CAT 2003 Slot 1 — QA Question 39
MeansEasy
If the product of n positive real numbers is unity, then their sum is necessarily
Answer & solution
Correct answer: never less than n
- A
a multiple of n
- B
equal to n + 1/n
never less than n
- D
a positive integer
Solution
Let a1, a2, a3,…, an be n positive real numbers.
Now, a1 × a2 × a3 × … × an = 1
We know that, A.M. ≥ G.M.
a1 + a2 + a3 + … + an ≥ n × (a1 × a2 × a3 × … × an)1/n
∴ a1 + a2 + a3 + … + an ≥ n × (1)1/n
∴ a1 + a2 + a3 + … + an ≥ n
Hence, option (c).