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27 Sep 2024, 12:29
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
100% (02:22) correct
0% (00:00) wrong based on 2 sessions
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n is a positive integer that is greater than 3 and has d positive divisors.
Quantity A
n
Quantity B
\(2^{d - 1}\)
Quantity A
n
Quantity B
\(2^{d - 1}\)
27 Feb 2025, 03:56
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OE
Since there is no obvious relationship between the quantities n and \(2^{d - 1}\), it is a good idea to try a few values of n to see what happens. Note that you are given that n is an integer greater than 3, so you can start comparing the quantities for the case n = 4 and proceed from there.
Case 1: n = 4. Te integer 4 has three positive divisors, 1, 2, and 4. So in this case, d = 3. Therefore \(2^{d - 1} = 2^{3 - 1} = 4\), and the two quantities are equal.
Case 2: n = 5. Te integer 5 has two positive divisors, 1 and 5. So in this case, d = 2. Therefore \(2^{d - 1} = 2^{2 - 1} = 2\), and Quantity A is greater than Quantity B.
In one case the two quantities are equal, and in the other case Quantity A is greater than Quantity B. Therefore the correct answer is Choice D.
Answer: D
Since there is no obvious relationship between the quantities n and \(2^{d - 1}\), it is a good idea to try a few values of n to see what happens. Note that you are given that n is an integer greater than 3, so you can start comparing the quantities for the case n = 4 and proceed from there.
Case 1: n = 4. Te integer 4 has three positive divisors, 1, 2, and 4. So in this case, d = 3. Therefore \(2^{d - 1} = 2^{3 - 1} = 4\), and the two quantities are equal.
Case 2: n = 5. Te integer 5 has two positive divisors, 1 and 5. So in this case, d = 2. Therefore \(2^{d - 1} = 2^{2 - 1} = 2\), and Quantity A is greater than Quantity B.
In one case the two quantities are equal, and in the other case Quantity A is greater than Quantity B. Therefore the correct answer is Choice D.
Answer: D
