[Grammar] lucky enough

[Ashiuhto]

Is the following sentence acceptable?

I am lucky enough to pass the admission test for the advanced math class.

 

[5jj]

I [STRIKE]am[/STRIKE] lucky enough to pass the admission test for the advanced math class.

I have been or I was ...

 

[Raymott]

Is the following sentence acceptable?

I am lucky enough to have passed the admission test for the advanced math class.

Or that.