Another GMAT Prep Question

Question

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.

gabriel · Answer

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

blah45 · Answer

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

gabriel · Answer

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 ...

bingojohn · Answer

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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