Officer Aptitude Rating (OAR) Test 2025 – 400 Free Practice Questions to Pass the Exam

Question: 1 / 400

In the equation 3^n - 2 = 27, what is the value of n?

5

7

8

None of the above

To determine the value of n in the equation \(3^n - 2 = 27\), first, we can isolate \(3^n\) by adding 2 to both sides of the equation. This gives us:

\[

3^n = 27 + 2

\]

This simplifies to:

\[

3^n = 29

\]

Next, we need to find a value of n such that raising 3 to the power of n equals 29. We know that \(3^3 = 27\) and \(3^4 = 81\). Since 29 falls between 27 and 81, we can conclude that n must be between 3 and 4. As \(3^n\) cannot equal 29 for any integer value of n, we look for possible fractional values, which don't match any of the available choices.

Because there is no integer solution for n that satisfies the equation \(3^n = 29\), the conclusion is that the correct response is "None of the above."

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