Can the total number of integers that divide \(x\) be expressed in the form of \(2k+1,\) where \(k\) is a positive integ

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Can the total number of integers that divide \(x\) be expressed in the form of \(2k+1,\) where \(k\) is a positive integer?

(1) \(\sqrt{12x}\) is an integer.
(2) The product of \(\sqrt{x}\) and \(\sqrt{y}\) is an integer, where the total number of factors of \(\dfrac{y}3\) is odd.

Answer: D

Source: e-GMAT
Source: — Data Sufficiency |