If integer a and n are greater than 1

[guest]

If integer 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

OA: B

Please explain your reasoning
Many thanks

[Gmat-crack]

[If integer 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
]

Given
1) a > 1, n> 1 where a.n are integers
2) 1.2.3.4.5.6.7.8 = k * (a ^ n), where k is an integer

Find all the prime factors of the product of first 8 positive integers

= 2^7 * 3^2 * 5 * 7

Since it is given n > 1 and the only factors which have power > 1 in the above expression are 2 and 3.

So a can be 2,3, or 6(2*3)

Now lets evaluate the statements

1) Statement 1 says a ^n = 64, since it is only possible with a =2 so statement is sufficient.
2) Statement 2 says n = 6, since only 2 has power greater than 2 in factorization so a= 2 so statement is sufficient.

Hence answer is D.

Let me know if it matches the answer and rationale sounds fine

[kylo]

i think the answer is B.

A - 2^6 or 4^3 = 64. hence a can be 2 or 4.




Thanks!

[shaji]

i think the answer is B.

A - 2^6 or 4^3 = 64. hence a can be 2 or 4.




Thanks!

Statement 1:It could be 8 as well!

[RonPurewal]

this problem has already been vivisected here.