We know that \(abc\) is odd and positive and since odd and positive are properties of integers it is safe to say \(abc\) is an integer.

Further more \(abcd\) is even which \(d\) is an even integer.


For example:

a=1, b = 3 , c=9 and d=2 so abc=27 and abcd=54.

Here d=2 or any even number greater than 2.

It is also possible that \(d= \frac{1}{a}\) or \(d= \frac{1}{b}\) or \(d= \frac{1}{b}\)

That would make \(abcd = bc\) or\(abcd = ac\) or \(abcd = ab\) respectively.

So \(abc\) is odd

\(b= 1\) \(c=\frac{1}{2}\) \(a=2\) and \(d=\frac{1}{a}= \frac{1}{2}\)

\(abc=1\) and \(abcd=2\)

Clearly d can be a fraction as well.

Hence D is the correct option!