SAT PREP 2015

Question

If n & k are positive integers and 8^n =2^k, what is the value of *n/k?

 

 

* (written as n over k like a fraction)

Answer 1

Since 8 = 2³, 8ⁿ is the same as (2³)ⁿ which is the same as 2³ⁿ

 

Since 2³ⁿ = 2^k, 3n = k, so it's easy to see that k/n = 3.  Since they're asking about n/k, that's the reciprocal of k/n, so the answer is 1/3.