Once you attempt the question then PrepInsta explanation will be displayed.

Solution:

For a number p^{a}q^{b}r^{c}, the total number of factors are (1+a)(1+b)(1+c) [here p,q and r are prime numbers] for a perfect cube all of the a,b,c has to be divisible by 3.

So, if a number is a perfect cube and having k factors then k has to be divisible by (1+n) where n is divisible by 3.

As w having 49 factors,

49=(1+6)(1+6)

As 6 is divisible by 3 so w is a perfect cube

X having 7 factors

7=(1+6)

So, x is also a perfect cube

Y having 21 factors now 21 is divisible by

21=(1+6)(1+2)

Here 6 is divisible by 3 but 2 is not divisible by 3

Any combination which proves that 21 is a perfect cube is not possible.

So, Y is not a perfect cube

Z having 81 factors but there is no (1+n) [where n is divisible by 3] which can divide 81.

So, Z is also not a perfect cube

Hence the answer is W and X

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