Only (conditional chain and parsing out nec &suf)

[hyk1310]

I'm having trouble identifying what's the sufficient and what's the necessary in certain unclear/complex sentence structures that use the word only.

for example: The only risky projects undertaken are those for which a single individual has decision-making power.

The 'only' here definitely modifies risky projects, but for some reason it seems just wrong to say: decision-making power --> risky projects undertaken.

Another example is:

"The only way that bookstores can profitably sell books at below-market prices is to get the books at a discount from publishers."

I am unsure of this too but my gut tells me that the "that" shows that the 'only' is modifying discount from publishers so the profitably sell books part is the sufficient.

Could you please explain how these two conditionals can be explained, and how to tell which part of the clause the 'only' is modifying?

Thank you!

[ManhattanPrepLSAT1]

The following uses of the word only introduce sufficient conditions:

The only
If only

And these uses of the word only introduce necessary conditions:

Only if
Only
Only when

And for more context here are some other language cues introducing sufficient and necessary conditions: