(1) Since we are told nothing about the value of t here, we might conclude that statement (1) is insufficient. However, if n=1 (and only 1), then statement (1) would be suffficient since 1 is a factor of all positive integers. So, let's make sure that n cannot equal 1. When we plug n=1 into the equation we see that it doesn't work. So, n doesn't equal 1.mkhanna wrote:data sufficiency problem:
If n and t are positive integers, is n a factor of t?
1) n = 3(to power of (n-2))
2) t = 3 (to power of n)
Since n doesn't equal 1 we know that statement (1) cannot be sufficient since we don't know anything about the value of t.
(2) no info about n --> insufficient
(1)&(2) We want to determine whether n is a factor of t. If n is a factor of t then t/n will be an integer (and vice versa). So, we can take our question "is n a factor of t?" and rewrite it as "is t/n an integer?"
Now examine t/n.
t/n = 3^n divided by 3^(n-2)
Using the quotient rule for powers, we can see that t/n = 3^2
Since 3^2 is an integer, we know that n is a factor of t.
So, (1) and (2) combined are suifficient.
The answer is C
