The arithmetic mean and the geometric mean of two positive numbers p and q (p > q) are A and G respectively. Which one of the following is correct?

The arithmetic mean and the geometric mean of two positive numbers p and q (p > q) are A and G respectively. Which one of the following is correct? Correct Answer A > G

Given:

A is the arithmetic mean of p and q 

G is the geometric mean of p and q

And p > q 

Concept Used:

For andy two numbers

A.M ≥ G.M

Calculation:

For any two positive numbers p and q

A ≥ G

So, options 1) and 3) both can be the answer 

But for option 3)

We have to take p = q 

Now, if we put p = q in A ≥ G

i.e in (p + q)/2 ≥ √pq, we get 

2p/2 ≥ √p²

⇒ p ≥ p

i.e p = p 

But According to the question we have

p > q 

∴ The only 1) option will be correct.