GMAT Hard Quant Question 38 | Arithmetic

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 n³?

1. n⁴
2. n⁶
3. n⁹
4. n⁵
5. Cannot be determined

Video Explanation

Explanatory Answer | GMAT Number Properties

Key Data
'n' is a positive integer.
Product of the factors of n² is n³.

If the product of the factors of n² = n³, the only factors of n² are 1, n, and n².
So, we can infer that n does not have any factor other than 1 and itself.
Therefore, n is a prime number.

Factors of n³ if n is a prime number are 1, n, n² and n³.
So, the product of the factors of n³ = 1 × n × n² × n³ = n⁶

Choice B is the correct answer.