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Let (x(1),y(1)),(x(2),y(2)),…,(x(n),y(n)...

Let `(x_(1),y_(1)),(x_(2),y_(2)),…,(x_(n),y_(n))` are n pairs of positive numbers. The arithmetic mean and geometric mean of any of positive numbers `(c_(1),c_(2),…,c_(n))` are denoted by `M(c_(i)),G(c_(i))` respectively.
Consider the following :
1. `M(x_(1)+y_(1))=M(x_(i))+M(y_(i))`
2. `G(x_(i)y_(i))=G(x_(i))G(y_(i))`
Which of the above is/are correct?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

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