
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If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a ^ n , what is the value of a?

1. a^n = 64
2. n =6
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Joined: 17 Jun 2008
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Re: DS [#permalink]  10 Aug 2008, 05:31
dishant007 wrote:
If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a ^ n , what is the value of a?

1. a^n = 64
2. n =6

8*7*720=k *a^n k is any integer

(1)a^n=64 =2^6=8^2 => INSUFFI
(2)n=6
2^3 *7 * 2^6 *3^2 * 5*2=a^6 *k only possible power of 6 is for 2

hence a =2
IMO B
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Joined: 06 Apr 2008
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Re: DS [#permalink]  10 Aug 2008, 09:06
dishant007 wrote:
If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a ^ n , what is the value of a?

1. a^n = 64
2. n =6

Product of first eight positive intgers = 8! = $$2^7 * 3^4 * 5 * 7$$
Statement 1), a=8, n=2 or a=2, n=6 . Hence insuff.

Statement 2) n=6 which means a=2 since 2 is only number with power of greater than equal to 6
Re: DS   [#permalink] 10 Aug 2008, 09:06
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