"That" modifies "system," but what do we know about the system? It's "an especially efficient solar heating and cooling system." We don't want to treat individual parts of the sentence as if the rest isn't there.
Here's another example:
"My daughter has a fluffy toy lion that often sits at breakfast with us."
Am I saying that a lion really sits at breakfast with us? Well, yes, a toy lion. I wouldn't want to isolate the portion from "lion" on and ignore the preceding modifiers. Whether we say "that often sits . . . " modifies only "lion" or the whole noun phrase, the meaning is the same. The lion sits with us, but it is a fluffy toy.
In some cases, when we have a noun phrase, we are clearly modifying an earlier noun in the phrase. For instance, I might say "The King of Sweden, who is vacationing in Morocco, has a bad sunburn." Clearly it is the king, not Sweden, who is vacationing. This is correct usage. The "preceding noun" in this case is the noun phrase "The King of Sweden." In other cases, I might need to interpret flexibly depending on meaning:
On the table there was a basket of chips that were
cold and stale. (The chips were cold and stale.)
On the table there was a basket of chips that looked like it
had been sitting there for a month. (The basket of chips had been sitting there.)
I hope this helps!
Dmitry Farber | Manhattan GMAT Instructor | New York
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