# NMAT Tricky Math Problem: 3^(n+2)+(3^(n+3)-3^(n+1)) = ?

1. Nov 30, 2012

1. The problem statement, all variables and given/known data
The problem is from an NMAT Practice Exam. The problem is multiple choice.

3^(n+2)+(3^(n+3)-3^(n+1)) = ?

a.)1/(3^(n+1))
b.)1/(3^(n+2))
c.)3/8
d.)1/3

The answer given is 1/3, but I don't know how they got that.

2. Relevant equations
none

3. The attempt at a solution

My attempts:
3^(n+2)+(3^(n+3)-3^(n+1)) =3^(n)*(9+27-3)=33*3^n

Another attempt using self similarity...

y=3^(n+2)+(3^(n+3)-3^(n+1))
3y=3^(n+3)+(3^(n+4)-3^(n+2))
3y-y=3^(n+4)-2*3^(n+2)+3^(n+1)

2. Nov 30, 2012

### symbolipoint

None of the choices is correct. My result is 11*3^(n+1)

Did you type the expression exactly as given to you?

3. Nov 30, 2012

Thanks for the reply. Yes I typed it correctly. That's the same answer I got, but it's none of the choices. It's a practice exam for entrance into Medical School (I'm helping someone out with the math part) so I thought I was overlooking something, but I guess the practice problem is just wrong. However, it is under the inductive reasoning section of the practice exam so I thought it was trick question. Thanks again.

4. Nov 30, 2012

I asked it on Math Stack Exchange and they figured out that + is probably a test typo and suppose to be a divide symbol, which gives an answer of 3/8. Sorry for the trouble. Thanks.