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
1. a^n = 64
2. n = 6
Product of first 8 positive integers = 1*2*3*4*5*6*7*8 = (2*4*2*8)*(3*3*5*7) = (2^7)*(3^2)*(5*7)psm12se wrote: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
As a and n are both positive integers greater than 1, only possible values for a and n are either {a = 2 and 2 ≤ n ≤ 7} or {a = 3 and n = 2} or {a = 4 and 2 ≤ n ≤ 3} or {a = 8 and n = 2}
Statement 1: a^n = 64 = 2^6 = 4^3 = 8^2
Hence, possible values of a are 2, 4, and 8
Not sufficient
Statement 2: As n = 6, only possible value of a is 2
Sufficient
The correct answer is B.
