How do I write this statements using "only if"? Consider the following statements -
If I study for four hours, then I will get an A.
If it is currently raining, then my lawn is wet.
If you don’t get to work on time, then you’re fired.
If you are eligible to be president of the United States, then you’re at least 35 years old.
The following statements are my answers -
I study for four hours only if I get an A.
It is currently raining only if my lawn is wet.
I do not reach work on time only if I'm fired.
I am eligible to be the president of the United States only if I'm at least 35 years old.
As you can see, they sound very awkward. Is it possible to rephrase using "only if"?
 A: Some of the sentences sound awkward because even though the logical conditional is not the same as some kind of temporal or causal claim, we do typically have that in the back of our minds, and so we find that there is some kind of tension/awkwardness when the logical 'arrow' points one way, but the temporal/causal 'arrow' the other way.
For example, suppose I say:
You pass the course only if you complete all HW
To symbolize this in logic (and using $H$ for completing homework and $P$ for passing the course), you do not want to use $H \to P$, because that means that anyone who completes the HW will automatically pass the course, but that is not what the English statement says:  it says that completing the HW is a necessary condition for passing the course, but it does not say that it is a sufficient condition.
However, we can symbolize the sentence as $P \to H$. And the way to think about that is:  If I ever find out that you passed the course, then I can infer that you must have completed all the HW.  OK, but the literal translation of $P \to H$ is:
if you pass the course, then you complete all HW's
which is really awkward!  One would think that you first complete all the HW's, and then, at some later time, pass the course ... partially thanks to completing all the HW.  So the temporal and causal arrow would go from HW to passing ... but logically, it goes from passing to HW.  So yeah, there is tension and awkwardness here.
Now, one thing you can do to relieve some of this tension is to use a contrapositive, which turns the logical arrow the other way around. To continue our example, we can say:
if you don't complete the HW, then you don't pass the course
and note that this sentence is a lot less awkward, because the temporal/causal arrow 'lines up' with the logical one.
I think you can use this technique to some of your sentences as well.
For example, that first one can be stated as:
I fail to get an A only if I don't study for 4 hours
I think this is less awkward, but clearly what you want: the only way to not get an A is to not study, because as soon as you study, you'll get that A
The third one could be rephrased as:
I won't be fired only if I get to work on time
(the only way to not get fired is to get to work on time, because if I won't get on time, I'll get fired)
Your second statement actually sounds pretty ok to me ... it sounds like an expression of deduction with the arrow going from the wetness of the lawn to inferring something about it raining. That is, your 'only if' version sounds like: if my lawn is not wet, then we can infer it is not raining ... which is not an awkward sentence .... and of course just the contrapositive of the original sentence.
And the fourth one does not sound awkward at all. Indeed, for this one, it is with the original sentence that the 'arrow' is felt to go in the wrong direction, and hence it is the original sentence that sounds more awkward.
