Which if the following is equal to (3^n + 3^(n + 1) + 3^(n + 2))

Question

Which if the following is equal to  \frac{3^n+3^{n+1}+3^{n+2}}{3^{n-2}+3^{n-1}+3^n} ?

A.  3^{-2}

B.  3^{-n}

C.  3^n

D.  3^2

E.  1

as19 · Answer

3^N + 3^N+1 + 3^N+2 -> 3^N(1+3+3^2) -> 3^N(13)

3^N-2+ 3^N-1+3^N -> 3^N-2(1+3+3^2) -> 3^N-2(13)

When you divide both results you get:

3^N/3^N-2 =
3^N-(N-2) =

3^2

Is my approach correct?

thank you

ScottTargetTestPrep · Answer

If we say n = 1, then we have:

(3 + 9 + 27)/(1/3 + 1 + 3)

39/(4 1/3)

39/(13/3) = 9

Thus, the correct answer is 3^2 = 9.

Answer: D

SaquibHGMATWhiz · Answer

Solution:

We are asked the value of  \frac{3^n+3^{n+1}+3^{n+2}}{3^{n-2}+3^{n-1}+3^n} 
 ⇒\frac{3^n+3^n.3^1+3^n.3^2}{3^n.3^{-2}+3^n+3^{-1}.3^n} 
 ⇒\frac{3^n(1+3+9)}{3^n(\frac{1}{9}+\frac{1}{3}+1)} 
 ⇒\frac{1+3+9}{\frac{1}{9}+\frac{1}{3}+1}   
 At this point we can  mark option D as the answer  
  We have  gotten rid of 'n' thus eliminating options A, B and C  
 And definitely   1+3+9≠\frac{1}{9}+\frac{1}{3}+1  thus eliminating option E

We have  \frac{1+3+9}{\frac{1}{9}+\frac{1}{3}+1} 
 ⇒\frac{13}{\frac{1+3+9}{9}} 
 ⇒\frac{13}{\frac{13}{9}} 
 ⇒9

Hence the right answer is    Option D

Which if the following is equal to (3^n + 3^(n + 1) + 3^(n + 2))

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GMAT Problem Solving (PS) Questions

Which if the following is equal to (3^n + 3^(n + 1) + 3^(n + 2))

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