The first and last are good.
In the first, the subject is cost, and that cost is rising.
In the last, the subject is rise, and we are told that the rise that occurred is in cost.
There's a subtle meaning difference here. In the first, the rising cost is the cause, while in the last, the rise itself is the cause. In this context, there's not much difference between those two meanings, but in other situations, the difference might be crucial.
The second one doesn't work idiomatically--we'd never say "the rising of cost." Same thing for the third one. Let's look at cases where those constructions do
work so we can see why they don't work here:The rising of the sun is beautiful to behold.
Here, the subject is "rising"--the event of the sun rising (not necessarily the sun itself) is what is beautiful. This construction refers to a particular event--in this case, a daily one. You can't really see cost rising in the same sense, especially just one cost. The rise of the Roman Empire changed the world dramatically.
Here, "the rise" is the subject, and in this context it means a gradual ascent that happened once. We might talk about "the rise of online piracy" or "the rise of television sitcoms," but not "the rise of cost." Cost isn't something that appeared and just started going up. It's a measurement that might go up and down over time.
As for the plural, costs, this is appropriate when there is more than one cost. Either the problem will describe multiple costs, or it will use the verb (is/are) to force one version or the other. Keep in mind that cost/costs can also be a verb. ("That car costs too much.") In that case, costs is singular and cost is plural. English is crazy that way, but at least it's fairly consistent.
Dmitry Farber | Manhattan GMAT Instructor | New York
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