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

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Manager
Joined: 04 Nov 2006
Posts: 158
Followers: 3

Kudos [?]: 8 [0], given: 0

If the integers a and n are greater than 1 and the product [#permalink]  11 Nov 2006, 15:54
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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
Manager
Joined: 26 Oct 2006
Posts: 127
Followers: 1

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

(1) => 8^2,4^3,2^6 Insuff.
(2) => a = 2 because 2^6 is the only number that can divide 1*2*3*4*5*6*7*8 evenly. Suffcient.

B.

I almost said C when I first looked at the problem
Manager
Joined: 04 Nov 2006
Posts: 158
Followers: 3

Kudos [?]: 8 [0], given: 0

G.Matter,

How did you determine that 2^6 is the only number that can divide 1*2*3*4*5*6*7*8 evenly. Is there a trick to knowing this?

Artis
Manager
Joined: 26 Oct 2006
Posts: 127
Followers: 1

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

Unfortunately I did not employ any trick. As I mentioned, in this case I almost chose C, then what made me stop was I realized that I wasnt using this information anywhere ->
the product of the first 8 positive integers is a multiple of a^n,

Then I just wrote down all the factors and realized 2 is the only possibility. It did take me sometime.
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