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Another GMAT Prep Question

by mindruna » Sat Aug 04, 2007 11:21 am
If the integers a and n are greater than 1 and the product of the first 8 integers is a multiple of a^n, what is the value of a?

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


The OA is b, but I'm not certain how that is sufficient. Any insight would be really appreciated! Thanks.
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Re: Another GMAT Prep Question

by gabriel » Sun Aug 05, 2007 6:53 am
mindruna wrote:If the integers a and n are greater than 1 and the product of the first 8 integers is a multiple of a^n, what is the value of a?

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


The OA is b, but I'm not certain how that is sufficient. Any insight would be really appreciated! Thanks.
the question seems incomplete to me ... what is the darkened part supposed to mean .. which integers are we talking about .. plz take a look at the question again and repost ..
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Re: Another GMAT Prep Question

by blah45 » Sun Aug 05, 2007 11:35 am
mindruna wrote:If the integers a and n are greater than 1 and the product of the first 8 integers is a multiple of a^n, what is the value of a?

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


The OA is b, but I'm not certain how that is sufficient. Any insight would be really appreciated! Thanks.
product of the first 8 integers is a multiple of a^n
so, ( 1*2*3*...*8 )/(a^n) = k => where a, n, and k are all integers.

(1)
4^3 = 64 => a=4, n=3
8^2 = 64 => a=8, n=2
2^6 = 64 => a=2, n=6
INSUFF
(2)
n=6 => only a=2 can satisfy this.
SUFF
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Re: Another GMAT Prep Question

by gabriel » Mon Aug 06, 2007 7:42 am
Anonymous wrote:
blah45 wrote:
mindruna wrote:If the integers a and n are greater than 1 and the product of the first 8 integers is a multiple of a^n, what is the value of a?

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


The OA is b, but I'm not certain how that is sufficient. Any insight would be really appreciated! Thanks.
product of the first 8 integers is a multiple of a^n
so, ( 1*2*3*...*8 )/(a^n) = k => where a, n, and k are all integers.

(1)
4^3 = 64 => a=4, n=3
8^2 = 64 => a=8, n=2
2^6 = 64 => a=2, n=6
INSUFF
(2)
n=6 => only a=2 can satisfy this.
SUFF

Well, the above means the answer should be [D], not . We are looking to justify . Good thinking though. Thanks


actually that means the answer is C .. anyway, that does not matter bcoz u cant reach the conclusion in blah45's solution without knowing which "first 8 integers" is supposed to be meant over here ...
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Re: Another GMAT Prep Question

by bingojohn » Tue Aug 07, 2007 11:22 am
Anonymous wrote:
Anonymous wrote: Well, the above means the answer should be [D], not . We are looking to justify . Good thinking though. Thanks



How is it (D)? I mean it's clear from statement (1) 'a' could have three possible values. ONLY statement (2) indicates that a=2 and n=6 work.


I am sorry, my bad. The answer would be , in fact. The original answer is , which is correct. Here is how:

product of first 8 integers:
8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

taking (2) into consideration, n = 6... then prime factorize the left hand side:

(2^3) x 7 x (2 x 3) x 5 x (2 x 2) x 3 x 2 x 1 = (a^6) k
(2^7) x (3^2) x 5 x 7 = (a^6) k

The only value of 'a' that satisfies the above is: a = 2

Hence (2) alone is SUFFICIENT... (1) alone is NOT SUFFICIENT...
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