Can the total number of integers that divide x be

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

(1) âˆš(12x) is an integer
(2) The product of âˆšx and âˆšy is an integer, where the total number of factors of y/3 is odd.

The OA is the option D.

Each statement is sufficient? How can I prove it? Experts, I need your help. Thanks in advanced.

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