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n is a positive integer
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18 Nov 2019, 09:08
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46% (01:04) wrong based on 134 sessions
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\(n\) is a positive integer
Quantity A
Quantity B
\(\frac{1}{3^n}\)
\(3 (\frac{1}{4^n}\))
A. The quantity in Column A is greater B. The quantity in Column B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given
n is a positive integer
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18 Nov 2019, 09:29
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Carcass wrote:
\(n\) is a positive integer
Quantity A
Quantity B
\(\frac{1}{3^n}\)
\(3 (\frac{1}{4^n}\))
A. The quantity in Column A is greater B. The quantity in Column B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given
We can solve this question using matching operations
Given: Quantity A: \(\frac{1}{3^n}\)
Quantity B: \(3 (\frac{1}{4^n})\)
Multiply both quantities by \(4^n\) to get: Quantity A: \(\frac{4^n}{3^n}\)
Quantity B: \(3\)
Apply the property above to get: Quantity A: \((\frac{4}{3})^n\)
Quantity B: \(3\)
At this point we might readily recognize that by changing the value of n, we can vary the value of Quantity A. We can demonstrate this by testing some different values of n.
case i: Since n is a positive integer it COULD be the case that n = 1 We get: Quantity A: \((\frac{4}{3})^1 = \frac{4}{3}\) Quantity B: \(3\) In this case, Quantity B is greater
case ii: Since n is a positive integer it COULD be the case that n = 4 We get: Quantity A: \((\frac{4}{3})^4 = \frac{256}{81}\) = some number greater than 3 Quantity B: \(3\) In this case, Quantity A is greater
Re: n is a positive integer
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07 Feb 2024, 13:26
Hello from the GRE Prep Club BumpBot!
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