Explanation

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. The 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. The 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.
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can you tell me why we included 1 in positive divisors?

Please Sir look at our math book: Integers chapter. It is pivotal you do know this notions

https://greprepclub.com/forum/gre-quant ... tml#p51913

Regards

Thankyou, I went through.

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