Mathematics Quizzes Progressions

Question:
If the product of n positive integers is nⁿ, then their sum is:

Option A):
A negative integer
Option B):
Never less than n²
Option C):
Equal to n+(1/n)
Option D):
Equal to n

Correct Answer is Option B):
Never less than n²

Explanation:
Clearly, since the given integers are positive, their sum can't be negative. Also, since the numbers are all integers their sum can't be a fraction. Let's take 1, 3 and 9. The product of these three integers is 27 = 3³. This can also be written as nⁿ where n=3. As we can see, the sum of these 3 integers is not equal to 3. Therefore, we are left with the fourth option.