QA – Placement Quizzes | Progressions | Question 9

For n positive integers, if their product is nⁿ, then what will be their sum?

(A)

Equal to n+(1/n)

(B)

Equal to n

(C)

A negative integer

(D)

Never less than n²

Answer: (D)

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.

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