TOUGH GUY wrote:
If n and t are positive integers, is n a factor of t ?
(1) n = 3^(n-2)
(2) t = 3^n
We need to determine whether t/n = integer
Statement One Alone:
n = 3^(n - 2)
Since we do not have any information regarding t, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
t = 3^n
We can substitute some numbers for n. For example, if n = 1, then t = 3^1 = 3 and 1 is a factor of 3. However, if n = 2, then t = 3^2 = 9 but 2 is not a factor of 9. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Using the information from statements one and two, we can substitute 3^(n - 2) for n and 3^n for t in our question: t/n = integer ?
(3^n)/3^(n - 2) = integer ?
Since we are dividing similar bases, we can subtract the exponents and keep the base. Then we have:
3^(n - n + 2) = integer ?
3^2 = integer ?
9 = integer ?
Since 9 IS an integer. We have answered “yes” to the question.
Answer: C