vgmat2 wrote:Hi ,
I have enclosed the problem from gmat focus, this seems to be wrong explanation or my understanding is not correct, can you please comment on the explanation of combining both,
i.e (3)^(3)^(n-2) = 3^(3n-6) is this correct ?
thanks
vgmat2[/img]
You've definitely found a mistake in their explanation. You ask above whether:
(3)^(3)^(n-2) = 3^(3n-6) is true.
This question is ambiguous- it depends where you put the brackets on the left side.
[3^3]^(n-2) does certainly equal 3^(3n-6). That's one of the exponent rules. That's what they did in the solution in the attached file in the OP. *But*, the brackets should be, for the question in the attachment, as follows:
3^[3^(n-2)]
That's *not* the same thing as [3^3]^(n-2) (plug in, say, n=2 to see why). They've incorrectly simplified this expression. This is certainly tested on GMAT questions- I've seen expressions like x^(x^2) on questions, and it is a mistake to simplify that to x^(2x).
Worse still, they make another mistake: they then go on to say that:
3^[3(n-2)] = (3^3)*(3^(n-2)).
If you multiply two exponential terms with the same base, you add the powers; you do not multiply the powers, which is what they've done.
Looking at the right side above, (3^3)*(3^(n-2)) is equal to 3^(n+1); it is not equal to 3^[3(n-2)] for any integer value of n.
Long story short, the explanation is not worth reading, and contains two basic errors with powers, which is a bit shocking...
The question is much simpler to answer:
n is a positive integer. Is n a factor of t?
Statement 1 tells you that n = 3^(n-2)
Statement 2 tells you that t = 3^n
I'll assume it's clear that neither statement is sufficient on its own.
Together, recalling that n and t are integers, the question asks is 3^(n-2) a factor of 3^n, or 'is 3^n divisible by 3^(n-2)?' Well, of course it is. When you divide 3^n by 3^(n-2), the quotient is 3^2 = 9. The statements are sufficient together.
While you don't need to see this for this question, the first statement actually tells you even more; if n is a positive integer, and n = 3^(n-2), n has to be equal to 3.
