The given question is a challenging GMAT hard quant problem solving question testing concepts in number properties - Product of factors of cubes and squares of numbers.

Question 38: What is the product of all the factors of the cube of a positive integer 'n' if the product of all the factors of square of n is n^{3}?

- n
^{4} - n
^{6} - n
^{9} - n
^{5} - Cannot be determined

@ INR

**Key Data**

'n' is a positive integer.

Product of the factors of n^{2} is n^{3}.

If the product of the factors of n^{2} = n^{3}, the only factors of n^{2} are 1, n, and n^{2}.

So, we can infer that n does not have any factor other than 1 and itself.

Therefore, n is a prime number.

Factors of n^{3} if n is a prime number are 1, n, n^{2} and n^{3}.

So, the product of the factors of n^{3} = 1 × n × n^{2} × n^{3} = n^{6}

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