Quote:
MathRevolution wrote:
[GMAT math practice question]
\(\frac{3^n+3^{n+1}+3^{n+2}}{3^{n-2}+3^{n-1}+3^n}=?\)
\(A. 3^{-2}\)
\(B. 3^{-n}\)
\(C. 3^n\)
\(D. 3^2\)
\(E. 1\)
2) put n as 2, so that DENOMINATOR does not have any fraction, leading to some extra calculations
..
\(\frac{3^n+3^{n+1}+3^{n+2}}{3^{n-2}+3^{n-1}+3^n}=\frac{3^2+3^{2+1}+3^{2+2}}{3^{2-2}+3^{2-1}+3^2}=\frac{3^2(1+3+3^2)}{1+3+3^2}=3^2\)
D
Both C and D yield \(3^2\) when n=2.
As a result, a test-taker would have to test another case to determine whether the correct answer is C or D.
When plugging in values, we should avoid numbers that appear in the answer choices.
Here -- since 2 appears in the answer choices -- we should test a value other than 2.
Plug n=3 into the given expression:
\(\frac{3^3+3^{3+1}+3^{3+2}}{3^{3-2}+3^{3-1}+3^3}\)
\(\frac{3^3+3^4+3^5}{3^1+3^2+3^3}\)
\(\frac{3^3(1+3+3^2)}{3(1+3+3^2)}\)
\(3^2\)
The correct answer must yield \(3^2\) when n=3.
In this case, only D is viable.
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