If the integers a and n are positive and the product of the first 8 po

Question

If the integers a and n are positive 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
\(2^6 , 4^3 , 64^1 , 8^2\) - we get multiple answers, so Option I - NOT SUFFICIENT

(2) n = 6
We do not know the value of a, Option II - NOT SUFFICIENT

(1) and (2) together
n=6 and \(a^n\)=64, so we know that a = 2
(1) and (2) tother - SUFFICIENT

Ans C

ginevrafratto · Answer

I would say C

1. a^n = 64 2^6= 64 but also 8^2=64 not suff
2. n=6 not sufficient alone

3. 1+2 a^n = 64 and n=6 -> a^6= 64 so we can be sure that a= 2

let me know if I'm wrong please

TarunKumar1234 · Answer

If the integers a and n are positive 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
\(2^6 , 4^3 , 64^1 , 8^2\) - we get multiple answers, so Option I - NOT SUFFICIENT

(2) n = 6
We do not know the value of a, Option II - NOT SUFFICIENT

(1) and (2) together
n=6 and \(a^n\)=64, so we know that a = 2
(1) and (2) tother - SUFFICIENT

Ans C

akadiyan · Answer

If the integers a and n are positive 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
 2^6 , 4^3 , 64^1 , 8^2  - we get multiple answers, so Option I -  NOT SUFFICIENT

(2) n = 6
We do not know the value of a, Option II -  NOT SUFFICIENT

(1) and (2) together
n=6 and  a^n =64, so we know that a = 2
(1) and (2) tother -  SUFFICIENT

Ans  C

juju17 · Answer

so is the given information "the product of the first 8 positive integers is a multiple of a^n" irrelevant?

noobieTopro · Answer

(a^n) x k = 1x2x3x4x5x6x7x8
(a^n) x k = (1)x(2^6)x(3^2)x(5)x(7).

(1) a^n = 64
2^6 = 64
(2^5)x2 = 64
4^3 = 64
(4^2)x4 = 64
8^2 = 64

'a' can have many possible values.
Therefore statement (1) alone is insufficient.

(2) n = 6
(a^n) x k = (1)x(2^6)x(3^2)x(5)x(7).
'a' could be 1 or 2.
Therefore statement (2) alone is insufficient.

Combining (1) and (2) together. 
'a' = 2

Answer C - Statement (1) and (2) together are sufficient.

Marcost · Answer

I think that information is a trap because if you don't consider a=1 (1^6) as a quotient of 8! { 1^6  x  2^7 x 3^2 x 4 x 5 x 7 ) you can end concluding that b alone is sufficient to answer the question. 
Notice that 8! only have two values with exponents where n can equal 6 (1^6 and 2^7).

Hope this helps.

bumpbot · Answer

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If the integers a and n are positive and the product of the first 8 po

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If the integers a and n are positive and the product of the first 8 po

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